Microeconomics I - Module

MODULE FOR MICROECONOMICS I (ECON 111)

BY: WODAJO WOLDEGIORGIS (PHD) WONDAFERAHU MULUGETA (MSC) TSEGA WONDIMAGEGNEHU (MA) HASSEN ABDA (MSC)

ORGANIZED BY: FACULTY OF BUSINESS AND ECONOMICS JIMMA UNIVERSITY

SEPTEMBER, 2008 JIMMA

Table of Contents Page CHAPTER ONE: INTRODUCTION ............................................................................. 1 1.1 Introduction............................................................................................................... 1 1.2 Chapter Objectives.................................................................................................... 2 1.3 Definitions, Scope and Nature of Economics ........................................................... 2 1.4 The Fundamental Economic Problems and the Alternative Economic Systems...... 7 1.5 Scarcity, Opportunity Cost and Efficiency ............................................................. 13 1.6 Decision Making Units and the Circular Flow of Economic Activities ................. 15 1.7 The Concept of Market Structure ........................................................................... 18 1.8 Microeconomic Theory and the Price System ........................................................ 18 1.9 Lesson Summary..................................................................................................... 19 1.10 Review Questions ................................................................................................. 21 CHAPTER TWO: THE THEORY OF CONSUMER BEHAVIOR ......................... 24 2.1 Introduction............................................................................................................. 24 2.2 Chapter Objectives.................................................................................................. 26 2.3 What Is the Theory of Consumer Behavior? .......................................................... 27 2.4 The Rational for the Theory of Consumer Behavior .............................................. 27 2.5 Methods of Comparing Utility................................................................................ 28 2.5.1 The Cardinal Utility Theory......................................................................... 28 2.5.2 The Ordinal Utility Theory .......................................................................... 35 2.6 The Market Demand for a Commodity................................................................... 71 2.7 Elasticity of Demand............................................................................................... 75 2.8 Choice under Uncertainty ....................................................................................... 89 2.9 Lesson Summary..................................................................................................... 96 2.10 Review Questions ................................................................................................. 97 CHAPTER THREE: THEORY OF PRODUCTION ............................................... 103 3.1 Introduction........................................................................................................... 103 3.2 Chapter Objectives................................................................................................ 103 3.3 The Production Function....................................................................................... 104 3.4 The Short Run Production Function and Stages of Production ............................ 109 3.5 Laws of Production ............................................................................................... 121 3.6 Returns to Scale and Homogeneity of the Production Function........................... 123

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3.7 Equilibrium of the Firm: Choice of Optimal Combination of Factors of Production.......................................................................................... 125 3.8 Lesson Summary................................................................................................... 133 3.9 Review Questions ................................................................................................. 134 CHAPTER FOUR: THE THEORY OF COST ......................................................... 137 4.1 Introduction........................................................................................................... 137 4.2 Chapter Objectives................................................................................................ 138 4.3 Short-Run Costs .................................................................................................... 138 4.4 The Relationship between Product Curves and Cost Curves in the Short Run .... 149 4. 5 Long-Run Costs ................................................................................................... 152 4.6 The Relationship between Short-Run and Long-Run Average and Marginal Costs............................................................................... 154 4.7 Derivation of Cost Function from Production Function ....................................... 158 4.8 Dynamic Changes in Costs – The Learning Curve............................................... 161 4.9 Lesson Summary................................................................................................... 163 4.10 Review Questions ............................................................................................... 164 CHAPTER FIVE: PERFECT COMPETITION ....................................................... 168 5.1 Introduction........................................................................................................... 168 5.2 Chapter Objectives................................................................................................ 169 5.3 Characteristics of Pure and Perfect Competition .................................................. 169 5.4 Market Equilibrium............................................................................................... 173 5.4.1 The Market Period Equilibrium ................................................................. 173 5.4.2 The Short Run Equilibrium of a Firm and Industry/Market ...................... 174 5.4.3 The Long Run Equilibrium........................................................................ 184 5.5 Perfect Competition and Consumers' Welfare...................................................... 187 5.6 Lesson Summary................................................................................................... 188 5.7 Review Questions ................................................................................................. 189 CHAPTER SIX: PURE MONOPOLY ....................................................................... 192 6.1 Introduction........................................................................................................... 192 6.2 Chapter Objectives................................................................................................ 193 6.3 The Characteristic Features of Pure Monopoly .................................................... 193 6.4 Origins of Monopoly Power ................................................................................. 196 ii

6.5 Short Run Equilibrium of a Pure Monopolist ....................................................... 199 6.6 The Long Run Equilibrium of a Pure Monopolist ................................................ 207 6.7 Price Discrimination ............................................................................................. 213 6.7.1 Definition and Necessary Conditions ........................................................ 213 6.7.2 Types of Price Discrimination ................................................................... 214 6.8 A Multi-Plant Monopolist..................................................................................... 221 6.9 The Social Cost of Monopoly ............................................................................... 226 6.10 Lesson Summary................................................................................................. 234 6.11 Review Questions ............................................................................................... 236 References …………………………………………………………………………..…239 Answers to Selected Review Questions ……………………………………….……..240

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CHAPTER ONE INTRODUCTION LESSON STRUCTURE 1.1

Introduction

1.2

Chapter Objectives

1.3

Definitions, Scope and Nature of Economics

1.4

The Fundamental Economic Problems and the Alternative Economic Systems

1.5

Scarcity, Opportunity Cost and Efficiency

1.6

Decision Making Units and the Circular Flow of Economic Activities

1.7

The Concept of Market Structure

1.8

Microeconomic Theory and the Price System

1.9

Lesson Summary

1.10 Review Questions

1.1 INTRODUCTION This lesson tries to acquaint students with basic economic concepts and terminologies, which are necessary to understand any subject of economics (particularly this one – microeconomics). It attempts to present some reasons why you as a student learn economics. The two fundamental facts, limited resources and unlimited wants, which provide a reason for the existence of the subject of economics, are also briefly explained. The lesson will present the fundamental economic problems, which are common to all countries, and how they are solved in different economic systems in some detail. The lesson will also provide an illumination of some basic concepts like scarcity of economic resources, opportunity cost and efficiency. The circular flow of economic activities presents how decision-making units interact in the market economy system. Towards its end, the chapter describes the concern of microeconomics. 1

1.2 CHAPTER OBJECTIVES After working through this lesson, you should be able to: •

Define economics;

•

Explain the nature and scope of economics in general and microeconomics in particular;

•

Understand different methods of economic analysis;

•

Explain what economic resources are, and the issue of scarcity;

•

Understand the different economic systems and how each of them answer the basic economic problems;

•

Understand the concept of opportunity cost and efficiency;

•

Have an overview of the different types of market structure;

1.3 DEFINITIONS, SCOPE AND NATURE OF ECONOMICS Why Do You Study Economics? Economics is a word commonly used in our daily conversation. What is economics and why do you need to learn economics? Before defining economics first let us try to see the reasons why people want to study economics. Many people study economics for various reasons. Some people want to study economics because they hope to make money. Some, on the other hand, need to study economics because they feel illiterate if they cannot know and understand the law of demand and supply. Many want to learn economics because they want to know and understand how inflation and budget deficit will affect their future life. Generally, knowledge about economics is important because each one of us faces economic problems at different levels and makes economic decision throughout his/her life knowingly or unknowingly. For instance, on a personal level, we often make some personal decisions on issues like: Which job should we take? How can we best spend our income? Shall we buy or rent a house? And so on. 2

If someone enters into business, he/she will face many economic decisions like: what to produce or what type of service to provide? How and in what quantity to produce? And so on. Also in politics, we face many economic decisions like how much the nation should spend on defense, on health care and environment, on education and on different physical infrastructure? Even as a voter, we evaluate candidates partly on the basis of their economic view. That is, on the basis of their view on unemployment, on inflation and over all on their socio-economic programs. In short, economic literacy is important because economic issues facing government and individuals shape the future of the nation and affect the well being of its citizens. Therefore, for these and the like reasons, it is essential that economics be made accessible to everyone.

What is Economics? Before defining economics, again, we better first introduce some terminologies which are necessary for better understanding of the definition of economics. A. Resources Resource is anything that can be used to produce goods and services. Resources are also called inputs or factors of production. Resources (factors or inputs of production) are divided into four categories, namely: i. Land ii. Labor iii. Capital iv. Entrepreneurship i. Land: is a natural gift, which includes all natural resources which are found inside and on the surface of the land. These are like: •

Different minerals

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•

Soil, river, lake pond

•

Timber or forest resources and other natural materials necessary to produce goods and services.

ii. Labor: is mental and physical human effort (ability) used in the production process. The skill and amount of labor will be important in determining level and quality of production. iii. Capital: capital is a man-made means of production used in the production process. Here belong resources like: •

Machineries, equipments, tools used in the production process.

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Buildings and materials attached to it, and

•

Financial capital

iv. Entrepreneurship: it is managerial skill of organizing and combining the above three resources for production purposes. The above resources cannot be productive and be changed into goods and services without the creative effort of entrepreneur. Entrepreneur is an individual who organizes resources for production, introduces new products or techniques of production. The principal role of entrepreneur includes: •

Introducing new product and new methods of production

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Setting the overall direction of the firm

•

Being a risk taker

Factors of production are combined differently by entrepreneur in the production process and will be converted into goods and services. Inputs (Resources)

Land, Labor, Capital, Entrepreneurship

Output

(production process) 4

(Goods and Services)

B. Goods versus Services The distinction between goods and services is based on whether the output (product) is tangible or intangible. Tangible Outputs (Goods) are those like clothes, shoes, beverage, automobile and the like. These goods are feasible and their existence can be sensed. Intangibles Outputs (Services) are those like haircut, computer repairs, teaching and consultation, and so on. C. The Fundamental Economic Facts There are two fundamental facts, which constitute the economizing problems and provide foundation for the subject economics. These are unlimited wants and limited economic resources. Society's wants for material goods and services are unlimited: Our needs for goods and services are insatiable or can not be fully satisfied because, i. Wants are multiplicative. Introduction of a new commodity creates need for many other commodities. For example, purchasing of a car creates needs for parking place, fuel, oil and so on. ii. Wants are recurrent. Even if a specific want is satisfied at a particular time, it may recur. Take for instance food consumption. Need for food may reoccur several times a day. The same thing is true for clothing. In short, people will consume most of the commodity many times throughout their life. iii. Wants multiply endlessly. If one want is satisfied, the need for another arises. If we satisfy our need for food in a particular period of time, need for cloth arises and if we satisfy our need for it, need for shelter comes. In such manner, human wants multiply continuously. iv. Human nature is accumulative. People accumulate things beyond their present need. Even if all needs were satisfied at a particular period of time, people would like to keep it more for consumption sometimes in the future.

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In general, people have insatiable desires for goods and services to raise their standard of living. Limited economic resources: Economic resources like various types of labor, natural resources, capital and entrepreneurial ability we use to produce goods and services are limited. If economic resources are not sufficient to produce all goods and services needed by a society, then we have to make choice as to which good to produce first. Thus, unlimited wants and limited resources will give us the problem of scarcity. Because of scarcity, economic resources must be allocated efficiently. Scarcity implies that resources are insufficient to produce all goods and services desired by consumers or society as a whole. To solve this and related issues we have a discipline called Economics. Therefore, economics is the study of how scarce resources are allocated among alternative and competing ends or uses in order to maximize the consumption of material goods and services. In addition to the above concepts, there are others which are very important in understanding this course. Some of them are given below. I. Microeconomics versus Macroeconomics Economics is typically divided into two parts: microeconomics and macroeconomics. Microeconomics is the part of economics which studies the decision making process by individuals (households) and by firms. It studies the behavior of individual components of the economy like households and business firms. Macroeconomics, on the other hand, is the part of economics which studies the behavior of the economy taken as a whole. It deals with phenomenon at overall economy level

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like: unemployment, inflation and national income. It studies the function of the economy taken as a whole. II. Positive Economics versus Normative Economics Positive Economics is that part of economic science which deals with specific statements that are capable of verification, by reference to the facts about economic behavior. That is, it is concerned with describing and analyzing the economy as it is. It is an economic analysis strictly limited to make purely descriptive statements of scientific prediction. For example, if the price of oil increases relative to all other prices, then the amount that people will buy will fall. Here economics will tell us what will happen if some action is taken. Normative Economics, on the other hand, is analysis involving value judgment. It is that part of economic science which involves someone’s value judgments about what the economy should be like or what particular policy action should be recommended to solve economic problems based on a given economic generalization or relationship. Here the economics will tell us what should be done. For example, if the price of oil goes up, people will buy less of it, therefore, we should not allow the price to go up. Such statement is a normative economic statement.

1.4 THE FUNDAMENTAL ECONOMIC PROBLEMS AND THE ALTERNATIVE ECONOMIC SYSTEM Economic system is the set of organizational arrangement and institutions established to solve the fundamental economic problems, what, how and for whom to produce. Economic systems are different from each other on the basis of the ownership of economic resources and the method by which economic activities are coordinated. Economic system is a basic means of achieving economic goals that are inherent in the economic structure of a society.

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The fundamental role of an economic system in any society is to provide a set of rules for allocating resources and/or consumption among individuals who can't satisfy their wants, given limited resources. The rules that each economic system provides function within a framework of formal institutions (e.g., laws) and informal institutions (e.g., customs). As we have mentioned earlier, because of scarcity, there must be a choice in the use of economic resources. The important characteristics of economic resources are that they can be put into alternative uses. Society, therefore, must choose the best ways of using scarce resources. Nations, be it rich or poor, developed or underdeveloped, will all face the problem of choice. In every nation, no matter what the form of government, what the type of economic system, who controls the government, or how rich or poor the country is, three basic economic questions must be answered. They are: i. What to produce? ii. How to produce? iii. For whom to produce? What and how much will be produced? Literally, billions of different outputs could be produced with society's scarce resources. Some mechanism must exist that differentiates between products to be produced and others that remain as either unexploited inventions or as individuals' unfulfilled desires. How will it be produced? There are many ways to produce a desired item. It may be possible to use more labor and less capital, or vice versa. It may be possible to use more unskilled labor to substitute for fewer units of skilled labor. Choices must be made about the particular input mix, the way the inputs should be organized, how they are brought together, and where the production is to take place.

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For whom will it be produced? Once a commodity is produced, some mechanism must exist that distributes finished products to the ultimate consumers of the product. The mechanism of distribution for these commodities differs by economic system. Historically, four different types of economic systems are observed. These are: 1. Pure Capitalism (Free Market Economy) 2. Pure Socialism (Command Economy) 3. Mixed Economy (Hybrid Economy) 4. Traditional Economy (Customary Economy) Market versus Command Economic Systems One way to define economic systems is to classify them according to whether they are market systems or command systems. In a market system, individuals own the factors of production and individually decide how to use them. The cumulative decisions of these individuals are reflected in constantly changing prices, which result from the supply and demand for different commodities and, in turn, impact that supply and demand. The prices of those commodities are signals to everyone within the system indicating relative scarcity and abundance. Indeed, it is the signaling aspect of the price system that provides the information to buyers and sellers about what should be bought and what should be produced. In a market system the interaction of supply and demand for each good determines what and how much to produce. For example, if the highest price that consumers are willing to pay is less than the lowest cost at which a good can be produced, output will be zero. That doesn't mean that the market system has failed. It merely implies that the demand is not high enough in relation to supply to create a market; however, it might be someday. In a market economy the efficient use of scarce inputs determines how output will be produced. Specifically, in a market system, the least-cost production method will have to be used. If any other method was used, firms would be sacrificing potential profit. Any

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firm that fails to employ the least-cost technique will find that other firms can undercut its price. That is, other firms can choose the least-cost or any lower-cost production method and be able to offer the product at a lower price, while still making a profit. This lower price will induce consumers to shift purchases from the higher-priced firm to the lower-priced firm, and inefficient firms will be forced out of business. In a market system, individuals make the choice about what is purchased; however, ability to pay, as well as the consumer's willingness to purchase the good or service, determine that choice. Who gets what is determined by the distribution of money income. In a market system, a consumer's ability to pay for consumer products is based on the consumer's money income. Money income in turn depends on the quantities, qualities, and types of the various human and non-human resources that the individual owns and supplies to the resource market. It also depends on the prices, or payments, for those resources. When you are selling your human resources as labor services, your money income is based on the wages you can earn in the labor market. If you own non-human resources – capital and land, for example – the level of interest and rents that you are paid for your resources will influence the size of your money income, and thus your ability to buy consumer products. Critics commonly argue that in a market system the rich, who begin with a disproportionately large share of resources, tend to become richer while the poor, who begin with a disproportionately small share of resources, tend to become poorer. They further argue that a government, which is designed to protect private-property rights, will tend to be exploited by those in power, which tends to be the economically wealthy. These critics argue that a market economy leads to selfish behavior rather than socially desirable outcomes. In contrast, a command system is one in which decision making is centralized. In a command system, the government controls the factors of production and makes all decisions about their use and about the consumption of output. The central planning unit

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takes the inputs of the economy and directs them into outputs in a socially desirable manner. This requires a careful balancing between output goals and available resources. In a command system the central planners determine what and how much will be produced by first forecasting an optimal level of consumption for a future period and then specifically allocating resources projected to be sufficient to support that level of production. The "optimal" level of production in a command economy is determined by the central planners and is consistent with government objectives rather than being a function of consumer desires. As a part of the resource allocation process, the central planners also determine how production will take place. This process could focus on low-cost production or high quality production or full-employment of relatively inefficient resources or any number of other governmental objectives. Finally, the command system will determine for whom the product is produced. Again, the focus is on socially-desirable objectives. The product can be allocated based on class, on a queuing process, on a reward system for outstanding or loyal performance, or on any other socially-desirable basis for the economy. Critics commonly argue that because planned economies cannot effectively process as much relevant information as a market does, command economic systems cannot coordinate economic activity or satisfy consumer demand as well as market forces do. For example, consider an economic planning board of twenty people that must decide how many coats, apartment buildings, cars, trains, museums, jets, grocery stores, and so forth should be built in the next five years. Where should these planners begin? How would they forecast the future need for each of these? Critics argue that, at best, planners would make a guess about what goods and services would be needed. If they guess wrong, resources would be misallocated and too much or too little production would take place. These critics argue that private individuals, guided

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by rising and falling prices and by the desire to earn profits, are better at satisfying consumer demand. The Mixed Economic System In practice, most economies blend some elements of both market and command economies in answering the three fundamental economic questions: What and how much will be produced? How will it be produced? For whom will it be produced? Furthermore, within any economy, the degree of the mix will vary. The economy of the United States is generally considered to be a free market or capitalist economic system. However, even in the United States the government has determined a "minimum wage", has set rules and regulations for environmental protection, has provided price supports for agricultural products, restricts the imports of items that might compete with local production, restricts the exports of sensitive output, provides for public goods such as a park system, and provides health and retirement services through Medicaid and Medicare. All of these detract/depart from the essential nature of a capitalist economy. However, most decisions continue to be left to free markets, leaving the United States as a mixed economy that leans heavily toward the capitalist economic system. In contrast, the economy of the former Soviet Union is generally considered to be communist. However, the strict controls of the central planning unit of the country tended to be more intensely focused on heavy industry, including the defense and aerospace industries, than on agricultural industries. Farmers often had significant freedom to produce and sell (or barter) what they wished. The former Soviet Union is thus an example of a mixed economy that leans heavily toward the socialist economic system.

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1.5 SCARCITY, OPPORTUNITY COST AND EFFICIENCY If human desire were fully satisfied, we don't need to worry about the efficient use of resources. Because all of us could have as much as we please and no one would care about the distribution of income among people. But, the reality is somewhat different. Because, we cannot have all we want from nature with out sacrifices. The law of scarcity states that goods are scarce because there are no enough resources to produce all the goods that people want to consume. This implies that there is always a tradeoff between alternative choices. As we have mentioned it earlier, because of scarcity, there must be a choice in the use of economic resources. The important characteristics of economic resources are that they can be put into alternative uses. Societies or individuals, therefore, must choose the best ways of using scarce resources. Nations be it rich or poor, developed or under developed, will all face the problem of choice. Tradeoff here implies the economy can only produce more of one item if it gives up the production of some other good(s). The value of trade off is called opportunity cost. Opportunity Cost is the value (amount) that must be sacrificed to attend something. That is, Opportunit y Cost =

the amount sacrificed of one good the amount obtained of other good

Although opportunity cost can be hard to quantify, the effect of opportunity cost is universal and very real on the individual level. In fact, this principle applies to all decisions, not just economic ones. Since the work of the Austrian economist Friedrich von Wieser, opportunity cost has been seen as the foundation of the marginal theory of value. Opportunity cost is one way to measure the cost of something. Rather than merely identifying and adding the costs of a project, one may also identify the next best

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alternative way to spend the same amount of money. The forgone profit of this next best alternative is the opportunity cost of the original choice. A common example is a farmer that chooses to farm his land rather than rent it to neighbors, wherein the opportunity cost is the forgone profit from renting. In this case, the farmer may expect to generate more profit himself. Similarly, the opportunity cost of attending university is the lost wages a student could have earned in the workforce, rather than the cost of tuition, books, and other requisite items (whose sum makes up the total cost of attendance). Note that opportunity cost is not the sum of the available alternatives, but rather the benefit of the single, best alternative. Possible opportunity costs of the city's decision to build the hospital on its vacant land are the loss of the land for a sporting center, or the inability to use the land for a parking lot, or the money that could have been made from selling the land, or the loss of any of the various other possible uses—but not all of these in aggregate. The true opportunity cost would be the forgone profit of the most lucrative of those listed. One question that arises here is how to assess the benefit of dissimilar alternatives. We must determine a dollar value associated with each alternative to facilitate comparison and assess opportunity cost, which may be more or less difficult depending on the things we are trying to compare. For example, many decisions involve environmental impacts whose dollar value is difficult to assess because of scientific uncertainty. Valuing a human life or the economic impact of an Arctic oil spill involves making subjective choices with ethical implications. Efficiency occurs when the economy is using its resources so well that producing more of one good results in less of other goods, i.e., no resources are being wasted. Note that the employment of all available resources is insufficient to achieve efficiency. Full production must also be realized. Full production implies two kinds of efficiency: allocative efficiency and productive efficiency. Allocative efficiency means that resources are being devoted to those combinations of goods and services most wanted by society. In addition, productive efficiency is realized when the desired goods and services

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are produced in the least costly ways. Thus, full production means producing the “right goods” (allocative efficiency) in the “right way” (productive efficiency).

Check Your Progress 1. What are resources? Explain how resources are classified? 2. What are the principal roles of Entrepreneur? 3. Society’s want for material goods and services is unlimited. Explain! 4. What are the two fundamental facts of economics? How do these fundamental facts lay ground for the foundation of economics? 5. Compare and contrast microeconomics and macroeconomics? 6. What are fundamental (basic) problems of economics? And how are these problems solved under the alternative economic systems?

1.6 DECISION MAKING UNITS AND THE CIRCULAR FLOW OF ECONOMIC ACTIVITIES What are the major decision making units in the economy? The major decision-making units in the economy are households, business firms and government. Households: Households are consumers of final goods and services produced in the economy. Consumers are the owners of economic resources (land, labor, and capital and entrepreneurship). They earn income from their labor and from the property they own. Households are generally assumed to maximize their well-being or what economists call "utility”. Business Firms: Business firms are the producing unit in the economy. They hire workers and pay for the use of various property owned by households. They use economic resources to produce goods and services needed by households and other firms.

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Firms come in all size and forms. However, regardless of their size all firms share common objective, i.e. profit maximization. Government: The term government used to broadly include all government and quasigovernment bodies at the federal, state and local levels. Unlike the households and business firms, government is not assumed to have a single goal. In a pure market economy, the role of the government is limited to such activities as law entertainment. Generally, how the market economic system functions can be shown using the simple model called circular flow diagram depicted in Figure 1.1 below. The Circular Flow of Economic Activities The circular flow diagram tries to illustrate how an economic system works and how solutions to the basic economic problems are made. It also captures the interrelationship between resource markets and product markets. Households need goods and services on which they spend their income. Business firms need economic resources (owned by households) to produce goods and services needed by households. To buy goods and services, households will sell their economic resources (labor, capital, land and entrepreneur skill) and generate income which will be spent on goods and services produced by business firms as shown in Figure 1.1 below. Business firms will pay for the resources in the resource market in the form of wage (for the labor resource), interest rate (for capital) and rent (for land), and use these resources to produce goods and services demanded by households. There are two different markets in the diagram: resource market and product market. In the resource market economic resources are traded. From the resource market, money in the form of consumers' income flow to households and economic resources flow to business firms. Similarly in the product market, money income in the form of revenue flow to business firms and goods and services flow to households. Generally, both

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households and firms participate in both markets but on different side of each, once as a demander then as a supplier. Households are suppliers in the resource market and demanders in the product market; firms are demanders in the resource market and suppliers in the product market.

Firms’ Expenditure on Economic Resources

Income to Resource Owners Resource Market

Flow of Resources

Flow of Resources

Business Firms

Households

Flow of Goods and Services

Flow of Goods and Services Product Markets Consumption Expenditure

Revenue of Firms

Figure 1.1: The Circular Flow Model

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1.7 THE CONCEPT OF MARKET STRUCTURE Market is a place or condition in which buyers and sellers meet to exchange goods and services for the price they agree on. In the theory of the firm we are concerned with the question: “How are prices of commodities determined in the market?” The determination of price of a commodity depends on the number of sellers and buyer in the market. The number of buyers and sellers determine the nature and degree of competition in the market. The nature and degree of competition makes or creates the structure of the market. Thus, the market structure is determined or defined by the nature and degree of competition in market. Depending on the number of sellers and the degree of competition, the market structure is broadly classified as follows. 1. Perfect competition (competitive market), and 2. Imperfect markets (noncompetitive markets). Here belong market structures of: a. Monopoly, b. Monopolistic competition, and c. Oligopoly. This particular course gives focus only to the perfectly competitive and monopoly markets and how prices of goods and services are determined in these market structures.

1.8 MICROECONOMIC THEORY AND THE PRICE SYSTEM Microeconomics (or price theory) is a branch of economics that studies how individuals, households, and firms make decisions to allocate limited resources in consumption and/or production.

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One of the goals of microeconomics is to analyze the market mechanisms that establish relative prices amongst goods and services, and the allocation of limited resources amongst many alternative uses. Microeconomics also analyzes market failure, where markets fail to produce efficient results, as well as describing the theoretical conditions needed for perfect competition. Significant fields of study in microeconomics include general equilibrium, markets under asymmetric information, choice under uncertainty and economic applications of game theory. Also considered is the elasticity of products within the market system. This course (Microeconomics I) deals with the price theory, where the price system plays the fundamental role of determining what to produce, how to produce, and for whom to produce. In the chapters to follow, we will analyze the behaviors of consumers (chapter two) and firms (chapters three and four) separately. Chapters five and six bring the two economic units, consumers and producers, in perfectly competitive and purely monopolistic market structures.

Check Your Progress 1. What do you understand by opportunity cost? 2. What are the decision-making units in an economy and what are their objectives? 3. Explain the difference between product market and resources market. 4. What are payments for labor, land, capital and entrepreneurial skill?

1.9 LESSON SUMMARY # Though different people have different motives to study economics, knowledge about economics in general is essential because everyone faces economic problems at different levels, and makes economic decision throughout his/her life knowingly or unknowingly.

Therefore, economic literacy is important because economic

issues facing government and individuals shape the future of the nation and affect the well being of its citizens. 19

# Limited economic resources and unlimited societal wants for material goods and services are the two fundamental facts, which lay foundation for the economizing problem and economics as discipline. Economic resources like, different types of labor, land, capital and entrepreneurial skill are limited. Whereas society’s need for goods and services are unlimited as wants are multiplicative, recurrent and as human nature is accumulative.

The limited availability of resources and the

unlimited wants give rise to the problem of scarcity. Scarcity forces us to make choices. Making a choice, in turn, implies the need for the efficient utilization of resources. # Economics is, therefore, the study of how scarce resources are allocated among alternative and competing ends in order to maximize the consumption of goods and services. # The basic divisions in economics are microeconomics and macroeconomics. Microeconomics studies the behavior of individual components of the economy: households and business firms. Macroeconomics, on the other hand, deals with issues at the overall economic level like unemployment, inflation and national income. Economics can be positive or normative. Positive economics is limited to making purely descriptive statements of scientific prediction. Normative economics involves value judgments and it tells us what should be done. # The three major or fundamental problems of economics are what to produce, how to produce, and for whom to produce. These problems are universal to all countries regardless of their level of development. However, different countries having different economic system use different approach to solve them. Economic systems are different from each other on the basis of the ownership of economic resources and the method by which economic activities are coordinated. The four economic systems are free market economy, command economy, mixed economy and traditional economy system. # Opportunity cost is the amount of one product, which must be given up to obtain additional unit of another product. Efficiency occurs when the economy is using its resources so well that producing more of one good results in less of other goods, i.e., no resources are being wasted. But full production must also be realized. Full

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production means producing the “right goods” (allocative efficiency) in the “right way” (productive efficiency). # Households, business and government are the major decision-making units of an economy. While households attempt to maximize their utility, firms seek to maximize their profits. The link between them is shown by the circular flow diagram.

1.10 REVIEW QUESTIONS I. Multiple Choice Questions 1. Which of the following is addressed by microeconomics? a. How tax and price controls affect consumers and producers b. The extent to which the economy’s resources are employed c. Overseas trade d. ‘a’ and ‘b’ 2. Ceteris paribus means, a. Other things positively sloped b. Supply is positively sloped c. Demand is positively sloped d. Other things remaining constant e. None of the above 3. In a free market economy, the fundamental problems of the economy are solved by: a. The agreement among economists b. Individuals who make price in a market c. The planning committee of the country d. Intervention of the government in every aspect of the economy e. the price mechanism 4. Economic resources are also called a. Capital goods b. Consumption goods

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c. Free goods d. Factors of production e. None 5. The dual role of firms comprises of: a. providing resources and using goods and services b. providing resources and producing goods and services c. employing resources and producing goods and services d. All of the above e. None of the above 6. Which of the following is not true about the roles of entrepreneur? a. Determines the price of the commodity b. Takes risk c. Introduces new technology d. Introduces new product e. None 7. If the amount of a commodity available at zero price could fully satisfy the human need, then this good is a/an: a. Free good b. Economic good c. Scarce good d. Efficient good e. None 8. Macroeconomics is a branch of economics which deals with: a. Price determination of the individual sellers/firms b. The level of total output in the economy as a whole c. Movements in the overall price level (inflation) d. ‘b’ and ‘c’ e. ‘a’ and ‘b’

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II. True or False Questions 1. Scarcity is ever present because every economy faces the problem of not having enough resources to produce all the goods and services that people want. 2. A market system always produces the combination and amounts of goods that are best for society. III. Discussion Questions 1. What are the fundamental (basic) problems of economies? How are these problems solved? 2. How do you relate the concepts of scarcity, opportunity cost and efficiency to one another and to the discipline of economics?

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CHAPTER TWO THE THEORY OF CONSUMER BEHAVIOR LESSON STRUCTURE 2.1 Introduction 2.2 Chapter Objectives 2.3 What is the Theory of Consumer Behavior? 2.4 The Rational for the Theory of Consumer Behavior 2.5 Methods of Comparing Utility 2.5.1 The Cardinal Utility Theory 2.5.2 The Ordinal Utility Theory 2.6 Market Demand 2.7 Elasticity of Demand 2.8 Choice under Uncertainty 2.9 Lesson Summary 2.10 Review Questions

2.1 INTRODUCTION As it has been mentioned in the first chapter, there are three decision making units in economics and they are households (the primary consuming units), firms (the primary producing units) and government. As you recall from the topic “Alternative Economic Systems” of chapter one, the decision making units in a pure market economy are households and firms. Hence, in order to understand the pure market system it is better to analyze the behavior of households and firms. Thus, in this chapter we will study the behavior of households (consumers) under the “Theory of Consumer Behavior “and in the next two chapters we will be concerned with the behavior of firms under “The Theories of Production and Costs”.

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In a given economy it is a must to find a market for a commodity. And in any market we find the demanders as well as the suppliers. Hence, there is a need to study about the markets so as to know the behavior of the economy; and, in order to know about the market, it is necessary to deal with the components of the market i.e. demanders and suppliers. The analysis of the demand side and the supply side of the market involves the study of the behaviors of households (demanders of final goods and services in the product market) and firms (suppliers of final goods and services in the product market). Thus, the rational for studying the theory of consumer behavior is the fact that it is the basis for the theory of demand. This is because the market demand is assumed to be the horizontal summation of the demand of the individual consumers. That means, we first analyze the behavior of a consumer to determine the individual demand, and then stepping on the demand of an individual consumer we will develop the market demand. However, in our attempt to study the behavior of the consumer, we deal with the traditional demand theory which has the following important features. # The traditional theory of demand examines only the final consumer’s demand for durables and non- durables. It deals only with consumers’ demand, i.e., it does not deal with the demand for investment good, nor with the demand for intermediate products. # It examines the demand in one market in isolation without considering the conditions of demand in other markets (what is referred to as partial equilibrium analysis). # It also assumes that firms sell their product directly to the final consumers. In order to determine the various factors that affect demand we need to deal with the theory of demand. As demand is a multivariate relationship determined by many factors simultaneously, we need to go beyond the law of demand which states that there is negative relationship between market demand and price under the assumption of ceteris

25

paribus (other things remaining constant). All those important determinants of demand are related with the behavior of the consumer. Thus, the traditional theory of demand starts with the behavior of a consumer. Under the theory of consumer behavior, the following important assumptions are made: 1. The consumer is assumed to be rational. Given his/her income and the market prices of the commodities, he/she spends his/her income on the basket of goods and services that give the highest possible satisfaction or utility. This is the axiom/postulate of utility maximization. 2. It is also assumed that the consumer has all relevant information important for his/her decision. This means that the consumer has perfect knowledge about his/her income, complete knowledge of the available commodities in the market, and exact knowledge of the prices of all available commodities in the market. At this point it is important to mention that the theory of consumer behavior in this chapter will be dealt with in two parts. The first part is in line with the second assumption which considers that the consumer has full knowledge of all the information relevant to his/her decision. The second part relaxes this assumption and tries to involve the possibility of the existence of uncertainties in the market. In short, the first part deals with the behavior of the consumer under the condition of certain information (Choice under certainty), while the second part is concerned with choice under uncertainty.

2.2 CHAPTER OBJECTIVES This chapter has a general objective of enabling the students know how consumers decide on baskets of goods and services to maximize their satisfaction. The specific objectives of the chapter are: # Help students know the basis of the theory of demand; # Enable students derive a consumer’s demand under some alternative sets of information; # Enable students know the concepts of utility and preferences;

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# Help students understand different types of utility functions; # Help students understand the determinants of individual and market demands, and the concept of elasticity.

2.3 WHAT IS THE THEORY OF CONSUMER BEHAVIOR? Before looking at what the theory of consumer behavior is all about, let’s first see what a consumer is. A consumer is an individual or a household who uses/consumes final goods and services with a primary objective of maximizing utility. The theory of consumer behavior is a description of how consumers allocate income among different goods and services to maximize their well-being. It answers the question: “How can a consumer with a limited income decide which goods and services to buy with the objective of maximizing their utility?” It deals with how consumers allocate their income across various goods and services and explain how these allocation decisions determine the demands for the various goods and services.

2.4 THE RATIONAL FOR THE THEORY OF CONSUMER BEHAVIOR Understanding the consumers’ purchasing decisions will help us understand how changes in income and prices affect demands for goods and services, and why the demands for some products are more sensitive than others to changes in prices and income. In general, as it has been mentioned above, we study the theory of consumer behavior since it is the basis for the theory of demand. We have said that consumers are the primary consuming units with an objective of maximizing their utility/satisfaction. In order to attain this objective, the consumer must

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be able to compare the utility/satisfaction of the various baskets of goods and services which he/she can buy with his/her income.

2.5 METHODS OF COMPARING UTILITY Utility is the level of satisfaction/pleasure that the consumer can derive from consumption of goods and services or by undertaking a certain activity. It is the power of a good or service to satisfy a certain human need. There are two basic approaches to the problem of comparison of utilities. These approaches are: 1. The Cardinalist Approach, and 2. The Ordinalist Approach. In the next section, we will examine the two approaches one by one. In each case, we first state the assumptions underlying the approach, and then derive the equilibrium of the consumer. From this equilibrium of the consumer, we will determine the demand for individual products which will help us establish the market demand for the commodity. Finally, we will point out the critics of each approach. Let’s first see the Cardinalist Approach. 2.5.1 The Cardinal Utility Theory There are some theories of utility that attach significance to the magnitude of utility. These are known as Cardinal Utility Theories. The cardinalist school postulates that utility can be measured. The advocates of this school have given various suggestions for the measurement of utility. With the

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assumption of complete knowledge of market conditions and income levels over the planning period i.e. under certainty, some economists have suggested that utility can be measured in monetary units, say, by the amount of money the consumer is willing to sacrifice for another unit of a commodity. And others suggested the measurement of utility in subjective units, called Utils. Thus, in a theory of cardinal utility, the size of the utility difference between two bundles of goods and services is supposed to have some sort of significance. In its attempt to reach at the equilibrium of the consumer, the cardinal utility approach makes the following assumptions. Assumptions of the Cardinal Utility Theory 1. Rationality: The consumer is rational. He/she aims at the maximization of his/her utility subject to the constraint imposed by his/her given income. This means that the consumer is able to allocate his/her limited income first on the good that gives him/her the highest possible level of satisfaction, and then move to the next best, and so on. 2. Cardinal Utility: The utility of each commodity is measurable. It is assumed that utility is a cardinal concept. The most convenient measure of utility is money: the utility is measured by the monetary units that the consumer is willing to pay for another unit of the commodity. 3. Constant Marginal Utility of Money: This assumption is necessary if the monetary unit is used as the measure of utility. The essential feature of a standard unit of measurement is that it is constant. If the marginal utility of money changes as income changes (increase or decrease) the measuring rod for utility becomes, like an elastic ruler, inappropriate for measurement. 4. Diminishing Marginal Utility of Commodities: The utility gained from successive units of a commodity diminishes. In other words, the marginal utility of a

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commodity diminishes as the consumer consumes larger quantities of it. This is what is referred to as the axiom of diminishing marginal utility. 5. The Total Utility of a Basket of Goods and Services Depends on the Quantities of the Individual Commodities. For example , if there are n commodities in the bundle with quantities x1, x2,…………,xn, the total utility is given by: U = f(x1, x2,…………,xn) 6. Additivity of Utility: In very early version of the theory of consumer behavior, it was assumed that the total utility is additive. This means, if there are n commodities in the bundle with quantities x1, x2,…………,xn, the total utility is: U = u1(x1) + u2(x2) + ………+un (xn) However, the additivity assumption is dropped in later versions of the cardinal utility theory because additivity implies independent utilities of the various commodities in the bundle, and this is an assumption which is clearly unrealistic and unnecessary for the cardinal utility theory. Equilibrium of the Consumer under the Cardinal Utility Theory Let’s begin our analysis of the equilibrium of the consumer with a simple model of a single commodity, X. The consumer has two alternatives for the use of his/her income: either to buy X or retain the money income, Y. Under this condition, the consumer is in equilibrium (at the highest possible level of satisfaction) when the marginal utility of X is equal to its market price (Px). Marginal utility of a commodity is the extra satisfaction that one can derive from one additional unit of the commodity. Symbolically, the equilibrium of the consumer can be represented as: MUx = Px Where: MUx is the marginal utility of the commodity (X), and Px is the price of the commodity (X) If the marginal utility of X is greater than its price (MUx > Px), the consumer can increase his/her welfare by purchasing more units of the commodity X. Similarly, if the

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marginal utility of the commodity is less than its price, the consumer can increase his/her total satisfaction by cutting down the quantity of the commodity X and keeping more of his/her income unspent. Therefore, the consumer attains the maximum level of satisfaction (utility) when MUx = Px. So far, for the sake of simplicity we have been assuming that there is only one commodity. However, in reality, since the consumer may consume more than one commodity, we can extend our analysis of the consumer into the case of many commodities. If there are more commodities, the condition for the equilibrium of the consumer is the equality of the ratios of the marginal utilities for the individual commodities to their prices. Symbolically, assuming that there are N commodities: X, Y, Z, ………..N, the equilibrium is attained when:

MU N MU X MU Y MU Z = = =…= PX PY PZ PN Mathematically, we can derive the equilibrium of the consumer as follows: Suppose the utility function in a simple model of single commodity X is given by: U= f (Qx) where U is total utility measured in monetary units and Qx is quantity of the commodity X. If price of the commodity is Px and the consumer buys Qx units of commodity X, the expenditure of the consumer will be the product, PxQx. Hence, the consumer wants to maximize the difference between his/her utility and his/her expenditure. i.e, Maximize (U- PxQx) In order to maximize the above mentioned difference there is necessary condition as well as sufficient condition. The necessary condition is that the partial derivative of the function with respect to Qx be equal to zero.

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Thus,

∂ ( PX Q X ) ∂U – =0 ∂Q X ∂Q X By rearranging the above expression we obtain:

∂ ( PX Q X ) ∂U = , but since price is constant we can factor it out and find ∂Q X ∂Q X P ∂Q ∂U = X X ∂Q X ∂Q X

1

∂U = PX ∂Q X

MU X = PX In the case of several commodities, the utility derived from spending an additional unit of money must be the same for all commodities. If the consumer derives greater utility from any one commodity, he/she can increase his/her welfare by spending more on that commodity and less on the others, until the above equilibrium condition is fulfilled. Derivation of the Demand of the Consumer The derivation of demand is based on the axiom of diminishing marginal utility. As it has been mentioned above, the marginal utility of a commodity (MUx) is the slope of the total utility of the commodity (U=f(Qx)). Total utility is the total amount of satisfaction that one can derive from the use of a certain bundle of goods and services or by undertaking a certain activity. Total utility of a commodity (X), TUx, increases, but at a decreasing rate initially up to a certain level of quantity, let’s say X1, and then starts declining. Thus, this implies that TUx is at its maximum point at X1 units of quantity (See Figure 2.1). Accordingly, the 1

∂Q X ∂U = 1 and only Px will be remaining on the right hand side, and is marginal ∂Q X ∂Q X utility of the commodity (X) which is the slope of total utility.

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marginal utility of the commodity (MUx) declines continuously when TUx increases at a decreasing rate, and becomes negative beyond quantity X1 i.e MUx is zero at the maximum point of TUx. Thus, the marginal utility of a commodity is depicted by a negatively sloped line (See Figure 2.2). Geometrically, marginal utility of a commodity is the slope of the total utility function U = f (X). That means, marginal utility of a commodity is an extra satisfaction as a result of one unit increase in the consumption of the commodity. Mathematically, given total utility function U = f (X), Marginal utility of the function is given by: MU =

d (TU X ) Where: MUx is the marginal utility of commodity d(X )

X, d(TUx) is change in the total utility of commodity X, and d(X) is change in the quantity of X consumed. TUx TUx

X1

X

Figure 2.1: Total Utility Function MUx

X1

X MUx

Figure 2.2: Marginal Utility Function

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NB. The slope of a tangent line to total utility function gives marginal utility of the commodity at that point. Hence, as can be seen on Figure 2.1 above the tangent lines on the total utility function are becoming flatter and flatter with increase in consumption of X. This implies that the slopes of the tangent lines, which are the slope of the total utility function, are declining with increase in consumption of the commodity. If the marginal utility is measured in monetary units the demand curve for commodity X is identical to the positive segment of the marginal utility curve since marginal utility of the commodity is equal to price of the commodity (MUx = Px). As depicted in Figure 2.3a below, at quantity level X1 the marginal utility is MU1 which is equal to the price level P1 by definition. Hence, at the price level P1 the consumer demands X1 units of he commodity (Figure 2.3b). Similarly, at X2 the marginal utility of the commodity is MU2, which is equal to P2. Hence, at P2 the consumer will buy X2 units of the commodity, and so on. Thus, we can observe that Figure 2.3b shows the demand curve which is derived from the marginal utility function of a commodity (Figure 2.3a) MUx

P

MUX1

P1

MUX2

P2

MUX3

P3

O X1

Demand Curve

X

X2 X3

O

MUx Figure 2.3a: Marginal Utility of X

X1

X2

X3

X

Figure 2.3b: Demand Curve for X

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NB. The negative section of the MUx curve does not form part of the demand curve since negative prices do not make sense in economics. Critiques of the Cardinal Utility Approach There are three basic weaknesses in the cardinal utility approach. a) The assumption of cardinal utility is extremely doubtful. This is because the satisfaction derived from various commodities can not be measured objectively. The attempt by Walras to use subjective units (Utils) for the measurement of utility does not provide any satisfactory solution. b) The assumption of constant utility of money is also unrealistic. As income increases the marginal utility of money changes. Thus, money can not be used as a measuring rod for utility since its own utility changes. c) The additivivty of utility is questionable since there is no objective measure of

utility.

Check Your Progress 1. Explain why we study the theory of consumer behaviour. 2. What does it mean by: the marginal utility of a commodity is diminishing? 3. Explain the meaning of MUx = 4. 4. Derive the demand curve using the approach you studied above. 2.5.2 The Ordinal Utility Theory The ordinalist school postulates that utility is not measurable, but is an ordinal magnitude. The consumer need not know in specific the utility of various commodities to make his/her choice. Under this approach, it suffices for the consumer to be able to rank the various baskets of goods and services according to the satisfaction that each bundle

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gives him/her. The consumer must be able to determine his/her order of preference among the different bundles of goods and services. There are two main ordinal utility theories, which are: 1. The Indifference Curves Theory 2. The Revealed Preference Hypothesis 1. The Indifference Curves Theory The indifference curves theory is one of the theories which argues that utility is not cardinally measured rather it is ordinally measured. This theory tries to show the equilibrium of the consumer using the concept of indifference curves as the name suggests. Assumptions of the Indifference Curves Theory 1) Rationality: The consumer is assumed to be rational – he/she aims at the maximization of his/her utility, given his/her income and the market prices. It is also assumed that the consumer has full knowledge (certainty) of relevant information. 2) Utility is Ordinal. It is taken as axiomatically true that the consumer can rank his/her preferences (orders the various baskets of goods and services) according to the satisfaction of each basket. Unlike the cardinal utility theory, he/she need not know perfectly the amount of satisfaction. It suffices that he/she expresses his/her preference for the various bundles of commodities. That means it is not necessary to assume that utility is cardinally measurable, but only ordinal measurement is required. 3) Diminishing Marginal Rate of Substitution: Preferences are ranked in terms of indifference curves which are assumed to be convex to the origin. This implies that the slope of the indifference curves decreases with increase in consumption of the commodity. The slope of the indifference curves is called the marginal rate of

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substitution of the commodities. Thus, the indifference curve theory is based on the axiom of diminishing marginal rate of substitution. (More will be said on marginal rate of substitution later in the chapter.) 4) The Total Utility of the Consumer Depends on the Quantities of the Commodity Consumed: U = f(X1, X2, …, Xn) 5) Consistency and Transitivity of Choice: It is assumed that the consumer is consistent in his/her choice, that is, if he/she chooses bundle A over B in one period, he/she will not use B over A in another period if both bundle are available to him/her, under exactly the same conditions. The consistency assumption may be symbolically written as follows: If A > B, then B ≯A. Similarly, it is assumed that consumer’s choices are characterized by transitivity: if bundle A is preferred to B and B is preferred to C, then bundle A is preferred to C. Symbolically, we may write the transitivity assumption as follows: If A > B and B > C, then A > C. Equilibrium of the Consumer under the Indifference Curves Theory To define the equilibrium of the consumer (that is his/her choice of the bundle that maximises his/her utility) we must introduce two concepts: ¾ the indifference curve and its slope which is the marginal rate of substitution, and ¾ the budget line. These are the basic tools of the indifference curves theory. The Indifference Curve An Indifference Curve is a curve representing all combinations of market baskets that provide a consumer with the same level of satisfaction. Hence, all points along the same indifference curve give the consumer the same level of satisfaction. The consumer is,

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therefore, indifferent among different combinations of goods represented by the points graphed on a curve. Y

Indifference Curve

X

O Figure 2.4: An Indifference Curve

An Indifference Map shows a set of indifference curves which rank the preferences of the consumer. Combinations of goods situated on an indifference curve yield the same level of satisfaction for the consumer. However, combinations of goods lying on a higher indifference curve yield higher level of satisfaction and are preferred. Combinations of goods on a lower (close to the origin) indifference curve yield lower level of satisfaction. Y

I3 I2 I1 O

X

Figure 2.5: An Indifference Map 38

An indifference curve is shown in Figure 2.4 and an indifference map is depicted in Figure 2.5. It is assumed that the commodities Y and X are can substitute one another to a certain extent but are not perfect substitutes. Symbolically, an indifference curve is given by the equation: U = f(X1, X2……..Xn) = K

Where K is a constant.

Given the above utility function, an indifference map can be derived by assigning every possible value to K in such a way that as we move away from the origin the level of satisfaction increases (Higher K). The negative of the slope of indifference curve at any one point measures the rate of change of commodity Y as a result of change in commodity X, and is called the marginal

rate of substitution of the two commodities. Geometrically, the marginal rate of substitution is given by the slope of the tangent line at that point: MRS X ,Y = −

dY = − Slope of the Indifference Curve dX

The marginal rate of substitution of X for Y is defined as the number of units of commodity Y that must be given up in exchange for an extra unit of commodity X so that the consumer maintains the same level of satisfaction. For example, MRSX,Y = 5 can be interpreted as: five units of Y must be sacrificed in order to increase the consumption of X by one unit and leave the consumer on the same level of satisfaction. Similarly, MRSY,X = 3 can be interpreted as: three units of commodity X must be sacrificed in order to increase the consumption of commodity Y by one unit and leave the consumer on the same level of satisfaction. With this definition, the proponents of the indifference curves approach thought that they could avoid the nonoperational concept of marginal utility.

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Marginal Utility (MU) and Marginal Rate of Substitution (MRS) The concept of marginal utility (MU) is implicit in the definition of the marginal rate of substitution (MRS), since it can be proved that the marginal rate of substitution (the slope of the indifference curve) is equal to the ratio of the marginal utilities of the commodities involved in the utility function: Symbolically:

MRS X ,Y =

MU X MU Y or MRSY , X = MU Y MU X

Where, MRSx,y is marginal rate of substitution of x for y MRSy,x is marginal rate of substitution of y for x MUx is marginal utility of commodity x MUy is marginal utility of commodity y We can prove the above relationship between MRS and MU

Proof: The slope of any curve at any one point is measured by the slope of the tangent line at that point. For example the slope of the curve f(x) at point a in the figure below (figure 2.6) is the slope of line one (L1) and the slope of the curve at point b is the slope of line two (L2). The equation of a tangent line is given by the total derivative2, which shows the total change of the function as its determinant changes.

2

The total derivative of a function is change in the dependent variable as a result of change in the independent variable. For example, if the function is given by Y= f(X), Y being the dependent variable and X the independent variable, then the total derivative of the function is and dX is change in X.

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dY , where dY is change in Y dX

Y

f(x) L2

b

L1 a O

X Figure 2.6: Slope of a Curve

# The total utility function in the case of two commodities x and y (assuming that the consumer is consuming only two commodities x and y) is: U = f(x,y). The equation of an indifference curve is: U = f (x,y) = K, where K is a constant. # The total differential of the utility function is measured by dU. dU shows the total change in utility as the quantities of both commodities change. dU =

[

∂U ∂U dY dX + ∂Y ∂X

∂U ∂U = MU X and = MU Y ] ∂X ∂Y

dU = ( MU X )dX + ( MU Y )dY In words, the total change in utility (dU) caused by changes in X and Y is approximately equal to the change in X (dX) multiplied by its marginal utility (MUx) plus the change in Y (dY) multiplied by its marginal utility (MUy). # By definition, along any particular indifference, the total change (differential) in utility is equal to zero since the consumer derives the same level of satisfaction along the same indifference curve.

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Hence, dU = 0

dU = ( MU X )dX + ( MU Y )dY = 0 # By rearranging the above equation we obtain:

dU = ( MU X )dX + ( MU Y )dY = 0 ( MU X )dX = −( MU Y )dY −

dY MUX . = dX MUY

[But, recall that MRSX,Y = −

MRS X ,Y = −

dY ] dX

dY MU X = dX MU Y

Similarly, MRSY , X = −

dX MU Y = . dY MU X

The indifference curves theorists substitute the assumption of diminishing marginal utility of commodities with the assumption of diminishing MRS of commodities since the indifference curves are convex to the origin (with declining slope in absolute value from left to right, i.e., declining MRSx,y). Properties of Well-Behaved Indifference Curves

a) Well-behaved indifference curves are negatively sloped. This denotes that if the quantity of one commodity (X) decreases, the quantity of the other commodity (Y) must increase, if the consumer is to stay on the same level of satisfaction.

b) The further away from the origin an indifference curve lies, the higher the level of utility it denotes. Bundles of goods on a higher indifference curve are preferred by the rational consumer.

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Y I3 > I2 > I1 I3

I2

I1 X

O

Figure 2.7: A Higher Indifference Curves Denote Higher Level of Utility

c) Indifference curves do not intersect to each other. If they did, the point of their intersection would imply two different levels of satisfaction, which is impossible. That means if indifference curves intersect to each other, they will violate the assumption of transitivity and consistency.

Y I2

I1

X

O

Figure 2.8: Intersecting Indifference Curves, Which Is Not Possible

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d) Indifference curves are convex to the origin: The slope of the indifference curves decline (in absolute terms) as we move along the curve from the left downwards to the right. This implies that the marginal rate of substitution of the commodity X for commodity Y (= MRSx,y) is diminishing. The axiom of decreasing marginal rate of substitution expresses the observed behavioral rule that the number of units of X that the consumer is willing to sacrifice in order to obtain an additional unit of Y increases as the quantity of Y decreases. It becomes increasingly difficult to substitute X for Y as we move to the right along the indifference curve. The case of convex indifference curves implies that the commodities are substitutes for one another, but are not perfect substitutes. However, depending on the type of the commodities there are different kinds of indifference curves which violate some of the above mentioned behaviors of an indifference curve. Consider the following different types of indifference curves. 1. The Case of Perfect Substitutes Substitute goods are goods which can serve similar needs of the consumer. For example, Coca Cola and Pepsi, Tea and coffee, Bread and ‘Injera’ may be considered as examples of substitute goods. If the two goods X and Y are perfect substitutes to each other, the indifference curves will be downward sloping straight line. Hence, the marginal rate of substitution between the two goods will be constant. In other words, two goods are perfect substitutes if the consumer is willing to substitute one good for the other at a constant rate. The simplest case of perfect substitutes occurs when the consumer is willing to substitute the goods on a one-to-one basis. For example, let us consider a choice between red pencil and blue pencil, and the consumer involved like pencils, but doesn’t care about colours at all. Pick a consumption bundle, say (10, 10). Then for this consumer, any other consumption bundle that has 20

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pencils in it is just as good as (10, 10). Mathematically speaking, any consumption bundle (X, Y) such that X + Y = 20 will be on the consumer’s indifference curves. Hence, the indifference curves for this consumer are parallel downward sloping straight lines. Y

O

X

Figure 2.9: Indifference Curves for Perfectly Substitute Goods

2. The Case of Perfect Complements Complement goods are goods which are consumed together to serve a single need of the consumer. Perfect complements are goods that are always consumed together in fixed proportions. For instance, Sugar and Tea, Photo camera and Film, Car and Fuel can be considered as examples of perfect complementary goods. This means that one good cannot be consumed without the other as the goods are consumed with fixed proportions. Thus if the two goods are perfect complements to each other, the indifference curves will be L-Shaped (right angled) as depicted in Figure 2.10 below. A good example of perfect complements is the case of right shoe and left shoe. The consumer likes shoes but always wear right shoe with left shoe together. Having many of left shoes and one right shoe doest allow the consumer to wear more than one pair of shoes, meaning, having only one out of a pair of shoes does not do a consumer a bit of

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good. The consumption bundle (10, 10), i.e., 10 units of left and 10 units right shoes, gives the consumer the same level of satisfaction for the consumer as a bundle which is composed of (11, 10) or (10, 11). Hence, the consumer always consume at the vertex of the indifference curves where the number of the two goods are the same or the proportion of the two perfectly complementary goods are the same. Y

X

O

Figure 2.10: Indifference Curve for Perfect Complements Increasing both the number of left shoes and right shoes at the same time will move the consumer to a higher indifference curve, or to a more preferred position. The important thing about perfect complement goods is that the consumer consumes the goods in fixed proportions, not necessarily that the proportion is one-to-one. For example, if the consumer always uses two teaspoons of sugar in his/her cup of tea and doesn’t use sugar for anything else, then the indifference curves will still be L shaped. In this case the corners of the indifference curves will occur at (2 teaspoons of sugar, 1 cup of tea), (4 teaspoons of sugar, 2 cup of tea), and so on. 3. The Case of ‘bad’ and ‘good’ Commodities If one of the two commodities is ‘good’ and the other is ‘bad’ (for example, alcohol (‘bad’) and milk (‘good’)), the consumer needs some compensation for every unit of the

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‘bad’ commodity he consumes. A bad is a commodity that the consumer doesn’t like to consume. And this compensation is by extra unit consumption of the ‘good’ commodity. This implies that the consumer increases his consumption of the ‘good’ commodity for increase in consumption of the ‘bad’ commodity. In such a case, the indifference curve will be upward sloping. The level of satisfaction increases as we move closer to the axis of the ‘good’ commodity. Y (Bad)

X (Good)

O

Figure 2.11: Indifference Curves for ‘good’ and ‘bad’ Commodities 4. The Case of Neutrals A good is a neutral good if the consumer doesn’t care about it one way or another. Let’s say that the consumer is neutral about good Y and likes good X. Then in this case, the indifference curves will be vertical lines. Y (Neutral)

X

O

Figure 2.12: Indifference Curves for a Neutral Good

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The Budget Constraint of the Consumer Economists assume that consumers choose the best bundle of goods and services they can afford. Suppose that there is some set of goods from which the consumer can choose. In real life there are many goods to consume, but for the sake of simplicity it is enough to consider the case of only two goods X and Y so that we can depict the consumer’s choice behavior graphically. Consider that the prices of the two commodities are given by Px and Py, and that the amount of money the consumer has to spend is I. Then the budget constraint of the consumer can be written as: Px Qx + PyQy ≤ I

where: Px is the price of commodity X Py is the price of commodity Y Qx is the quantity of commodity X Qy is the quantity of commodity Y, and I is the income of the consumer

The consumer maximizes his/her satisfaction given his/her income. That means the consumer’s utility maximization objective is constrained or limited by his/ her income. In other words, the consumer has a given income which sets limits to his/her maximizing behavior. Income acts as a constraint for utility maximization. In the above equation which shows the budget constraint of the consumer, PxQx gives the total amount of income that the consumer spends on commodity X and PyQy gives the total amount of income that the consumer spends on commodity Y. Hence, the total amount of spending of the consumer on the two goods, X and Y, is PxQx + PyQy. It is considered that this total amount of spending of the consumer on commodities X and Y (PxQx + PyQy) is equal to I (Income of the consumer) as it is assumed that the consumer spends all of his/her income on the consumption of the two commodities X and Y. Thus, if the consumer spends all of his/her income on the consumption of the two commodities, X and Y, the proportion of income spent on commodity X and commodity

48

Y is determined by dividing the total spending on X (= PxQx) by total income (I) and total spending on Y (= PyQy) by total income of the consumer, respectively.

Proportion of income spent on commodity X =

PX Q X I

Proportion of income spent on commodity Y =

PY QY I

The budget constraint of the consumer requires that the amount of money spent on the two goods be no more than the total amount of the consumer’s income. Hence, the consumer’s affordable consumption bundles are those that do not cost any more than I. The set of all affordable consumption bundles at prices Px and Py, and income I is called the budget set of the consumer. Properties of the Budget Line The budget line can be defined as the locus of points of all the combinations of the two commodities that cost exactly the consumer income. The budget line includes the bundles of goods that just exhaust the consumer’s income. In the case of two commodities the general budget line equation can be given by: PxQx + PyQy = I

--------------------------------------------------- Budget Line

We can present the income constraint graphically by solving for Qy from the general budget equation. From the general budget equation we know that PxQx + PyQy = I. By solving for Qy we obtain: PyQy = I – PxQx

Bringing PxQx to the right

PY QY P Q I − X X Dividing both the right hand side and the left hand side by Py = PY PY PY

49

Qy =

P Q I − X X …………………………………………………….. Budget line PY PY

Given the prices of the two commodities, Px and Py, and income of the consumer, I, we may find the corresponding values of Qy by assuming various values of Qx. Thus, if Qx = 0 (that is, if the consumer spends all his/her income on commodity Y), the consumer can buy

I units of Y. Mathematically, this will give us the vertical intercept PY

of the budget line. Similarly, if Qy = 0 (that is, if the consumer spends all his/her income on commodity X), the consumer can buy

I units of X, and this will give us the PX

horizontal intercept of the budget line. Let’s consider that we measure commodity Y on the y-axis and commodity X on the xaxis. Hence: # Vertical intercept of the budget line: when the consumer consumes commodity Y only (0, Y)

Qy =

P Q I − X X PY PY

Qy =

P I − X (0) , Since Qx = 0 PY PY

Qy =

I PY

# Horizontal intercept of the budget line: when the consumer consumes commodity X only (X, 0)

Qy = 0=

P Q I − X X PY PY P Q I − X X , since Qy = 0 PY PY

P Q I I = X X , bringing to the left hand side to solve for Qx PY PY PY

50

Qx =

P I , multiplying both sides by Y to solve for Qx PX PX

If we join the vertical and the horizontal intercepts on the X–Y set of axis, then we will obtain the budget line shown Figure 2.13. Y

Budget Line

A

I/Py

Budget set

B O

X

I/Px

Figure 2.13: Budget Line and Budget Set of the Consumer The area below the budget line is the budget set, which includes all affordable bundles by the consumer.

Geometrically, the slope of the budget line is −

I PY P OA =− =− X . OB I PX PY

Mathematically, the slope of the budget line is the derivative

∂QY P =− X . ∂Q X PY

The slope of the budget line has a nice economic interpretation. It measures the rate at which the market is willing to substitute commodity X for commodity Y. The negative sign is there since the change in X and change in Y must always have opposite signs. If you consume more of commodity X, you have to consume less of commodity Y and vice versa if you continue to satisfy the budget constraint. Economists sometimes say that the slope of the budget line measures the opportunity cost of consuming commodity X. This

51

is because in order to consume more of commodity X you have to give up some consumption of commodity Y. Changes in the Budget Line When prices and/or income change, the set of goods that a consumer can afford changes as well. How do these changes affect the budget set? Let us first consider changes in income. a. The Effect of Change in Income on the Budget Line An increase in income, assuming that Px and Py are constant, will increase the vertical intercept and the horizontal intercept, and does not affect the slope of the budget line. Thus, an increase in income will result in a parallel outward shift of the budget line. Similarly, a decrease in income will reduce both the vertical and the horizontal intercepts and as a result it will cause a parallel inward shift of the budget line. Y Y I2/Py

I1/Py

I1/Py

I2/Py

X O

I1/Px

I2/Px

X

Figure 2.14a: Effect of Increase in Income from I1 to I2 on the Budget Line

52

I2/Px

I1/Px

Figure 2.14b: Effect of Decrease in Income from I1 to I2 on the Budget Line

b. The Effect of Changes in Price on the Budget Line Let us first consider an increase in price of X while holding price of Y and income constant. According to the budge line equation, increase in Px will not change the vertical intercept (I/Py), since I and Py are constant. But it will make the budget line steeper since Px/Py (the slope of the budget line in absolute terms) will become larger. That means, increase in Px shifts the horizontal intercept inward, as a result the budget line rotates inward with a constant vertical intercept and a steeper slope. Similarly, if we consider the effect of decline in Px while holding Py and I constant, the vertical intercept remains constant but the slope becomes flatter and the horizontal intercept increases and shift outward, as a result the budget line rotates outward with a constant vertical intercept and a flatter slope. Y

Y

I/Py I/Py

O

X I/Px2

I/Px1

Figure 2.15a: Effect of Increase in Px from Px1 to Px2 on the Budget Line

O

X I/Px1

I/Px2

Figure 2.15b: Effect of Decrease in Px from Px1 to Px2 on the Budget Line

53

Note: 1. If both prices Px and Py increase in the same proportion, both the vertical and the horizontal intercepts shift inward by half of increase in prices. Thus, the budget line will shift inward. The opposite is true for proportionate decline in price of X and Y. 2. The budget set does not change when we multiply all prices and income by a positive number, the optimal choice of the consumer from the budget set doesn’t change either. 3.

The changes in commodities prices could be either the result of natural changes in market conditions (demand and/or supply conditions) or because of government policies (because of taxes imposed on or subsidies granted for the consumption of a particular commodity). For instance, if government imposes a value (an ad valorem), tax on the consumption of good X, at a rate of 5%, then the price this good increases from PX to PX + 0.05PX = (1 + 0.05)PX = 1.05PX. If the price of the other commodity (PY) and income (I) are kept constant, the effect of this tax on the budget line will be similar to the one shown in Figure 2.15a. Similarly, if a value subsidy of 10% is granted on the consumption of X, the budget line is affected in a way similar to that shown in Figure 2.15b. The Equilibrium of the Consumer under the Indifference Curves Theory

The consumer is at equilibrium when he/she maximizes his/her utility, given his/her income and the market prices of the commodities. Under the indifference curves theory, two conditions must be fulfilled for the consumer to be in equilibrium. The first condition is that the marginal rate of substitution be equal to the ratio of commodity prices. MRS XY =

MU X PX = . This is a necessary but not sufficient MU Y PY

condition for equilibrium. The second condition is that the indifference curves be convex to the origin. This is the sufficient condition for equilibrium.

54

This means that at equilibrium the consumer’s budget line is tangent to the highest possible indifference curve and at the tangency point the slope of the indifference curve ( = − MRS XY ) is equal to the slope of the budget line (= −

PX P ). That is, MRS XY = X at PY PY

equilibrium. Y

B

Y*

I3

E

I2 I1 O

X*

L

X

Figure 2.16: Equilibrium of the Consumer

The equilibrium of the consumer is attained at the tangency point of the budget line (BL) and the indifference curve (I2), consuming Y* units of commodity Y and X* units of commodity X (Figure 2.16). This is because, the consumer cannot consume on the third indifference I3 curve as it is not attainable given his/her income. And, the consumer does not consume on the first indifference curve (I1) as he/she can consume more given his/her income.

Check Your Progress 1. Explain the difference between the equilibrium conditions of the consumer under cardinal utility approach and ordinal utility (indifference curves) approach.

55

2

2. Suppose the total utility function of a consumer is given by TU(x) = 2x . What is the marginal utility of X? 3. Assuming the income of the consumer to be constant, what will be the effect of a decline in price of both commodity X and commodity Y by the same proportion? Explain your answer with the help of graph(s). 4. If the price of commodity X is 10 Birr per unit and the price of commodity of Y is 8 Birr per unit, write the budget line equation assuming that the consumer spends all of his 500 Birr income on the two commodities, X and Y. 5. Mention at least one assumption which is common for both the cardinal and the ordinal utility approaches. 6. Graphically explain: a. The effect of increase in price of Y on the budget line when price of X and income are constant. b. The effect of decrease in price of Y on the budget line when price of X and income of the consumer remain constant. Income Offer Curve and Engel Curve Previously when we were discussing the behavior of a budget line, we were able to identify that the budget line changes with changes in income of the consumer (I) and prices of the commodities (Px and Py). When the budget line changes due to change in income or prices or both, the equilibrium of the consumer will also change since the most preferred attainable indifference curve of the consumer also changes with the new budget line. With the new equilibrium there are also new levels of equilibrium quantities. Hence, in this section we see the effect of changes in income of the consumer on the equilibrium of the consumer. And in the next section we will see the effect of a change in the price of a commodity on the equilibrium of the consumer and on the level of the quantity consumed. In analysing the effect of a change in income on the equilibrium of the consumer, we use the concepts of Income Offer Curve and Engel Curve.

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Suppose that the initial income of the consumer is I1 with the budget line BL and the initial indifference curve is IC1. Thus, the initial equilibrium point of the consumer is E1 where the consumer consumes X1 units of commodity X (See Figure 2. 17). Given these initial conditions, suppose that the consumer’s income rises, ceteris paribus. If the income of the consumer increases, say, from I1 to I2, the budget line will shift upward from BL to B’L’ in a parallel manner and the consumer will be able to consume on a higher level of indifference curve, IC2. Thus, the equilibrium of the consumer will also change from E1 to E2 at the tangency point of the new budget line B’L’ and the now affordable indifference curve, IC2. Here, when the equilibrium changes from E1 to E2, E2 will be to the right of E1 if the good is normal3. In this case, the consumption of commodity X increases from X1 to X2. But, if the good is inferior good E2 will be to the left of E1 and the level of consumption will decline from X1 to X2. If income continues to increase, there will be successive equilibrium points with the changed budget lines and higher indifference curves, and the quantities of the commodity will also be changed. As can be seen from Figure 2.17, if we connect those successive equilibrium points which result from changes in income, we will find an Income Offer Curve. Income offer curve is also called income consumption curve or income expansion

path. For a normal good, income offer curve is positively sloped as the new equilibrium points lie to the right of the original ones. On the other hand, the income offer curve for an inferior good is negatively sloped since the new successive equilibrium points of the consumer (caused by increases in income) lie to the left of the original equilibrium point.

3

A commodity is defined as ‘Normal’ when its demand changes in the same direction as income, i.e., the demand of the commodity increases with increase in income and vice versa. However, if the demand for the commodity changes inversely with income, the commodity is called an inferior good. That is, for an inferior good demand for the commodity decreases with an increase in income and vice versa.

57

For each level of income, I, there will be some optimal/equilibrium choice for each of the goods, X and Y. Let us focus on good X and consider the optimal choice at each set of prices and income (Px, Py, I). This is simply the demand function for good X. Y

Y B’

B’

Income Offer Curve for normal

B

Income offer curve for inferior good

IC2

B

good E1

E2

E2

IC2

E1

IC1

IC1

O

X1

X X2 L L’ Figure 2.17a: Income Offer

O X1

X2

L

X L’

Figure 2.17b: Income Offer

Curve for a Normal Good X

Curve for an Inferior Good X I

I I2

Engel Curve for Normal Good

I1 Engel Curve for an Inferior Good

I2

I1

X

X

O X1

O

X2 X1 Figure 2.17c: Engel Curve

X2

Figure 2.17d: Engel Curve

for a Normal Good X

for an Inferior Good X

If we hold the prices of X and Y fixed and look at the how demand for X changes as we change income, we generate a curve which is known as the Engel Curve. That means,

58

depicting the relationship between changes in income and changes in the quantity consumed of a commodity while all commodity prices are held constant, will give as what is called Engel curve of the commodity. An Engle curve is a graph of the demand for one of the commodities as a function of income, with all prices held constant. The Engel curve is positively sloped for normal goods since consumption of the good increases with increase in income or since it decreases with a decrease in income. On the other hand, the Engel curve for an inferior good is negatively sloped since consumption of the good decreases with an increase in income or increases with a decrease in income. Derivation of the Demand Curve using the Indifference Curves Theory: Price Offer Curve and the Demand Curve From the equilibrium of the consumer under the indifference curves theory, we can derive the demand for a good graphically. As the price of a commodity (Px) falls, assuming that Py and I are constant, the budget line of the consumer rotates upward from its initial position to a new position (from BL to BL’ in Figure 2.18a) with a constant vertical intercept. This is due to the increase in the purchasing power of the given money income of the consumer. With more purchasing power in his/her possession, the consumer can buy more of X and/or more of Y. This means that the new budget line (BL’) is now tangent to a new indifference curve (I2) which is higher than the original indifference curve (I1). If we allow the price of the commodity (Px) to fall continuously and join the points of tangencies of the successive budget lines and higher indifference curves (equilibrium points with the changed prices), we form the so called the Price Consumption Curve. The price consumption curve is also referred to us the price offer curve. From the price consumption curve due to change in price of commodity X, we can derive the demand curve for commodity X. In the figure 2.18a below, at point E1, the consumer

59

buys X1 units of commodity X at the original level of price (say P1). At point E2, price has reduced from P1 to P2, thus the quantity demanded of commodity X has increased from X1 to X2, and so on. Now we can plot the price quantity pairs defined by the points of equilibrium (on the price consumption curve) to obtain a demand curve for commodity X (See Figure 2.18b below). Y

B

Price- consumption curve

E3

E2

I3

E1

I2 I1

O

X1

L X2 X3

L’

L’’

X

Figure 2.18a: Price Consumption/Offer Curve P

P1 P2 P3

Demand Curve

O

X1

X2

X

X3

Figure 2.18b: The Demand Curve

60

The demand curves for normal goods always have negative slope, denoting the ‘law of demand’. The law of demand states that price and quantity demanded are oppositely/negatively related, i.e. the quantity bought increases as the price falls. Substitution and Income Effects of a Change in Price So far we have seen that a fall in price of X (say, from P1 to P2) results in an increase in the quantity demanded (say, from X1 to X2). This is the total effect which can be split in to two separate effects, a substitution effect and the income effect. In the indifference curves theory, the ‘law of demand’ is derived from what is known as the Slutsky’s Theorem, which states that the substitution effect of a price change (relative to the price) is always negative; if the price increases, the quantity demanded decreases and vice versa. The substitution effect is due to the tendency of the consumer to consume more of a relatively cheaper good. Thus, it is assumed that the consumer will increase the consumption of the good whose price has declined by reducing the consumption of the other commodity and remain on the same level of satisfaction. Substitution effect is the increase in the quantity bought as the price of the commodity falls, after ‘adjusting’ income so as to keep the real purchasing power of the consumer the same as before. This adjustment in income is called compensating variation. The compensating variation can be shown graphically by a parallel shift of the new budget line until it becomes tangent to the initial indifference curve (See Figure 2.19). The purpose of the compensating variation is to allow the consumer to remain on the same level of satisfaction as before the price change. The compensated budget line will be tangent to the original indifference curve I1 at point E2 to the right of the original tangency (equilibrium E1), because this line is parallel to the new budget line which is less steep than the original one when the price of X falls.

61

Thus, the movement from E1 to E2 shows the substitution effect of the price change, i.e. because of decline in price of X, the consumer buys more of X which is now cheaper, substituting X for Y (movement from X1 to X2). However, the compensating variation is a device which makes possible the isolation of the substitution effect, but does not show the final equilibrium of the consumer. The final equilibrium of the consumer after the price decline is defined by point E3 at the tangency point of the new budget line and a higher indifference curve I2. Since the consumer’s purchasing power has now increased due to the decline in price of X he/she will spend some of his/her increased real income on X, if the commodity (X) is normal. Thus, the consumer moves from X2 to X3. This is the income effect of the price change. The income effect of a price change for normal goods is negative; when purchasing power increases due to a decline in price, quantity consumed increases and when purchasing power decreases due to an increase in price, quantity consumed declines if the good is normal. Y I2

I1 B

E1

B’

Original budget line

E3 E2

Compensated Budget line

O

X1

New budget line

X2 L

X3

L’’

L’ X

Substitution Income Effect Effect Total Price Effect Figure 2.19a: Substitution and Income Effect for a Normal Good X 62

If, however, the commodity is inferior, the income effect of the price change is positive (i.e., for an increase in price, the quantity demanded of an inferior good will also increase due to the decline in purchasing power; and conversely, for a decrease in price, the quantity demanded of an inferior good will also decline due to the increase in purchasing power). But the substitution effect of a price change is negative for normal goods as well as inferior goods – for price rise quantity will decline, and for price decline quantity will rise. Y

Original budget line

B E3

I2

E1

B’

Compensated Budget line

New budget line

E2 I1 O

X1

X3

Substitution Effect Total Price Effect

X2 L

L’’

L’

X

Income Effect

Figure 2.19b: Substitution and Income Effects for an Inferior Good X For normal goods, the negative substitution effect reinforces the negative income effect and as a result the total price effect is also negative. Similar to the case of normal goods, the substitution effect is negative for inferior goods as well. However, unlike the case of normal goods, the income effect is positive for inferior goods. Nevertheless, since the substitution effect is stronger than the income effect for most of the inferior goods, the

63

total effect is also negative. Thus, the negative substitution effect is in most cases adequate to establish the law of demand (the negative relationship between price and quantity demanded/consumed). It is when the income effect is positive and stronger than the substitution effect that the law of demand does not hold. This is the case of the Giffen Goods, which are inferior goods with a positive sloping demand curves4. Thus, for giffen goods, like the case of inferior goods, the substitution effect is negative and the income effect is positive. But the positive income effect is stronger than the negative substitution effect in the case of giffen goods. As a result, the total price effect for giffen goods is positive (quantity will increase for an increase in price, and vice versa). Y B E3 IC2 B’ E1 E2

IC1 O

X3

X1

X2 L’

L’’

L

Figure 2.19c: Substitution and Income Effects for a Giffen Good X Summary of Substitution and Income Effects of a Fall in the Price of X Type of Good

Substitution Effect

Income Effect

Total Effect

Normal Good

Negative (X

)

Negative (X )

Negative (X )

Inferior Good (that is not giffen)

Negative (X

)

Positive

(X )

Negative (X )

Giffen Good

Negative (X )

Positive

(X )

Positive (X )

4

Giffen goods are very rare in practice.

64

X

Check Your Progress 1. Explain the difference between the income offer curves for a normal good and for an inferior one. 2. Explain the difference between the Engel curves for normal and inferior goods. 3. Why is the substitution effect of a price change always negative regardless of whether the good is normal or inferior? 4. What does the compensated budget line represent? Mathematical Derivation of Individual’s Demand for a Commodity The demand (function) of a consumer for a commodity can be derived from the equilibrium condition of the consumer. As we have seen previously, the equilibrium condition of the consumer is given by the tangency point of the indifference curve and the budget line of the consumer. At this point, the slope of the two curves is equal. Thus,

MU N MU X MU Y = = ... = . PX PY PN And, the budget line is given by: N

I = ∑ Pi Qi . i =1

For Example, consider the case of two goods, X and Y. If the total utility function is given by: U =

1 XY ; where U is total Utility, X is quantity of good X and Y is quantity of 4

good Y, we can derive the demand functions for the two goods as follows.

Step 1: At equilibrium, MRS X ,Y =

MU X PX = . MU Y PY

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Given the total utility function, the marginal utilities of X and Y are5: MU X = MU Y =

∂U 1 = Y ………………………………………………….……..……… (1) ∂X 4

∂U 1 = X …………………………….…………………….……..……… (2) ∂Y 4

By substituting the marginal utilities into the equilibrium condition

MU X PX = , we MU Y PY

obtain: 1 Y 4 = PX …………………………………………………………………………..… (3) 1 X PY 4

Rearranging the above equation gives:

Y PX = . X PY

By criss-cross multiplying we obtain: PxX = PyY ………………………………………………………………….………….(4) Note that the equality of the expenditures on the two commodities is not a general rule rather it depends on the specific form of the utility function. Step 2: Now we can derive the demand function for commodity X by substituting equation number (4) above into the budget line equation. (Recall that the budget line is PxX + PyY = I). PxX + PyY = I Ö PxX + PxX = I

since PyY = PxX from (4)

Ö 2PxX = I Ö

2 PX X I = 2 PX 2 PX

Ö X =

5

I 2 PX

Or

dividing both sides by 2Px. X = 0 .5

I PX

We use the derivative rule, i.e., if Y = Xn, then

→

Demand for X

∂Y = nX n −1 . ∂X 66

Thus, the demand for X is negatively related to its own price, Px, and positively related to income, I. Similarly, we can derive the demand for commodity Y by substituting equation (4) into the budget line equation PxX + PyY = I. PxX + PyY = I Ö PyY + PyY = I

since PyY = PxX from (4).

Ö 2PyY = I Dividing both sides by 2Py gives: ÖY=

I 2 PY

Or

Y = 0.5

I PY

→

Demand for Y

Thus, the demand for Y is negatively related to its own price, Py, and positively related to income, I. Critiques of the Indifference Curves Approach Although the advantages of the indifference curves approach are important, the theory has indeed its own severe limitations. 1. The main weakness of this theory is its axiomatic assumption of the existence and the convexity of the indifference curves. The theory does not establish either the existence or the shape of the indifference curves. It assumes that indifference curves exist and have the required shape of convexity. 2. Furthermore, it is questionable whether the consumer is able to order his/her preferences as precisely and rationally as the theory implies. Also the preferences of the consumer changes continuously under the influence of various factors, so that any ordering of these preferences, even if possible, should be considered as valid for the very short run. 3. The theory has also retained some of the weaknesses of the cardinal utility theory with the strong assumption of rationality and the marginal utility implicit in the definition of the marginal rate of substitution.

67

4. Another defect of the indifference curves approach is that it does not analyze the effects of advertising, the effect of past behavior (habit persistence), and effect of interdependence of preferences among consumers which lead to behavior that would be considered as irrational. 2. The Revealed Preference Hypothesis The revealed preference hypothesis is considered as a major breakthrough in the theory of demand because it has made possible the establishment of the ‘law of demand’ directly (on the basis of the revealed preference axiom) without the use of indifference curves and all their restrictive assumptions. Regarding the ordering of consumers’ preferences, the revealed preference hypothesis has the advantage over the existence and convexity of the indifference curves as it does not accept them axiomatically. However, the indifference curves are redundant in the derivation of the demand curve. Assumptions of the Approach 1. Rationality: The consumer is assumed to behave rationally, in that he/she prefers bundles of goods that include more quantities of the commodity. 2. Consistency: The consumer behaves consistently, that is, if he/she chooses bundle A in a situation in which bundle B was also available to him/her, he/she will not choose B in an identical situation in which A is also available. Symbolically, if A > B, then B ≯ A. 3. Transitivity: If in any particular situation A > B and B > C, then A > C. 4. The Revealed Preference Axiom: The consumer, by choosing a collection of goods in any one budget situation, reveals his/her preference for that particular collection. That is, the chosen bundle is revealed to be preferred among all other alternative bundles available under the budget constraint. Thus, the chosen ‘basket of goods’ maximizes the utility of the consumer. The revealed preference for a particular collection of goods implies (axiomatically) the maximization of the utility of the consumer. 68

Derivation of the Demand Curve Using the Revealed Preference Hypothesis Assume that the consumer has the budget line BL as shown in Figure 2.20a below. If we assume that he/she chooses the collection of goods denoted by point A, this reveals his/her preference for this batch. Now, suppose that the price of X falls so that the new budget line facing the consumer is BL’ (Figure 2.20a). We will show that the new batch will include a larger quantity of X with the help of the figure below. Y B B’ A D

C

X O

X1

X2

L

X3 L’’

L’

Figure 2.20a: Equilibrium of the Consumer under the Revealed Preference Hypothesis Px

P1 Demand Curve P2 O

X X1 X2 Figure 2.20b: Demand Curve for a Normal Good Derived Using the Revealed Preference Hypothesis 69

Firstly, we make a ‘compensating variation’ in the income, which consists of the reduction of income so that the consumer will have just enough income to enable him/her to continue purchasing bundle ‘A’ if he/she so wishes. The compensating variation is shown in Figure 2.20a, by a parallel shift of the new budget line so that the compensated budget line B’L’’ passes through point A. Since the collection A is still available to him/her, the consumer will not choose any bundle to the left of A on the segment B’A. This is because his/her choice would be inconsistent, given that all the batches on segment B’A were revealed inferior to A in the original situation. Hence, the consumer will either continue to buy A (in which case the substitution effect is zero) or he/she will choose a batch on the segment AL’, such as C, which includes a larger quantity of X (namely X2). Secondly, if we remove the (fabricated) reduction in income and allow the consumer to move onto the new budget line BL’, he/she will choose a batch (such as D) to the right of C (if the commodity is normal – has a negative income effect). The new revealed equilibrium position (D) contains a larger quantity of X (i.e. X3) which results from the fall in its price. Thus, the revealed preference axiom and the implied consistency of choice open a direct way to the derivation of the demand curve: as price falls, more of X is purchased.

Check Your Progress 1. What are the differences and the similarities between the indifference curves approach and the revealed preference hypothesis? 2. Suppose that the total utility function of a consumer is given by TU(x,y) = 3X2Y, and the prices of X and Y are 1 Birr and 2 Birr per unit, respectively. If the income of the consumer is 600 Birr and if he spends all of his income on the consumption of commodities of X and Y, find the optimum amount of X and Y that the consumer will consume at equilibrium.

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2.6 THE MARKET DEMAND FOR A COMMODITY The market demand for a given commodity is the horizontal summation of the demands of the individual consumers. In other words, the quantity demanded in the market at each price is the sum of the quantities demanded by all consumers at that price. Derivation of the Market Demand In the real world, there may be millions of individual consumers in a market, but for simplicity, let us consider the case of only four individual consumers in a given market. In Table 2.1 we show the quantity demanded by four consumers at various prices of a certain commodity and the total (market) quantity demanded. These data are also presented graphically in Figure 2.21. Table 2.1: Individual and Market Demands Quantity

Quantity

Quantity

Quantity

Market

demanded by

demanded by

demanded by

demanded by

Quantity

consumer A

consumer B

consumer C

consumer D

Demanded

(DA)

(DB)

(DC)

(DD)

(QM)

2

90

45

20

110

265

4

80

40

30

100

250

6

70

35

40

90

235

8

60

30

50

80

220

10

50

25

60

40

175

12

40

20

70

20

150

14

30

15

80

10

135

16

20

10

90

5

125

Price

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From the table, we observe that the market demand is negatively sloped as the individual demands are. Sometimes, one or two of the individual demands may be positively sloped if the good is giffen for those individuals.6 For example, the demand for individual C is positively sloped implying that the good is giffen for consumer C. Although the commodity is giffen and the demand is positively sloped for consumer C, the market demand has the normal positive slope, because the demands of other consumer more than offset the giffen case of consumer C. Economic theory does not define any particular form of the demand curve. In textbooks, market demand is sometimes shown as a straight line (liner demand curve) and sometimes as a curve convex to the origin. The linear demand curve may be written in the form: Q = a – bP. This linear form implies a constant slope but with a changing elasticity at various prices. [We will see elasticity later on]. Figure 2.21: Individual and Market Demand Curves 300

QD

250

200

150

100

50

0 2

4

6

8

10

12

14

16

Price

DA DD

6

DB DM

DC

The classification of goods as normal, inferior or giffen depends on the individual consumer. That is, depending on the income, attitude, and preferences of the consumer, what is normal for one consumer may be inferior or giffen for another.

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Determinants of Demand Demand is a multivariate variable; it is determined by many variables. Traditionally the most important determinants of the market demand are considered to be the price of the commodity under consideration, the prices of other commodities, consumer’s income and tastes.

1. Own Price (Price of the Commodity) The law of demand states that the quantity demanded of a commodity increases when there is a decline in the price of the commodity (and vice versa), for an ordinary good7. This results in movement along the same demand curve as shown in Figure 2.22 below. P

A

P1 P2

B

O

Qx X1

X2

Figure 2.22: Movement along the Demand Curve as the Price of X Changes 2. Price of Other Commodities A change in the price of another related commodity, which could be either a substitute or a complement, is also a factor that affects the demand for a commodity. When the price 7

An ordinary good is a good which is either normal or inferior but not giffen. If the good is giffen the demand curve will be upward sloping as there is direct relationship between quantity demanded and price of the commodity.

73

of a substitute good increases, the quantity demanded of the commodity under consideration will also increase. Thus, this change shifts the market demand curve outward. For instance, if the price Coca Cola rises, the quantity demand of Pepsi is expected to rise at the prevailing price. When the price of a complementary good increases, the quantity demanded of the commodity under consideration will decline, and thus it will make the demand curve shift upward. As an example, if the price of petroleum rises, the quantity demanded of car falls.

3. Income of the Consumer As income of the consumer increases, the quantity demanded of a good will increase if the good is normal, and thus the demand curve will shift outward. However, if the good is inferior the quantity demanded of the commodity declines with an increase in income, and the demand curve will shift downward. P

P1

O

X1

Qx

X2

Figure 2.23: Shift of the Demand Curve as, for example, Income Increases Apart from the above determinants, market demand is also affected by numerous other factors, such as tastes and preferences, the distribution of income, the size of total population and its compositions, wealth, credit availability, etc.

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As can be seen from the above two figures, Figure 2.22 and Figure 2.23, the result of a change in the price of the commodity itself is shown by a movement from one point to another on the same demand curve, while the effect of changes in other determinants is shown by a shift of the demand curve. Thus, these other factors are considered as the shift factors of the demand curve. The demand curve is thus drawn under the ceteris paribus assumption; the shift factors (factors other than the price of the commodity) are assumed to remain constant in drawing the demand curve.

2.7 ELASTICITY OF DEMAND Elasticity can be defined as the responsiveness of a variable for a change in one of its determinants, holding the other factors constant. Thus, elasticity of demand is the measure of responsiveness of quantity demanded as a result of a change in one of its determinants, holding all the other factors constant. There are as many elasticities of demand as its determinants. The most important of these elasticities are: a) The Price Elasticity of Demand, b) The Income Elasticity of Demand , and c) The Cross- Price Elasticity of Demand. Let us start with the first one: the price elasticity of demand Price Elasticity of Demand The price elasticity of demand is the relative measure of the responsiveness of quantity demanded to changes in the commodity’s own price. If the changes in price are very small, we use the point elasticity of demand as a measure of the responsiveness of demand. If the changes in price are not small, we use the arc elasticity of demand as the relevant measure.

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At each point on the market demand curve, the price elasticity of demand is defined as the percentage change in the quantity demanded resulting from a one percent change in price of the commodity. In other words, it is the sensitivity of the quantity demanded to changes in price. Symbolically, the point elasticity of demand is given by the proportional/percentage change in quantity demanded divided by the proportional/percentage change in price.

ε pd = =

ε pd =

%age change in Quantity demanded %age change in Price of the commodity

dQ/Q dP/P dQ P . dP Q

If, for instance, the demand curve is linear with an equation of the form Q = a – bP, its slope will be

dQ = -b dP

Substituting this into the elasticity formula we obtain:

ε pd = -b

P . Q

This implies that the price elasticity of demand differs at the various points of the linear demand curve. That is, even though a linear demand has a constant slope, the price elasticity of demand is not constant. The above formula for the price elasticity is applicable only for infinitesimal (very small) changes in price. If the price changes appreciably (significantly), we use the following formula which measures the arc elasticity of demand:

ε pd =

dQ P1 + P2 ( ). dP Q1 + Q 2

The arc elasticity of demand measures the average elasticity, that is, the elasticity at the mid point of the chord that connects two points, lets say A and B, on the demand curve. These two points are defined by the initial and the new price levels. It should be clear that 76

the measure of the arc elasticity is an approximation of the true elasticity of the section from A to B on the demand curve. It is used when we know only the two points A and B but not the intermediate ones. P A Arc Elasticity B

Q

O

Figure 2.24: Arc Elasticity of Demand

We can also estimate the price elasticity of demand graphically. Suppose that we want to estimate the price elasticity of demand plotted in Figure 2.25 below. (/ ε p / = ∞) d

P A

(1 < / ε p / < ∞) d

(/ ε p / = 1) d

C

(0 < / ε p / < 1) d

(/ ε p / = 0) d

Qx

O

B Figure 2.25: Geometrical Demonstration of the Price Elasticity of Demand

For a linear demand curve, price elasticity of demand can be determined geometrically by the ratio of a segment below the point on the demand curve and above the point. For

77

example, the price elasticity of demand at point C on the demand curve in Figure 2.25 above is the ratio of the segment CB to the segment AC, i.e., CB/AC. Hence, if point C is the midpoint of the demand curve (i.e., if CB = AC), the price elasticity of demand would be one at this point; and, at this point demand is said to be unitary elastic. To the left of point C, the coefficient of price elasticity of demand is greater than one (in absolute value) as the segment below is greater than the segment above, and thus demand is price elastic. To the contrary, to the right of point C, the coefficient of the price elasticity of demand is less than one (in absolute value) as the segment below is less than the segment above, thus demand is price inelastic. At the two extreme points of the demand curve, point A and point B, price elasticity of demand is perfectly elastic and perfectly inelastic respectively. That means, 1. At point A, demand is perfectly elastic (/ ε pd / = ∞) 2. Between points A and C, demand is elastic (1 < / ε pd / < ∞) (a small change in price induces a more than proportionate change in quantity demanded). 3. At point C, demand is unitary elastic (/ ε pd / =1) (a change in price results in a proportionate change in quantity demanded). 4. Between point C and B, demand is inelastic (0 < / ε pd / < 1) (a change in price induces a less than proportionate change in quantity demanded). 5. At point B, demand is perfectly inelastic (/ ε pd / = 0)

Note that: ¾ Price elasticity of demand is always negative due to the inverse relationship

between price and quantity demanded (i.e., because of the law of demand). ¾ We usually talk of the coefficient ignoring the sign; or equivalently, we

sometimes define elasticity as ε pd = –

dQ P dQ P . instead of ε pd = . . dP Q dP Q

78

P

P

P

Q / ε pd / = 0: Perfectly Inelastic Demand

Q / ε pd / = ∞: Perfectly Elastic Demand

Q 0< / ε pd / <1, / ε pd / > 1 or / ε pd / = 1

Figure 2.26: Examples of Demand Curves with Different Elasticities

Factors Affecting Price Elasticity of Demand

Whether demand is elastic or inelastic is an important consideration, especially for government policy in individual commodity markets. For example, suppose the demand for wheat were highly price elastic. An increase in the price of wheat would accordingly result in a proportionately greater reduction in quantity demanded. Thus, total expenditures on wheat decline. Now, suppose the government established a minimum wheat price above the market equilibrium price. Wheat sales would be reduced, and so would farmers’ incomes be, unless the price support were accompanied by a minimum sales guarantee. Price elasticities range quite widely. The major factors that determine the price elasticity of demand are: 1. The availability and closeness of substitute goods: The more and closer the substitutes for a specific good are, the greater its price elasticity of demand tends to be. Goods with few and poor substitutes, for example, foods and fuel, will always tend to have low price elasticity of demand. Goods with many and very close substitutes will have higher elasticities. 2. The nature of the need that the commodity satisfies: 79

Goods can be either luxuries or necessities in satisfying human needs. Thus, the price elasticity of demand is more elastic for luxurious goods and less elastic for necessity goods.8 3. The proportion of income the good have in the total income of the consumer: If large proportion of the income of the consumer is spent on a commodity, the price elasticity of demand for the commodity would be more elastic. On the other hand, if small proportion of income is spent on a commodity, the price elasticity of demand would be less elastic. For example, the price elasticity of demand for salt may be less elastic for most individual consumers as it has a small share in the budget of many individuals. 4. The available time for the consumer: In the long run, the price elasticity of demand is more elastic as the consumer has enough time to respond to the price change by adjusting his/her consumption pattern and finding new substitutes. In the short run, the price elasticity of demand is less elastic. 5. The number of uses to which a commodity can be put: The more the possible uses of a commodity, the greater its price elasticity will be. Income Elasticity of Demand

The income elasticity of demand is defined as the proportionate change in the quantity demanded resulting from a proportionate change in income. Symbolically, we may write:

ε Id =

dQ I . dI Q

The income elasticity of demand is positive ( ε Id > 0) for normal goods and negative ( ε Id < 0) for inferior goods. Some writers have used income elasticity for classifying goods into luxuries and necessities. A commodity is considered to be luxury if the income

8

The classification of goods as luxuries and necessities depends on the income and preferences of the consumer; what is luxury for one individual may be necessity for the other.

80

elasticity for its demand is greater than unity ( ε Id > 1). A commodity is a necessity if the income elasticity for its demand is less than one (0 < ε Id < 1). The main determinates of income elasticity of demand are: 1. The nature of the need that the commodity covers. Generally, luxurious goods have greater income elasticity than necessity goods. 2. The initial level of income of a consumer or a country: The percentage of income spent on food declines as income increases (this is known as Engel’s Law and has sometimes been used as a measure of welfare and of the development stage of an economy). As another example, a TV set is a luxury good in an underdeveloped, poor country while it is a necessity in a country with higher per capita income. 3. The time period: Because consumption patterns adjust with a time lag to changes in income, demand income tends to be elastic in the long run. Cross Price Elasticity of Demand

Demand for a given commodity is determined not only by price of the commodity but also by prices of other related commodities. The cross price elasticity of demand is defined as the proportionate change in the quantity demanded of X resulting from a proportionate change in the price of Y. Symbolically,

ε Xd ,Y =

dQx PY . dPy Q X

The sign of the cross price elasticity of demand is negative if X and Y are complementary goods and positive if X and Y are substitutes. If the two commodities X and Y are not related to each other, the cross price elasticity of demand is zero. The higher the value of the cross price elasticity, the stronger will be the degree of substitutability or complementarily of the two goods, X and Y.

81

The main determinant of the cross price elasticity of demand is the nature of the commodities relative to their uses. If two commodities can satisfy the same need equally well, the cross price elasticity is high, and vice versa.

Check Your Progress 1. Graphically show the effect of an increase in price of Coca Cola on the demand of Pepsi Cola. 2. If the price elasticity of a commodity is -5, what will be the change in the quantity demanded of the commodity as a result of a 4 % rise in the price of this commodity? 3. Interpret the expression: "The cross price elasticity of demand between two commodities A and B is equal to 3". What can you say about the two commodities? 4. Explain the difference between arc elasticity of demand and point elasticity of demand. Price Elasticity and Total Expenditure

The total amount spent on a good (Total Expenditure) varies directly with the change in price when price elasticity of demand is less than one, and inversely related to the price when price elasticity of demand is greater than one. In other words, if demand is elastic (if ε Pd > 1), an increase in price reduces total expenditure and a decline in price increases total expenditure. However, if demand is inelastic (if ε Pd < 1), an increase in price raises total expenditure and a decrease in price reduces total expenditure. The intuition behind this result is straight forward. A price increase means that more is spent on each unit of the good purchased, which tends to increase the amount spent. Offsetting this is the fact that fewer units of the good are purchased at the higher price. If the price effect outweighs the quantity effect, then total expenditure rises. If the quantity effect outweighs the price effect, then total expenditure falls. Elasticity is the measure of the relative strengths of the two effects.

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If the price elasticity of demand is less than one (if ε Pd < 1), then a one percent increase in price induces a less than one percent decrease in quantity demanded. Thus, the price effect swamps (more than offsets) the quantity effect, and thus total expenditure rises. But, when price elasticity of demand exceeds one (if ε Pd > 1), a small increase in price induces a larger decrease in quantity, so the quantity effect dominates and consequently total expenditure falls. Note: Since total expenditure and total revenue are two sides of the same coin, the effect of change in price on total revue is the same as its effect on total expenditure when demand is elastic and inelastic. The total expenditure of a consumer (the buyer) is the total revenue for the producer (the seller). An important relationship exists between the price elasticity of demand and the total expenditure of consumers on the commodity (total revenue of producers). A decline in the price of a commodity: ¾ results in an increase in total expenditures if demand is price elastic; ¾ leaves total expenditure unchanged if demand is unitary elastic; and ¾ results in a decline in total expenditure if demand is price inelastic.

Specifically, when the price of the commodity falls, total expenditure (price times quantity) increases if demand is price elastic ε Pd > 1 because the percentage increase in quantity (which by itself tends to increase total expenditure) exceeds the percentage decline in price (which, by itself, tends to decrease total expenditure). Total expenditures is at its maximum when ε Pd = 1, and decline thereafter as ε Pd falls below 1. That is, when

ε Pd < 1, a reduction in the commodity price leads to an increase in the quantity demanded of the commodity that is smaller than the percentage reduction in price, and so total expenditure on the commodity declines. The hypothetical data in Table 2.2 below illuminate this point.

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Table 2.2: The Relationship between Price Elasticity of Demand and Total Expenditure

Price of X

Quantity of X

Total Expenditure

Absolute Value of

(Px)

(Qx)

(TE)

(/ ε Pd /)

A

2.00

0

0

∞

C

1.50

3

4.50

3

E

1.00

6

6.00

1

F

0.50

9

4.50

1/3

H

0

12

0

0

Point

From the above table, we see that between points A and E, / ε Pd / > 1 and total expenditure on the commodity increases as the commodity price declines. The opposite is true between points E and F over which / ε Pd / < 1. Total expenditure is maximized at point E (the geometric mid-point of the demand curve). Given that total revenue or total expenditure is the product of price and quantity demanded (i.e., TE = TR = P.Q; where TE is total expenditure, TR is total revenue, P is price and Q is quantity demanded), we can summarize the relationship between total expenditure and the price elasticity of demand as follows: ¾ When demand is price elastic ( ε Pd > 1): when demand is elastic, a small increase in

price results in a large decline in quantity demanded, then total revenue and total expenditure decline (↑P  Q↓ (↑P.Q↓) = ↓TE = ↓TR). Price and total expenditure change in opposite directions if ε Pd > 1. ¾ When demand is inelastic ( ε Pd < 1): when demand is inelastic, a large increase in

price results in a small decline in quantity demanded, then total revenue and total

84

expenditure increase (↑P  Q↓  (↑P.Q↓) = ↑TE = ↑TR). Price and total expenditure move in the same direction if ε Pd < 1. Market Demand, Total Revenue (TR) and Marginal Revenue (MR)

We can derive the total expenditure of consumers (or the total revenue of firms selling the particular product) from the market demand curve. As seen earlier, total revenue is the product of the quantity sold and the price, i.e., TR = P.Q. If the market demand is linear, the TR curve will be a curve which initially slopes upwards, subsequently reaches a maximum, and then starts declining. We can prove this from our previous discussion of the relationship between elasticity and TR (or TE). P

TR D

P1

TRmax

/ε / = 1 d P

A B

TR

P* C

P2

D’ Another important point in the theory of firm (to be discussed in the third and fourth chapters is the Qmarginal revenueO (MR). The Q* marginal revenue is Q the O Qin1 some Q* detail) Q2 change in total revenue resulting from selling an additional unit of the commodity. Figure 2.27: Price Elasticity of Demand and Total Revenue

P D 85

Graphically, MR at any one point is the slope of total revenue curve at that particular point. If the demand curve is linear, the MR curve is twice as steep as the demand curve. This can be proved mathematically as follows: MR is the derivative of the TR function: MR = =

d (TR ) d (Q) d ( P.Q) d (Q)

=P

d (Q) d ( P) +Q d (Q) d (Q)

MR = P + Q

d (P) d (Q)

If the demand curve is linear, its equation in terms of price is: P = a – bQ Substituting P into the TR function, we find: TR = PQ = (a – bQ)Q = aQ – bQ2 The MR is then: MR =

d (TR ) d (Q)

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MR =

d (aQ - bQ 2 ) d (Q)

= a – 2bQ. This proves that the MR curve starts from the same point (a) as the demand curve, and that the MR is a straight line with a negative slope (-2b) twice as steep as the demand curve (with a slope of -b). The Relationship between MR and Price Elasticity of Demand

The MR is related to the price elasticity of demand with the formula MR = P(1 −

1 / ε pd /

)

Proof: Assume that the demand function is P = f(Q) The total revenue is TR = PQ = [f(Q)]Q Above, just before a moment, we have shown that MR = P + Q

d ( P) d (Q)

We also know that the price elasticity of demand could be defined as: ε pd =

Rearranging this definition of elasticity, we obtain:

ε pd .

Q dQ = P dP

dP P = d dQ Q.ε p

Substituting

(criss-cross multiplication). (taking reciprocal).

dP P = into the expression of the MR, we find: dQ Q.ε pd

MR = P + Q

d ( P) d (Q)

MR = P + Q

P Q.ε pd

87

dQ P . dP Q

MR = P(1 + MR = P(1 + MR = P(1 −

Q ) Q.ε pd 1

ε pd

) 1

/ε / d p

(Since ε pd is negative, ε pd = – / ε pd /)

)

Total Revenue, Marginal Revenue and the Price Elasticity of Demand

We said that if the demand curve is falling linearly, the total revenue (TR) curve initially increases, subsequently reaches its maximum, and then starts declining. We can use the relationship among the marginal revenue (MR), price (P) and ε Pd derived earlier to establish the shape of the total revenue curve. ¾ The total revenue curve reaches its maximum at the point where / ε Pd / = 1, because

at this point its slope, the MR, is equal to zero. That is, 1 MR = P(1 − ) = P(0) = 0. 1 ¾ If / ε Pd / > 1, the TR curve has a positive slope, that is, it is still increasing and

hence has not reached its maximum point. If / ε Pd / > 1, then MR = P(1 −

1 / ε pd /

1 /ε / d p

< 1 implying that (1 −

1 / ε pd /

) > 0 . Given that P > 0, then

) > 0.

¾ If / ε Pd / < 1, the TR curve has a negative slope, that is, it is falling.

If / ε Pd / < 1, then MR = P(1 −

1 / ε pd /

1 /ε / d p

> 1 implying that (1 −

) < 0.

88

1 / ε pd /

) < 0 . Given that P > 0, then

Check Your Progress 1. What will happen to the total expenditure of a consumer as a result of a rise in the price of a commodity if the demand for this commodity is highly price elastic? Why? 2. What is the value of the price elasticity of demand for a commodity at the mid point of a linear demand curve?

2.8 CHOICE UNDER UNCERTAINTY The traditional theory of demand examined so far implicitly assumed a risk free world. It assumed that consumers face complete certainty as to the results of the choices they make. Clearly, this is not the case in most instances. In contrary to our earlier assumptions of price, income and other variables to be known with certainty, many of the choices that people make involve considerable degree of uncertainty. Although risk and uncertainty are usually used interchangeably, some people distinguish between the two. (I)

Uncertainty: refers to a situation when there are more than one possible outcomes

to a decision-maker and where the probability of each specific outcome is not known. This may be due to insufficient past information or instability in the structure of the variables. (II) Risk: refers to a situation where there are more than one possible outcomes to a

decision-maker and the probability of each specific outcome is known or can be estimated. (III) Certainty: refers to a situation where there is only one possible outcome to a

decision and this outcome is known precisely. For example, investing on treasury bills leads to only one outcome (i.e. the amount of the yield), and this is known with certainty.

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Expected Value and Variation of Risky Choices

We usually need two measures to describe and compare risky choices. These measures are: expected value and variation. 1. Expected value: is the weighted average of all possible payoffs/outcomes that can result from a decision under the various states of nature, with the probability of those payoffs used as weights. It measures the value that we would expect on average. If we multiply each possible outcome or payoff by its probability of occurrence and add up these products, we get the expected value. If, for instance, there are two possible outcomes having payoffs X1 and X2 and if the probability of each outcome is given by P1 and P2, then the expected value is: E(X) = P1X1 + P2X2

Example: If the probability that an oil exploration project will be successful is ¼ and the probability that it will be unsuccessful is ¾, and if success yields a payoff of 40 Birr per share while failure yields a payoff of 20 Birr per share, the expected value is: E(X) = P(success)(yield from success) + P(failure)(yield from failure) = ¼ (40 Birr/share) + ¾ (20 Birr/share) = (10 + 15) Birr/share = 25 Birr/share 2. Variability: is the extent to which the possible outcomes of an uncertain event may differ. We measure variability by recognizing that large differences between the actual and expected value imply greater risk. Standard deviation is the often used measure of variability. Standard deviation measures the dispersion of the possible outcomes from the expected value. The smaller the value of the standard deviation (σ), the tighter or less dispersed the distribution is and thus the lower would be the risk attached to it, and vice versa.

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Standard deviation (σ) =

P1 [ X 1 − E ( X 1 )]2 + P2 [ X 2 − E ( X 2 )]2

If two alternatives to choose from have the same expected value, the one with the lower/smaller standard deviation is less risky and is hence the preferred one. If, however, one alternative offers a higher expected value but is much riskier than the other one and vice versa, the preference depends on the individual – whether he/she is a risk averse, a risk neutral, or a risk loving person. Different Preferences towards Risk

1. A Risk Averse Person: is a person preferring a certain income to a risky income with the same expected value. For a risk averse person, losses are more important (in terms of the change in utility) than gains. Losses hurt him/her more seriously than gains benefit him/her. Thus, the marginal utility of income (MUI) diminishes as income rises. To illustrate, assume that a person can either have a certain income of 20 Birr, or an alternative decision yielding an income of 30 Birr with probability of 0.5 and an income of 10 Birr with probability 0.5. The expected income from this second alternative (A2) is: E(A2) = 0.5(30) + 0.5(10) = (15 + 5) Birr = 20 Birr. This is the same as the income earned without risk (from the first alternative – A1). A risk averse person facing this situation prefers to consume the risk free 20 Birr to trying the alternative in which he/she could have consumed 30 Birr if successful or 10 Birr if unsuccessful. The figure below makes this point more clear.

91

Utility 18

E

16

B D

14

10

C

A

0

10

16

20

30

Income

Figure 2.29: Utility Function for a Risk Averse Individual

From the figure, we see that utility at point B is greater than utility at point C. The utility of this risk averse person from the risk free income of 20 Birr is 16 (point B) and the expected utility from the risky alternative is: E(U) = 0.5U(10 Birr) + 0.5U(30 Birr) = 0.5(10) + 0.5(18) = 14 (point C). Note that the expected utility, E(U), is the sum of the utilities associated with all possible outcomes weighted by the probability that each outcome will occur. The risk averse person achieves the expected utility of 14 at a lower, but a risk free, income of 16 Birr. That is, a risk free income of 16 Birr gives the same level of satisfaction as a risky alternative with an expected income of 20 Birr. Thus, he/she is willing to pay or forgo 4 Birr (20 Birr – 16 Birr = 4 Birr) to avoid taking risk. The maximum amount of money (4 Birr in our case) that a risk averse person will pay to avoid taking a risk is called a risk premium.

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2. A Risk Neutral Person: is a person who is indifferent between a certain income and an uncertain income with the same expected value. For this person, the marginal utility of income is constant. Utility 18

E

12 C

6

A

0

10

20

30

Income

Figure 2.30: Utility Function for a Risk Neutral Individual

The utility of this risk neutral person from the risk free income of 20 Birr is 12 (point C) and the expected utility from the risky alternative is: E(U) = 0.5U(10 Birr) + 0.5U(30 Birr) = 0.5(6) + 0.5(18) = 12 (the same point C). As 12 = 12, the risk neutral person is indifferent between the risky and the risk free alternatives. 3. A Risk Loving Person: is a person who prefers a risky income to a certain income given that the risky alternative has the same expected value as the certain income. This person may prefer an uncertain income to a certain one even if the expected value of the uncertain income is less than that of the certain income. The expected utility of the uncertain income is greater than the utility of a certain income for a risk loving person and thus their utility of income curve is upward bending.

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Utility

18

E

C

10.5 8

B

3

A

0

10

20

30

Income

Figure 2.31: Utility Function for a Risk Loving Individual

The utility of this risk loving person from the risk free income of 20 Birr is 8 (point B) and the expected utility from the risky alternative is: E(U) = 0.5U(10 Birr) + 0.5U(30 Birr) = 0.5(3) + 0.5(18) = 10.5 (point C). As 10.5 > 8, the risk loving person prefers the risky alternative to the risk free alternative. Risk loving people prefer alternatives with high expected value and high standard deviation (risk) to a lower paying but less risky alternative (unlike the risk averse people). However, risk loving people are few at least with respect to major purchases or large amounts of income or wealth. Risk Aversion and Indifference Curves

We also describe the extent of a person’s risk aversion in terms of indifference curves that relate the expected income to the variability of income, the latter being measured by the standard deviation.

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An indifference curve shows the combinations of the expected value and the standard deviation of income that give the individual the same level/amount of utility. Indifference curves are upward sloping. This is because risk is undesirable (a ‘bad’) so that the greater the amount of risk, the greater the amount of income needed to make the individual equally well-off. An increase in the standard deviation (a higher variability of income) must be compensated by a higher expected value of income so as to a leave a person on the same level of utility. As opposed to the case of a highly risk avert person, a slightly risk avert person requires only a small increase in expected income, E(I) for a large increase in the standard deviation of income (σ). E(I)

U3

E(I)

U2 U1

O

U3 U2 U1

σ Panel (a): Indifference Curves of Person A

σ

O Panel (b): Indifference Curves of Person B

Figure 2.32: Person A is more Risk Averse than Person B Reducing Risk

In the face of a broad variety of risky situations, people are generally risk averse. Consumers and managers commonly reduce risk using various ways. The major ones are: diversification, insurance and obtaining more information.

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1. Diversification: refers to reducing risk by allocating resources to a variety of activities whose outcomes are not closely related –“Don’t put all your eggs in one basket.” 2. Insurance: If the cost of insurance is equal to the expected loss, risk averse people will buy enough insurance to recover fully from any losses they might suffer. For a risk averse consumer, the guarantee of the same income regardless of the actual outcome generates more utility than would be the case if that person had a high income when there was no loss and a low income when a loss occurred. 3. The value of information: People often make decisions based on limited information. If more information were available, one could make better predictions and reduce risk. Even though forecasting is inevitably imperfect, it may be worth investing in a marketing study that provides a reasonable forecast for the future.

2.9 LESSON SUMMARY # The theory of consumer behavior is the basis for the theory of demand. # There are two approaches for the measurement of utility: Cardinal Utility and

Ordinal utility approaches. The cardinal utility approach argues that utility is measurable and quantifiable with a unit of measurement of utils while the ordinal utility approach argues that utility has ordinal value and could only be ordered and ranked. # Under the cardinal utility approach, the consumer reaches equilibrium when the

marginal utility of the commodity is equal to its price in the case of one commodity (MUx = Px), and when the ratio of the marginal utilities of the commodities to their prices is equal for all commodities (

MUx MUy MUn = = ............... = ). Px Py Pn

# Under the ordinal utility approach, using the indifference curve theory, the

consumer reaches equilibrium at the tangency point of the indifference curve and

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the budget line. At the tangency point, the slope of the indifference curve is the same as the slope of the budget line ( MRS XY =

PX ). PY

# The individual demand curve is derived from the equilibrium of the consumer, and

then the market demand is derived from the individual demand curves, as the horizontal summation of the individual demand curves. # By using the revealed preference axioms, the revealed preference hypothesis allows

the derivation of the equilibrium of the consumer without the use of the indifference curves. # The total effect of a change in price of a commodity, while income and price of

other commodities is constant, can be decomposed into substitution and income effects. For normal goods, both the substitution and income effects are negative; and for inferior and giffen goods, the substitution effect is negative but the income effect is positive. In the case of the inferior goods, the negative substitution effect is stronger than the positive income effect, and as a result the total price effect is negative. In the case of giffen goods, the positive income effect is stronger than the negative substitution effect, and the total effect is positive. # Elasticity of demand measures the responsiveness of quantity demanded to a change

in one of the determinants of demand. In this module, we have tried to see three types of elasticities: the price elasticity of demand which is the responsiveness of quantity demanded to a change in price), the income elasticity of demand (the responsiveness of quantity demanded to a change in income), and the cross price elasticity of demand (the responsiveness of quantity demanded of a good to a change in the price of another related commodity). # The consumer’s decision with certain income and/or other variables is different

from the decision with uncertain income and/or other variables; hence, the optimum decision of the consumer is depends on the expected value and variation of income and the resulting expected utility of the consumer.

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2.10 REVIEW QUESTIONS I. Choose the Best Answer

1. For normal good, a. the income elasticity of demand is positive and greater than one. b. both the price offer curve and the demand curve are negatively sloped. c. both the Engel curve and the income offer curve are positively sloped. d. b and c are true. e. All are true. 2. If the cross price elasticity of demand between two commodities X and Y is negative, then X and Y are: a. substitutes b. giffen goods c. normal goods d. complements e. inferior goods 3. Assume a budget line is drawn for two commodities: X on the x-axis and Y on the y-axis. If the income of the consumer is 100 Birr, the y-intercept is 4, and the slope of the budget line is -2, the price of commodity X is: a. 25 Birr b. 12.5 Birr c. 50 Birr d. 8 Birr e. None 4. Assume that there are only two commodities, X and Y. If the marginal utility of the last unit of X consumed is twice the marginal utility of the last unit of Y consumed, the consumer is in equilibrium when: a. the price of Y is twice the price of X. b. the price of Y equals the price of X. c. the price of Y is half of the price of X.

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d. the consumer can’t reach equilibrium. e. None 5. An indifference curve will be L-shaped when the two goods are: a. perfect substitutes b. perfect complements c. imperfect substitutes d. unrelated e. bad and good commodities 6. The line joining the different points of consumer’s equilibrium resulting from the change only in the price of the commodity is called: a. demand curve b. income consumption curve c. Engel curve d. price consumption curve e. None 7. One of the following is not a shift factor of the demand curve for a given commodity. a. Income of the consumer b. Price of other related commodities c. Tastes and preferences d. Price of the commodity e. All f. None 8. If the demand function for a certain commodity is given by Q = 16 – 2P, where Q is the quantity demanded of the commodity and P is the price of the commodity, what is the price elasticity of demand when price is equal to 4 Birr per unit? a. Inelastic b. Perfectly elastic c. Perfectly inelastic d. Unitary elastic e. Elastic

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9. One of the following is not true about the characteristics of well-behaved indifference curves. a. Indifference curves do not intersect b. Indifference curves have negative slope c. Indifference curves are concave from the origin d. Indifference curves farther from the origin represent higher utility e. None 10. If the utility function of a consumer is given by U = X2Y2, what is the MRSxy? a. Y/X b. X/Y c. X/Y2 d. Y2/X e. X2/Y f. X/Y3 11. When we rank the utility gained from the consumption of different commodities as 1st , 2nd and 3rd etc, we are measuring utility: a. ordinally b. cardinally c. in both approaches d. traditionally 12. If price of an inferior good (which is not giffen) is rising, a. the substitution effect decreases but the income effect increases the quantity consumed of the commodity, and as a result the total effect is a decrease in quantity. b. both the substitution and the income effects increase the quantity consumed of the commodity, and as a result the total effect is an increase in the quantity demanded of the commodity. c. both the substitution and the income effects increase the quantity consumed of the commodity, but the total effect is a decrease in the quantity demanded of the commodity.

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d. both the substitution and the income effects decrease quantity consumed of the commodity, and as a result the total effect is an increase in the quantity demanded of the commodity. e. the substitution effect increases but the income effect decreases the quantity consumed of the commodity, but the total effect is an increase in quantity. II. True or False Questions

1. The revealed preference hypothesis is different from the indifference curves theory as the revealed preference hypothesis determines the equilibrium of the consumer without the use of the indifference curves, unlike that of the indifference curves theory. 2. The level of satisfaction is the same for a consumer along the same indifference curve. 3. Income elasticity of demand for a good is always positive 4. For a normal good, both the Engel curve and the demand curve are positively sloped. 5. The firm’s total revenue decreases for an increase in price of the commodity if demand is price inelastic. III. Short Answer and Workout Questions

1. Define the following terms: a. Utility b. Marginal Utility c. Marginal Rate of Substitution d. Engel Curve 2. Distinguish between the following pairs of economic concepts: a. An indifference curve and an indifference map b. Budget line and budget set

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c. Income offer curve and price offer curve d. Normal good and inferior good e. Ordinal utility and cardinal utility f. Indifference curve theory and revealed preference hypothesis 3. Explain the interpretation of MRSy,x is 12. 4. Suppose that the consumer is asked to contemplate a gamble with a probability of 60% of winning Birr 10,000 with a utility of 10 utils, and a 40% probability of winning Birr 15,000 with a utility of 12 utils. a. What will be the expected income and expected utility of the consumer? b. If the utility of this consumer from a risk free alternative which gives him an income equal to the expected income of the risky alternative given above is equal to 11 utils, is this consumer risk lover or risk averse? Why? Illustrate your answer with the help of a diagram. 5. Given MUx = X, MUY = 4Y, Price of X is 3 Birr per unit and price of Y is also 3 Birr per unit. If the income of the consumer is 1200 Birr, find the amounts of X and Y that the consumer chooses to consume so as to maximize his utility. 6. Given the demand function P = 20 – 5Q, find the price elasticity of demand when price of the commodity is 5 Birr per unit. Mention if the demand is price elastic or inelastic at this point. 7. Explain the substitution and income effects of a price rise for a normal good using a diagram. 8. Suppose Martha earns an of income 400 Birr currently, and her utility function is given by: U(m) = 4m, where m represents income. She has two options: Option 1: to buy a share. If she is successful her income will be 700 Birr and if she is not successful her income will be 100 Birr. Option 2: to do nothing and keep on earning 400 Birr. Assuming that success and failure are equally likely, a. What would be her expected income if she buys the share? b. What would be her expected utility of buying the share? c. Would Martha buy the share? Why? d. Is Martha risk averse, risk lover or risk neutral?

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CHAPTER THREE THEORY OF PRODUCTION LESSON STRUCTURE 3.1 Introduction 3.2 Chapter Objectives 3.3 The Production Function 3.4 The Short Run Production Function and Stages of Production 3.5 Laws of Production 3.6 Returns to Scale and Homogeneity of the Production Function 3.7 Equilibrium of the Firm: Choice of Optimal Combination of Factors of Production 3.8 Lesson Summary 3.9 Review Questions

3.1 INTRODUCTION Production is the process of conversion of inputs (factors of production) into a consumable form (goods and services). In this regard, in the production process or activity, firms turn inputs into output. This transformation of inputs (factors of production) into output is defined at a particular time period and at a given technology. By technology we mean the state of knowledge about the various methods that might be used to transform inputs into outputs, and it is described by a production function.

3.2 CHAPTER OBJECTIVES After studying this lesson thoroughly, you would be able to: ¾ understand the context of the production function ¾ illustrate the short-run production function and stages of production

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¾ understand and explain the laws of production ¾ explain the returns to scale and homogeneity of the production function ¾ have a knowledge of equilibrium theory of firms and optimum combination of

factors of production.

3.3 THE PRODUCTION FUNCTION The production function is a function that shows the highest output that a firm can produce for every specified combination of inputs. It is a purely technical relation which connects factor inputs to outputs. Assuming labor (L) and capital (K) as the only inputs, the production function can be written as: Q = f(L, K); where Q stands for the total quantity produced of an output/product. The production function allows inputs to be combined in varying proportions so that output can be produced in many ways (say, using either more capital and less labor, or more labor and less capital). For example, a unit of commodity X may be produced by the following processes:

Table 3.1: Three Processes for Producing a Unit of X

Units of Labor Units of Capital

Process 1 (P1)

Process 2 (P2)

Process 3 (P3)

2

3

1

3

2

4

These activities or methods of production can be shown by lines from the origin to the point determined by the labor and capital inputs combination.

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K 3

P1 P2

2

P3

1

0

2

3

4

L

Figure 3.1: Alternative Production Processes

The production function, which is a purely technical relationship that connects factor inputs and outputs, includes all the technically efficient methods of production. The technically inefficient methods are not included in the production function. A method of production ‘A’ is technically efficient if it uses less of at least one input and no more of the other factors to produce a given level of output as compared with any other method ‘B’. For example, suppose commodity Y can be produced by two methods (Method A and Method B) as shown below: Method A

Method B

Labor

2

3

Capital

3

3

If these are considered to be the only methods of production, method A is considered as technically the efficient method. This is because the two methods, A and B, use the same amount of capital (3 each), but method A uses less units of labor (2) than B does (3).

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The basic theory of production concentrates only on the efficient methods, and thus inefficient methods are excluded as a rational producer will not used them. If a process A uses less of one factor (say, L) and more of another (say, K) as compared to B, then A and B cannot be directly compared on the criterion of technical efficiency. For example, the two activities in the table below are not directly comparable. Method A

Method B

Labor

2

1

Capital

3

4

In such cases, both processes are considered as technically efficient and included in the production function. Which one of them will be chosen at any particular time depends on the price of factors (inputs). The choice of any particular technique among the set of technically efficient processes is an economic one, which is based on the price of factors of production. Note that a technically efficient method is not necessarily economically efficient. Isoquants and an Isoquant Map

In addition to defining the production function mathematically, it is also common to depict the technically efficient production processes with the help of isoquants. Assuming that labor (L) and capital (K) are the only two inputs used to produce an item, the output achievable for various combinations of inputs can be shown by using isoquants. An isoquant: is the locus of all the technically efficient methods (or all the technically efficient combinations of factors of production) for producing a given level of output. It is a curve showing all the possible combinations of inputs that yield the same level of output. Isoquants may assume different shapes depending on the degree of substitutability between the factors of production. The following are the common ones:

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1. Linear isoquant: this type assumes perfect substitutability of factors: a given output may be produced by using only labor, or only capital, or by an infinite number of combinations of K and L. See Panel (A) of Figure 3.2 below. 2. Input-output isoquant: this assumes strict complementarily (i.e., zero substitutability) of the factors of production. There is only one method of production for producing any particular level of a commodity. The isoquant takes the shape of a right-angle. This type of isoquant is also called “Leontief Isoquant” after the name Leontief who invented the input output analysis. Panel (B) of the figure below depicts such isoquants. 3. Kinked isoquant: this assumes limited substitutability between factors of production, say K and L, and that there are only few processes for producing a particular amount of a commodity. Substitutability of the factors is possible only at the kinks. See Panel (C) of Figure 3.2 below. 4. Smooth or convex isoquant: this form assumes a continuous (and a less than perfect) substitutability between factors (K and L) only over a certain range, beyond which factors cannot substitute each other. The isoquant is a smooth curve which is convex to the origin. This is depicted in Panel (D) of the figure below. Even though the kinked isoquant is more realistic, most of the time the smooth or convex isoquant is used in the traditional economic theory because it is mathematically simpler to handle by the simple rules of calculus.

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K

K

X (Level of Output)

O

X

L

O

Panel (A): A Linear Isoquant

L Panel (B): A Leontief Isoquant

K P1

P2 P3

X X P4

O

L

O

Panel (C): A Kinked Isoquant

L

Panel (D): A Convex Isoquant

Figure 3.2: Isoquants of Different Shapes

An Isoquant map: is simply a set of several isoquants. An isoquant map is another way of describing a production function, just as an indifference map (discussed in Chapter Two) is a way of describing a utility function. The level of output increases as we move upward to the right where as it remains constant along an isoquant (See points A, B and C in the

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figure below; 100 units of good X are produced both at A and C while 50 units are produced at B). K A

B

C X = 100 X = 50

O

L

Figure 3.3: Movement on an Isoquant versus Movement from an Isoquant to Another

Check Your Progress 1. What is meant by production function? What is the use of production function in production analysis? 2. Explain some important/common types of production function. 3. What are isoquants? Explain their main properties. 4. What are the differences between isoquant curves and indifference curves? 5. What is the reason behind an isoquant curve that is convex to the origin? When will an isoquant be straight-line, and when will it be right-angled?

3.4 THE SHORT RUN PRODUCTION FUNCTION AND STAGES OF PRODUCTION The production function in the traditional theory generally assumes the form: X = f(L, K, r, y)

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Where L is labor, K is capital, r is returns to scale which refers to the long run analysis of the laws of production since it assumes change in the plant, and y is the efficiency parameter related to the organizational and entrepreneurial aspect of the production. We usually abstract from the availability of many factors of production to two factors of production (L and K) only in order to simplify things. In this simplified case, any change in the amount of factors other than L and K is considered to shift a production function. The short run production function and its behavior for a change in amount of the fixed factors (as time goes to the long run) can be shown graphically, as follows: X’’ = f(L)k3,r3,y3

X

X’ = f(L)k2,r2,y2

X = f(L)k1,r1,y1

O

L

Figure 3.4: The Short Run Production Function and How It Shifts as the Amount of Fixed Factors of Production Change with the Passage of Time

In Figure 3.4, the quantity of output X produced is drawn as a function of the amount of labor, for fixed amounts of the other factors. For a given curve (X), as labor increases, ceteris paribus (the others factors fixed at k1, r1 and y1), output increases and we move along the curve depicting the production function. If any one or all of the fixed factors (K, r, y) increases, the production function shifts upwards. If, for instance, the levels of the three fixed inputs rise from (k1, r1 and y1) to (k2, r2 and y2), the curve X shifts upward to X’’, and so on.

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The time period for which we assume that some factors are fixed in amount is called the short run. Thus, curve X in the figure above is drawn for the short run. If we could increase (or change in general) the amount of all factors, then we are in a long run. The slope of the production function (say, X = f(L)) is the marginal product of the factor of production L (MPL) . Similarly, the slope of the production function X = f(K) is the marginal product of capital (MPK). The marginal product of a factor is defined as the change in output resulting from the change in the factor by a unit, keeping all other factors constant. That is: MPL =

∂X ∂X and MPK = . ∂L ∂K

Graphically, the MPL is shown by the slope of the production function X = f(L) and the MPK is shown by the slope of the production function X = f(K). As you remember from chapter two, the slope of a curve at any one point is the slope of a tangent line at that point. The average product of an input is the total product divided by the units of the input used to produce it. Graphically, the average product of a factor at a given point is given by the slope of a straight line from the origin to the point. Let’s derive the average product and marginal product of labor from the total product of labor graphically. By doing so, we will also distinguish among three stages of production. As shown in Panel (A) of Figure 3.5, as the units of labor used in the production process goes on increasing, the output initially increases at an increasing rate (up to point A), then rises at a decreasing rate (from point A to point C), reaches a maximum (at point C), and then starts falling. As a result, since marginal product is the slope of the total product curve, the marginal product of labor initially increases, reaches maximum, and then starts declining. The marginal product of labor (MPL) is even negative when the total product declines (beyond

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point C). The average product of labor (APL), which is the slope of the line drawn from the origin to the corresponding point on the total product (TPL) curve, initially increases, reaches maximum (at point Z) and then starts declining. The APL and MPL curves are shown in Panel (B) of the same figure. The following points are clearly reflected in Figure 3.5 below: # Before point Z is reached, in Panel A of the figure, the slope of a tangent line at a

point on the TPL curve is greater than the slope of a line from the origin to the point. In other words, the MPL is above the APL. # At point Z, where the APL reaches its maximum, the slope of a tangent line at a

point on the TPL curve is greater than the slope of a line from the origin to the point. That is, APL and MPL are equal at the maximum of the APL (Panel B of Figure 3.5). # When TPL curve reaches its maximum (point C in Panel A), the MPL equals zero.

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X

C D B Z

TP = f(L)

A

O

Panel (A): The TPL Curve

LA LZ LB

LC

LD

L

MPL APL

A’

Z’

Panel (A): The MPL and APL Curves C’

APL O

LZ’

LC’

L MPL

Figure 3.5: The Relationship among TPL, MPL and APL

Now, let us study the three stages of production. Figure 3.6 below is partly reproduced from Panel B of the above figure to assist us to this end. Accordingly, we divide this production function into three stages as: Stage I (from zero TPL up to the maximum of APL), Stage II (from the maximum of APL to zero MPL), and Stage III (from zero MPL onwards).

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MPL APL

Stage I

Stage II

Stage III

Z’ C’

APL O

LZ’

LC’

L MPL

Figure 3.6: The Three Stages of Production

At stage I, MPL > APL, and both of them are rising initially while MPL falls latter on. Since each additional unit of labor is coming up with a contribution larger than the average (MPL > APL), it is rational to hire more labor and produce more output. Thus, it is not reasonable to produce at this stage. A rational producer (firm) observes that using more labor is preferred to the existing situation and thus moves out of this stage. At the third stage, where both APL and MPL are declining and MPL < APL, it is not rational to produce at all because each additional unit of labor makes the total product to decline (i.e. its contribution is negative). Thus, it is in the second stage that a rational firm operates. Here each additional labor contributes positively to the production but less than the average. Where exactly in this stage does a rational firm produce? The answer is, it depends on factor prices. At this stage as the use of a variable input (labor) increases with other inputs (like capital) being fixed, the resulting additions to output (MPL) will eventually decrease. This manner is captured by a principle known as the law of variable proportions or the law of diminishing marginal returns.

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In summary, the production theories concentrate only on the efficient part of the production function, that is, on the ranges of output over which the marginal productivities are positive but declining. The second stage of production in the above analysis corresponds to this efficient stage in the short run. No rational firm would employ labor less than OLZ’ or beyond OLC’ (in Figure 3.6). This means over the range where MPL > 0 but

∂ ( MPL ) <0 ∂L

In the long run, where all factors of production (L and K for simplicity) are variable, we use isoquants to define the rational/efficient stage of production. In this case, the traditional theory of production defines the rational stage of production as the range of the isoquants over which their slopes are negative and convex to the origin. In the figure below, the production function is depicted by a set of isoquants. The locus of points of isoquants where the marginal products of the factors are zero forms the ridge line. At points a, b and c, the MPK is zero. This forms the upper ridge line. Similarly, the lower ridge line shows the path along which the MPL is zero (points d, e and f). Outside the ridge lines the marginal product of the factors is negative and the methods of productions are inefficient, since they require more quantities of both factors for producing a given level of output. Thus, production techniques are efficient only inside the ridge lines. K a

b

c

Upper Ridge Line (MPK = 0) Lower Ridge Line (MPL = 0)

f e d O

L

Figure 3.7: The Ridge Lines and the Region of Efficient Production

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The Marginal Rate of Technical Substitution

The slope of the isoquant (in absolute value) defines the degree of substitutability of the factors of production. As we move downwards along the isoquant, the slope ( = −

dK ) dL

decreases in absolute terms, showing the increasing difficulty in substituting L for K. The absolute value of the slope of the isoquant is called the rate of technical substitution, or the marginal rate of technical substitution (MRTS) of factors: MRTS LK =

dK = − slope of an isoquant dL

MRTSLK is defined as the amount of K that the firm must sacrifice in order to use one more unit of L so that it produces the same level of output. It can be proved that the MRTSLK is equal to the ratio of the marginal products of the factors. That is,

MRTS LK =

∂X dK ∂L = MPL = dL ∂X MPK ∂K

Proof: The production function can be written as X = f(K,L) = C. It is equal to C because the TP is constant along an isoquant. The slope of a curve is the slope of a tangent line at that point. The slope of a tangent line is defined by the total differential. The total differential (dX) is zero along an isoquant since the TP is constant. Thus,

dX = (

∂X ∂X )dK + ( )dL = 0 ∂K ∂L

Ö ( MPK )dK + ( MPL )dL = 0 Ö − ( MPK )dK = ( MPL )dL

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Ö −

dK MPL = dL MPK

which is the definition of the MRTSLK

Along the upper ridge line, we have: MPK = 0 ⇒ MRTS LK =

MPL =∞ MPK

And along the lower ridge line, MPL = 0 ⇒ MRTS LK =

MPL =0 MPK

The MRTS as a measure of the degree of substitutability of factors has a serious defect since it depends on the units of measurement of the factors. A better measure of factor substitutability is provided by the elasticity of factor substitution (σ). It is given by:

σ=

Percentage Change in K

L Percentage Change in MRTS LK

d( K L)

σ=

d ( MRTS LK )

( K L) ( MRTS LK )

The elasticity of substitution is a pure number independent of the unit of measurement of K and L since both the numerator and the denominator are measured in the same unit. Factor Intensity

Factor intensity refers to a measure of the intensity of a method of production in the sense that it measures whether a given method of production is labor intensive (uses more labor and less capital) or capital intensive (uses more capital and less labor). It can be measured by the slope of the line from the origin to a particular point on the isoquant representing a particular process. Or equivalently, it is measured by the capital labor ratio at a particular point.

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In the figure below, process P1 is more capital intensive than process P2 because the slope of line OP1 is higher than the slope of line OP2 or the ratio

K1 K is greater than 2 . This L1 L2

implies that the upper part of the isoquant includes more capital intensive techniques where as the lower part includes more labor intensive techniques. K P1

K1

P2

K2

O

L1

L2

L

Figure 3.8: Factor Intensity

Example: Let us illustrate the above concepts with a specific form of production function, namely the Cobb-Douglas production function. This form is the most popular in applied research, because it is easier to handle mathematically. It is of the form:

X = ALb K c 1. The marginal product of factors:

MPL =

∂X = bALb −1 K c ∂L

= b( ALb K c ) L−1 = b( X ) L−1 X = b( ) L = b( APL )

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Similarly, MPK =

∂X X = cALb K c −1 = c( ) = c( APK ) K ∂K

2. The marginal rate of substitution of labor for capital:

∂X

MRTS LK

b( X ) bK ∂ L L = = . = ∂X c( X ) cL K ∂K

3. The elasticity of substitution: d( K L)

σ=

d ( MRTS LK ) d( K L)

σ=

d (bK cL)

( K L) ( MRTS LK )

( K L) (bK cL)

σ=

d( K L) (bK cL) . ( K L) d (bK cL)

σ=

d( K L) (b c).( K L) • ( K L) (b c).d ( K L)

σ=

d( K L) ( K L) • = 1. ( K L) d ( K L)

4. Factor intensity: In a Cobb-Douglas function factor intensity is measured by the ratio b . The higher the ratio, the more labor intensive the technique is and vice c versa. Given that MPL = b(

X X ) , we can rearrange to find that L = b( ). L MPL

Similarly, MPK = c(

X X ) ) gives us K = c( K MPK

b( X ) MPL L Then, = K c( X ) MPK =

b( MPK ) c( MPL )

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=

b MRTS LK c

=

b since MRTSLK = 1 (as shown above). c

b L The higher the ratio means the higher the ratio, and hence the technique is laborc K intensive. 5. The efficiency of production. The efficiency in the organization of factors of production is measured by the coefficient A. It is clear that if two firms have the same K, L, b and c, and still produce different quantities of output, the difference can be due to the superior organizational and entrepreneurial quality of one firm. The more efficient firm will have a higher A than the less efficient one. 6. The returns to scale. In the Cobb-Douglas production function, the returns to scale are measured by the sum of the coefficients b + c. This point will be discussed latter on.

Check Your Progress 1. Distinguish between the following and show their importance in production theory: (a) short run and long run (b) variable input and fixed input (c) the upper and the lower ridge lines 2. Define and distinguish between marginal product and average product. Draw the marginal product and average product curves from your own hypothetical data. And check whether there is any relation between them. 3. Define marginal rate of technical substitution. Why does it decrease along the isoquant? 4. What is factor intensity? When do we say a technique of production is labor intensive? When is capital intensive? 5. What is elasticity of factor substitution?

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3.5 LAWS OF PRODUCTION The laws of production describe the technically possible ways of increasing the level of production. This can be done in various ways. Output can be increased by changing all factors of production which is possible in the long run. This is called the law of returns to scale. On the other hand, output can be increased by changing only the variable input while keeping the fixed inputs constant, which is possible in the short run. Let us see these laws one by one. The Law of Variable Proportions

This is a law for the case of short run where there is at least one fixed input. The MP of the variable factor will decline eventually as more and more quantities of this factor are combined with the fixed amounts of other factors. This is known as the law of variable proportions. In our earlier discussion of the short run production function and stages of production, we have assumed labor as a variable input and capital as a fixed input. From that graph, what we can understand is that as the use of a variable input (labor) increases with other inputs (capital) fixed, the resulting addition to output will eventually decreases. This is shown by a downward sloping MPL curve after its maximum point. This principle is known as the law of variable proportion or the law of Diminishing returns. The Law of Returns to Scale

The law of returns to scale refers to the long run analysis of production. In the long run, where all inputs are variable, output can be increased by changing all factors by the same proportion. The rate at which output increases as inputs are increased by the same proportion is called returns to scale. We have three cases of returns to scale: increasing, constant and decreasing returns to scale.

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Increasing returns to scale: this is the case where increasing all factors by the same proportion, say m, leads to an increase in output by more than m scale. Constant returns to scale: if we increase all inputs by some factor m and output is increases by the same proportion as inputs, m, and then it is called constant returns to scale. In this case the size of the firm’s operation doesn’t affect the productivity of its factors. Decreasing returns to scale: if scaling up all inputs by m scales output up by less than m, it is called decreasing returns to scale. This is because, may be difficulties in organizing and running a large scale operation leads to decreased productivity of both labor and capital. Examples: 1. Suppose Q = 2K + 3L. To tell the returns to scale, we will increase both K and L by a

factor m and create a new production function Q*. Then we will compare Q* and Q. Q* = 2(mK) + 3(mL) = 2mK + 3mL = m(2K + 3L) = mQ. After factoring, we can replace (2K + 3L) by Q, as we were given that from the start. Since doing so gives Q* = mQ, we note that by increasing all of our inputs by the multiplier m, we have increased production exactly by a factor of m. So we have constant returns to scale. 2. Q = 0.5KL. Again we put in our multipliers and create our new production function. Q* = 0.5(mK)( mL) = 0.5KLm2 = Qm2. Since m > 1, then m2 > m. This implies that our new production has increased by more than m. so we have increasing returns to scale. 3. Q = K0.3L0.2. Again we put in our multipliers and create our new production function.

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Q* = (mK)0.3(mL)0.2 = K0.3L0.2m0.5 = Qm0.5. Since m > 1, then m0.5 < m. So we have decreasing returns to scale.

3.6 RETURNS TO SCALE AND HOMOGENEITY OF THE PRODUCTION FUNCTION Suppose we increase both factors of production in the function X = f(L,K) by the same proportion m, and we observe the resulting new level of output X* as X* = f(mK,mL). If m can be factored out (that is, can be taken out of the bracket as a common factor), then the new level of output can be expressed as a function of m (to the power n) and the initial level of output X as follows: X* = mnf(L,K) or X* = mnX. If so, the function is called homogeneous. If m cannot be factored out, the production function is called nonhomogeneous. The above three examples are homogeneous functions since m can be factored out in each case. Thus, a homogeneous function is a function such that if each of the inputs is multiplied by m, then m can be completely factored out of the function. The power n of m is called the degree of homogeneity and is a measure of the returns to scale. ¾ If n = 1, we have a constant returns to scale. ¾ If n < 1, we have a decreasing returns to scale. ¾ If n > 1, we have an increasing returns to scale.

Given a Cobb-Douglas production function X = ALbKc, returns to scale is measured by the sum of the powers of the factors. That is, ¾ If b + c = 1, then there is a constant returns to scale. ¾ If b + c > 1, then there is an increasing returns to scale. ¾ If b + c < 1, then there is a decreasing returns to scale.

Proof Let L and K increases by m. The new level of output is 123

X* = A(mL)b(mK)c = AmbLbmcKc = Amb+cLbKc = mb+c(ALbKc) X* = mb+c(X) This implies the function is homogeneous of degree b+c and the type of the returns to scale depends on the sum. Product Line: It shows a physical movement from one isoquant to another as we change

either both factors and a single factor. It describes the technically possible alternative paths of expanding output. What path will actually chosen by the firm will depend on the prices of factors. The product curve passes through the origin if both factors are variable. But if only one factor is variable (the other being kept constant), the product line is a straight line parallel to the axis of the variable factor. K

K

K

Product Lines

Product Lines Product Line

K

O

L

O

L

O

L

Panel (A): Product Lines

Panel (B): Product Lines for

Panel (C): A Product Line

for a Homogenous Function

a Non-Homogenous Function

where K is Fixed

Figure 3.9: Different Kinds of Product Lines

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A special type of product line which is the locus of points of different isoquants at which the MRTS of factors is constant is called an isocline. For homogeneous production functions, the isoclines are straight lines through the origin. In such a case, the K/L ratio is constant along any isocline (refer to the Panel A of Figure 3.9).

Check Your Progress 1. What is the law of variable proportions? How does it differ from the laws of returns to scale? 2. How is the degree of homogeneity of a production function related to the returns to scale of the production function?

3.7 EQUILIBRIUM OF THE FIRM: CHOICE OF OPTIMAL COMBINATION OF FACTORS OF PRODUCTION A firm is said to be in equilibrium when it employs those levels of inputs that will maximize its profit. This means the goal of the firm is profit maximization (maximizing the difference between revenue and cost). Thus the problem facing the firm is that of constrained profit maximization, which may take one of the following forms: I. Maximizing profit subject to a cost constraint. In this case, total cost and prices are given and the problem may be stated as follows: Max П = R – C = PxX – C Clearly maximization of П (profit) is achieved in this case if X (quantity of output) is maximized, since C (cost) and Px (price of the product) are constants. II. Maximize profit for a given level of output. Max П = R – C = PxX – C Clearly in this case maximization of profit is achieved by minimizing cost, since X and Px are given. To derive the equilibrium of the firm graphically, we will use the isoquant map and the isocost lines. As discussed earlier, an isoquant is a curve that shows the various 125

combinations of K and L that will give the same level of output. It is convex to the origin whose slope is defined as:

−

∂X dK ∂L = MPL = MPK dL ∂X ∂K

The isocost line is defined by the cost equation: C = rK + wL; where w = wage rate, and r = price of capital services. The isocost line is the locus of all combinations of factors that the firm can purchase with a given monetary cost or outlay. The slope of the isocost line is equal to the ratio of the prices of the factors of production in absolute terms, −

w . r

From the isocost equation given by: C = wL + rK => rK = C - wL => K = From this the slope is − K

C w − L. r r

w r

C r

O

C w

L

Figure 3.10: An Isocost Line

Now, let us see how the equilibrium of the firm is determined in the two cases mentioned above.

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Case 1: Maximization of Output Subject to a Cost Constraint

Given the level of cost and the price of the factors and output, the firm will be in equilibrium when it maximizes the quantity of output it produces. This is at the point of tangency of the isocost line to the highest possible isoquant curve. In the following graph (Figure 3.11), the equilibrium of the firm is obtained at point e, where the firm produces X2 with K1 and L1 units of the two inputs. Higher levels of output (to the right of e) are desirable but not attainable due to the cost constraint. Other points below the isocost line lie on a lower isoquant than X2. Hence X2 is the maximum output that can be achieved given the above assumptions (C, w, r and Px being constant). K

K1

e

X3 X2 X1

O

L1

L

Figure 3.11: Maximizing Output subject to Cost

At the point of tangency: a. Slope of isoquant = slope of isocost

−

w MPL = = MRTS LK . This is a necessary condition for profit maximization. r MPK

b. The isoquant is convex to the origin. This is the sufficient condition for profit maximization.

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The mathematical derivation of the above equilibrium condition is as follows. A rational producer seeks the maximization of its output, given total cost outlay and the prices of factors. That is, Maximize X = f (K, L) subject to C = wL + rK This is a constrained optimization which can be solved by using the Lagrangean method. The steps are: a. Rewrite the constraint in the form: wL + rK – C = 0 b. Multiply the constraint by a constant λwhich is the Lagrangean multiplier:

λ(wL + rK – C) = 0 c. Form the composite function: Z = X – λ(wL + rK – C) d. Partially differentiate the function with respect to each factor as well as the multiplier, and then equate to zero. *

∂Z ∂X = − λw = 0 ∂L ∂L

Ö MPL = λw Ö λ=

*

MPL …………………………………………………………………… (1) w

∂Z ∂X = − λr = 0 ∂K ∂K

Ö MPK = λr Ö λ=

*

MPK …………………………………………………………………… (2) r

∂Z = wL + rK − C = 0 ∂λ

Ö wL + rK = C ……………………………………………………………… (3)

From equations (1) and (2) we understand that:

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MPL MPK w MPL = or = = MRTS LK w r r MPK

This shows that the firm is in equilibrium when it equates the ratio of the marginal productivity of each factor to its price. It can be shown that the second order conditions for the equilibrium of the firm require that the marginal product curves of the two factors have a negative slope.

∂ ( MPL ) ∂ 2 X = < 0, Slope of the MPL = ∂L ∂L2 ∂ ( MPK ) ∂ 2 X = < 0, and Slope of the MPK = ∂K ∂K 2 ∂2 X ∂2 X ∂2 X 2 <( . ) . ∂L.∂K ∂L2 ∂L2 Case 2: Minimization of Cost for a Given Level of Output

The condition for the equilibrium of the firm is formally the same as in case 1. That is, there must be tangency of the given isoquant and the lowest possible isocost line, and the isoquant must be convex. However, in this case we have a single isoquant which denotes the desired level of output, but we have a set of isocost lines. Curves closer to the origin show a lower total cost outlay. Since isocosts are drawn on the assumption of constant prices of factors, they are parallel to each other and their slopes (−

w ) are equal. r

Thus, the firm minimizes its cost by employing the combination of K and L determined by the point of tangency of X isoquant with the lowest possible isocost line. Points below e in Figure 3.12 below are desirable because they show lower cost but are unattainable

for output X. Points above e show higher costs. Hence, point e is the least cost point.

129

K

K1

e

X

O

L1

L

Figure 3.12: Minimizing Cost for a Given Level of Output

In this case also, the Lagrangean method can be followed to derive the equilibrium condition mathematically. But the problem is different. That is, Minimize C = wL + rK subject to X* = f(K,L) a. The Lagrangean function will be: Z = (wL + rK) + λ[X*- f(K,L)] b. Partially differentiate Z with respect to L, K and λ and equate to zero. *

∂Z ∂f ( L, K ) = w−λ =0 ∂L ∂L

Ö w = λ .MPL Ö λ=

*

w …………………………………………………………………… (1) MPL

∂Z ∂f ( L, K ) = r −λ =0 ∂K ∂K

Ö r = λ .MPK Ö λ=

*

r …………………………………………………………………… (2) MPK

∂Z = X * − f ( L, K ) = 0 ∂λ

Ö X * = f ( L, K ) …………….………………………………………………… (3)

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From equations (1) and (2) we understand that:

w r w MPL = or = = MRTS LK r MPK MPL MPK

This is the same as the condition in case one. In a similar way, the second condition will be: ∂ ( MPL ) ∂ 2 X = < 0, Slope of the MPL = ∂L ∂L2 ∂ ( MPK ) ∂ 2 X = < 0, and Slope of the MPK = ∂K ∂K 2 ∂2 X ∂2 X ∂2 X 2 . ) . <( ∂L.∂K ∂L2 ∂L2 The following numerical example clarifies the optimization of a firm for the two cases discussed above. Example: If the production function of a firm is given by Q = K 2 L3 , and the input prices

are r = Birr 8 per unit and w = Birr 2 per unit, a. Find the levels of labor and capital that maximize the level of output for a total outlay of Birr 240. b. Find the units of labor and capital that minimize the cost of the firm for producing 53,747,712 units of output. Solution:

a. Maximize Q = K 2 L3 subject to 240 = 2 L + 8 K , with respect to L and K. The equilibrium condition (from case 1 above) is given by: MPL =

Thus,

∂Q ∂Q = 3K 2 L2 , and MPK = = 2 K 1 L3 . ∂L ∂K

w MPL 2 3K 2 L2 = ⇒ = . r MPK 8 2 KL3

131

w MPL = . r MPK

⇒

12 K 2 L 1 3K ⇒ 12 K = 2 L ⇒ = ⇒ L = 6K . = 2 2 4 2L

Substitute L = 6 K into the budget constraint: 240 = 2 L + 8 K and solve. 240 = 2 L + 8K ⇒ 240 = 2(6 K ) + 8K ⇒ 240 = 12 K + 8K ⇒ 240 = 20 K 240 20 K = 20 20 ⇒ K = 12 ⇒

Since L = 6K, we also have L = 6 K ⇒ L = 6(12) = 72. The output maximizing levels of labor and capital under the given constraints (or, the optimum combination of labor and capital) are L = 72 units and K = 6 units. b. Minimize C = 2 L + 8 K subject to Q = K 2 L3 = 53,747,712 , with respect to L and K. The equilibrium condition (from case 2 above) is given by: MPL = Thus,

w MPL = . r MPK

∂Q ∂Q = 3K 2 L2 , and MPK = = 2 K 1 L3 . ∂L ∂K

w MPL 2 3K 2 L2 = . ⇒ = r MPK 8 2 KL3

⇒

1 3K 12 K 2 L = ⇒ 12 K = 2 L ⇒ = ⇒ L = 6K . 4 2L 2 2

Substitute L = 6 K into the output constraint: Q = K 2 L3 = 53,747,712 and solve. Q = K 2 L3 = 53,747,712 ⇒ K 2 (6 K ) 3 = 53,747,712 ⇒ K 5 6 3 = 53,747,712 ⇒ 216 K 5 = 53,747,712 53,747,712 = 248832 216 K = 5 248832 = 12

⇒ K5 =

Hence, L = 6 K = 6(12) = 72. The cost minimizing levels of labor and capital under the given constraints (or, the optimum combination of labor and capital) are L = 72 units and K = 6 units.

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Verify that the second order conditions are fulfilled in both cases!

Check Your Progress 1. What is the necessary condition for a firm to maximize production given a fixed total outlay? Is this the same as the necessary condition required for minimizing cost for a given level of output?

3.8 LESSON SUMMARY # Firms are organized by entrepreneurs to produce outputs by combining inputs. The

entrepreneur does this in such away as to maximize profit. Non-profit private sector and non-profit governmental enterprises face different incentives than for-profit firms. We are concerned with for-profit firms. The single proprietorships are the dominant form of business organization by number. # Production function is the technical relationship between factors of production and

outputs. # In the short-run, some factors are fixed; but in the long-run, all factors are variable. # In the short-run, as variable factors are added to the fixed factor, the firm may

experience increasing returns at low levels of output but eventually will incur diminishing returns at some higher levels of output. # Firms choose their input mix from the production function to maximize output

subject to cost constraints.

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3.9 REVIEW QUESTIONS I. Choose the Best Answer

1. Short run is a period: a. less than one year b. in which supply of certain inputs is perfectly inelastic c. in which supply of all inputs is perfectly inelastic d. None of the above 2. Long run is period: a. which is longer than three years b. in which supply of labor is elastic c. in which supply of all inputs is elastic d. None of the above 3. When total production increases at a constant rate, then a. average and marginal output increase at the same rate b. average product increases faster than the marginal product c. marginal product increases faster than the average product d. marginal product equals average product 4. When total production increases at increasing rates, then a. average and marginal output increase at the same rate b. average product increases faster than the marginal product c. marginal product increases faster than the average product d. marginal product equals average product 5. In case of a convex isoquant, as we move from left to right, MRTSLK: a. decreases at a decreasing rate, b. decreases at increasing rate, c. neither increases nor increases, d. increases along the isoquant. 6. When an isoquant is L-shaped, then a. MRTSLK = 0

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b. MRTSLK > 1 c. MRTSLK < 1 d. MRTSLK = 1 7. When MRTSLK = 1, then a. MPL / MPK = 2 b. MPL / MPK = 1 c. MPL / MPK =0 d. MPL / MPK = ∞ 8. Laws of variable proportion are associated with: a. change in the variable input b. change in all the inputs c. change in return to scale d. None of the above 9. The law of diminishing returns implies that: a. quantity of an input is decreasing. b. quantity of an input is increasing but at a decreasing rate. c. quantity of output is either decreasing or increasing at a decreasing rate d. quantity of output is either decreasing or increasing at an increasing rate 10. The law of diminishing returns comes into force because of: a. indivisibility of variable input b. indivisibility of fixed factors c. indivisibility of both variable and fixed factors d. indivisibility of products 11. Laws of returns to scale apply only when there is: a. a change in one input only. b. proportionate and simultaneous changes in all inputs. c. disproportionate change in inputs d. more than proportionate changes in outputs 12. A Cobb-Douglas production function shows: a. A constant returns to scale, b. An increasing returns to scale,

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c. A decreasing returns to scale d. One of the three returns to scale 13. The laws of variable proportions and the laws of returns to scale: a. Are exactly the same b. Are different and have no similarity c. Are similar but not exactly identical. d. No answer 14. Expansion path is a strait line when production function is: a. Homogeneous b. Non-homogeneous c. Of any form

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CHAPTER FOUR THE THEORY OF COST LESSON STRUCTURE 4.1

Introduction

4.2

Chapter Objectives

4.3

Short-Run Costs

4.4

The Relationship between Product Curves and Cost Curves in the Short Run

4.5

Long-Run Costs

4.6

The Relationship between Short-Run and Long-Run Average and Marginal Costs

4.7

Derivation of the Cost Function from the Production Function

4.8

Dynamic Changes in Costs – The Learning Curve

4.9

Lesson Summary

4.10 Review Questions

4.1 INTRODUCTION In the previous chapter, we saw the laws of production, i.e., how output is changed when the amounts of input(s) are changed. The laws of production are expressed in terms of physical quantities, e.g., labor as number of workers, capital as unit of plants or machinery, and output as unit or some other measurements of output, e.g., tones or quintals of wheat. However, most decisions regarding price and production are taken on the basis of money value of inputs and outputs. In this chapter we go beyond the technical analysis of the theory of the firm – theories of production – and look at the economic analysis in firms’ decision making process. The two chapters (chapter three and four) together make up a complete discussion of the behavior of business firms. Do you recall that, in the theory of consumer behavior of Chapter Two, we derived the demand for a commodity? As you 137

complete this chapter, you would be ready to derive the other component of a market – the supply of a commodity, and to bring together the two sides (the demand and supply sides) of a market in the subsequent chapters. Cost functions are derived functions (derived from production functions). Economic theory distinguishes between short-run and long-run costs. Both in the short-run and in the long-run, total cost is a multivariate function, i.e., total cost is determined by many factors such as output, technology, prices of variable and fixed factors. To simplify the analysis, we consider cost as a function of output [C = f(X)] on a ceteris paribus assumption. Thus, determinants of costs, other than output, are called shift factors.

4.2 CHAPTER OBJECTIVES After studying this lesson thoroughly, you would be able to: # understand the theory of cost; # differentiate between short-run costs and long-run costs; # know the details of the relationship between the following pair of concepts: ¾ average total cost and average variable cost ¾ marginal cost and average total cost ¾ marginal cost and average total cost ¾ product curves and cost curves ¾ short-run and long-run average and marginal costs; and # derive the cost function from the production function.

4.3 SHORT-RUN COSTS In theory of the firm, the short run is defined as any time period in which the quantity of at least one input (factor of production) cannot be changed. Practically, this is a time period that is so short that the firm cannot alter its current plant size. In other words, during the short run, a firm works with whatever heavy equipment and factory size it already has. No matter how much more it wants to produce, say because of an increase in 138

the demand for its product, it cannot change its plant size in the short run. However, it may change the amount of other inputs like labor. Thus, in the short run, we have two types of inputs – fixed inputs and variable inputs. The following are the types of cost a firm incur to produce a given good in the short run: Total Costs (TC): are all costs of a firm incurred to produce goods and services. The

total cost (TC) includes both implicit costs (sacrifices) and explicit (out of pocket) costs. The total cost can be divided into two: the Total Fixed Cost (TFC) and the Total Variable Cost (TVC), i.e., TC = TFC + TVC Total Fixed Costs (TFC): are those costs that must be incurred by the firm whether or

not production takes place, or whether the firm produces less or more quantity of a given product. In other words, these are costs that do not fluctuate/vary with the level of output; whether the firm changes (increases or decreases) its production level or not, they remain unchanged. Examples of the fixed cost include: ¾ Property tax, ¾ Fire insurance ¾ Salaries of the administrative staff, say, salaries of a secretary and a guard, ¾ Payments for the land (rent) and expenses for land maintenance, ¾ Expenses for depreciation and repairs (of machinery, building, etc).

Graphically, the total fixed cost can be depicted as follows:

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C= Cost

TFC

Q

O

Figure 4.1: The Total Fixed Cost

Total Variable Costs (TVC): are the costs of production that th vary with the level of

output the firm produces. Unlike the total fixed costs, these costs depend on the level (amount) of output produced. If the firm wants to increase its production, it must use more of the variables inputs and incur more variable costs. If there is no production, there will be no variable input used, and thus, there won’t be any variable cost incurred. Examples of the total variable costs include: ¾ Payments for raw materials used for production (like cotton in textile factory,

seed in agriculture, etc.), ¾ Electricity bills, ¾ Wage payments for direct labor, ¾ The running expenses of fixed capital, such as fuel, ordinary repairs and routine

maintenance. The total variable cost has usually an inverse-S shape, which reflects the law of variable proportions. According to this law, at the initial stage of production with a given plant

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size, as more of the variable factor is employed, its productivity increases and thus total variable cost(TVC) increases at a decreasing rate. For example, to increase the level of output by one unit may require one more worker, and if the price of this additional worker (the wage rate) is 10 Birr (per given period of time), the TVC increases by 10 Birr. As the productivity of the variable input (labor) falls, larger and larger units of the variable input will be needed to increase output by the same unit. To continue with our hypothetical example, two more workers may be needed to increase output by a unit in which case the TVC increases by 2x10 = 20 Birr. Thus, the total variable cost (TVC) first increases at a slower rate and then at an increasing rate because of the law of variable proportions (discussed in Chapter Three). Since the TC is the sum of the TFC and the TVC, and as the TFC doesn’t change, the TC behaves just like the TVC. Figure 4.2 below shows the TC, TFC, and TVC curves a firm. TC Cost TVC

TFC

O

Output (X) Figure 4.2: The TC, TVC and TFC Curves

141

From the total fixed cost, the total variable cost and the total cost curves, we obtain the average fixed cost, the average variable cost and the average (total) cost curves respectively. Average Fixed Cost (AFC): is the total fixed cost divided by the amount of output, i.e.,

AFC =

TFC . X

Since TFC is constant, an increase in X reduces the ratio

TFC , and thus the AFC X

approaches the quantity (output) axis as output rises. This is depicted in Figure 4.3 below. Cost

AFC O

X Figure 4.3: The Average Fixed Cost (AFC) Curve

Average Variable Cost (AVC): is the total variable cost divided by the level of output,

i.e.,

AVC =

TVC . X

Graphically, the AVC at a given level of output is equal to the slope of a line drawn from the origin to the point on the TVC curve corresponding to the particular level of output. For example, in Figure 4.4 below, the AVC at X1 is the slope of the ray OA; and similarly, the AVC at X2 is the slope of the ray OB; and so on. It is clear from the figure that the slope of a ray through the origin declines continuously until the ray becomes 142

tangent to the TVC curve at point C. To the right of this point the slope of ray through the origin starts increasing. Thus, the AVC curve falls initially as the productivity of the variable factor increases, reaches a minimum when the plant is operated optimally and rises beyond that point. TVC

Cost ($) D

C

B A

O Cost ($)

X1

X2

X3

X4

X AVC

A

B

D C

O

X1

X2

X3

X4

X

Figure 4.4: Deriving the AVC Curve from the TVC Curve

The graphical derivation of the ATC curve is done in the same way as the derivation of the AVC curve. That is, the ATC at any one level of output is the slope of a line from the

143

origin to the point on the TC curve corresponding to the level of output. Like the AVC curve, the average (total) cost (AC or ATC) curve is also U-shaped, reflecting the law of variable proportions.

Note that: AC or ATC =

TC TFC + TVC TFC TVC = + = AFC + AVC = X X X X

Marginal Cost (MC): is the additional/extra cost incurred in order to produce one more unit of output. That is, MC =

d (TC ) d(X )

It is straight forward to prove that marginal cost could be defined as the change in the total variable cost for a unit increase in output, i.e., MC =

d (TVC ) . d(X )

Proof: MC =

d (TC ) (As defined earlier) d(X )

d (TFC + TVC ) d(X ) d (TFC ) d (TVC ) = + d(X ) d(X ) d (TVC ) = 0+ (Since there is no change in fixed cost) d(X ) d (TVC ) MC = . d(X ) MC =

Graphically, the marginal cost at a given level of production is the slope of the TC curve (which of course is the same at any point as the slope of the TVC). The slope of the TC curve at any one point is the slope of a tangent line at that point. As we can see from the following graph (Figure 4.5), the tangent line initially becomes flatter and flatter as output expands up to X3 level of output, and then becomes steeper and steeper as the output goes on increasing. This means that the slope of the TC (or TVC) curve (MC) 144

initially decreases, reaches a minimum, and then starts increasing. Thus, the MC curve is also U-shaped. Cost ($)

TVC

d c b a

O Cost ($)

X1

X2

X3

X4

X MC

a d b c

O

X1

X2

X3

X4

X

Figure 4.5: Deriving the MC Curve from the TVC Curve

In summary, the traditional theory of cost postulates that in the short run the average and marginal cost (AVC, ATC and MC) curves are U-shaped, reflecting the law of variable proportions. In the short run with a fixed plant there is a phase of increasing productivity (falling unit costs) and a phase of decreasing productivity (increasing unit costs) of the variable factor. Between these two phases of plant operation, there is a single point at which unit costs are at a minimum. In general, these short run cost curves are as shown in Figure 4.6 below.

145

Cost ($)

AC MC AVC

c b

a AFC O

XM

XV

XT

X

Figure 4.6: The Short Run Unit Cost Curves

Figure 4.6 above also shows various relationships between the following pairs: AVC and ATC; ATC and MC; and AVC and MC. These relationships are discussed below. (A) The Relationship between AVC and ATC

The AVC is a part of the ATC: ATC = AFC + AVC. Both AVC and ATC are U-shaped, reflecting the law of variable proportions. However, the minimum point of the ATC occurs to the right of the minimum point of the AVC. This is due to the fact that ATC includes AFC which falls continuously with increase in output. Initially, the fall in the AFC offsets the rise in the AVC and thus the ATC declines. But later on, the rise in the AVC more than offsets the fall in the AFC and thus the ATC will start rising. The AVC approaches the ATC asymptotically as X increases since the AFC, which is the difference between the two, declines continuously. (B) The Relationship between MC and ATC

146

The MC cuts the ATC at its minimum point. We said that MC is the change in TC for producing an extra unit of output. To illustrate the relationship, assume that we start from a level of Xn units of output. If we increase the output by one unit the MC is the change in TC resulting from the production of the (Xn+1)th unit. That is, MC = TCn+1 – TCn. The AC at each level of output is found by dividing TC by X. Thus, the ATC at the level of Xn is: ATC n =

TC n Xn

And at the level of Xn+1: ATC n +1 =

TC n +1 . X n +1

Clearly, from the first relationship above, TCn+1 = TCn + MC. Thus, if the MC of the (Xn+1)th unit is less than the ATCn (the ATC of the previous Xn units), the ATCn+1 will be smaller than the ATCn. On the other hand, if the MC of the (Xn+1)th unit is higher than the ATCn (the ATC of the previous Xn units), the ATCn+1 will be higher than the ATCn. In general, as far as the MC is below the ATC (i.e., MC < ATC), it pulls the ATC downward; and, whenever the MC is above the ATC (i.e., MC > ATC), it pulls the latter upward. From this, it follows that the MC curve intersects the ATC at the minimum point of the ATC. This relationship between the ATC and the MC can also be proofed by using a simple calculus: ¾ From ATC = ¾ MC =

TC ⇒ TC = ( ATC ) • X , and X

d (TC ) by definition. d(X )

147

d (TC ) d(X ) d ( ATC • X ) = d(X ) d(X ) d ( ATC ) = ATC • +X• d(X ) d(X ) MC = ATC + X • (Slope of the ATC)

⇒ MC =

Given that X and ATC are positive, the last line above shows that: ¾ MC < ATC if the slope of ATC is negative. ¾ MC = ATC if slope of ATC = 0, (at the minimum of the ATC). ¾ MC > ATC if slope of ATC > 0. (C) The Relationship between MC and AVC

The relationship between MC and AVC is similar to the relationship between MC and ATC seen above; the MC curve intersects the AVC curve at the minimum point of the latter one.

¾ From AVC = ¾ MC =

TVC ⇒ TVC = ( AVC ) • X , and X

d (TC ) d (TFC + TVC ) d (TVC ) = = because there is no change in TFC. d(X ) d(X ) d(X )

d (TVC ) d(X ) d ( AVC • X ) = d(X ) d(X ) d ( AVC ) = AVC • +X• d(X ) d(X ) MC = AVC + X • (Slope of the AVC)

⇒ MC =

Given that X and AVC are positive, the last line above shows that: ¾ MC < AVC if the slope of AVC is negative.

148

¾ MC = AVC if slope of AVC = 0, (at the minimum of the AVC). ¾ MC > AVC if slope of AVC > 0.

4.4 THE RELATIONSHIP BETWEEN PRODUCT CURVES AND COST CURVES IN THE SHORT RUN In short, assuming that there is only one variable factor of production, the average variable cost is the mirror image of the average product; and similarly, the marginal cost is the mirror image of the marginal product. That is, if labor is the only variable factor of production, the following relationships hold: # when the average product of labor (APL) rises, the average variable cost of

production (AVC) falls; # when the average product of labor (APL) falls, the average variable cost of

production (AVC) rises; # when the average product of labor (APL) is at its maximum, the average variable

cost of production (AVC) is at its minimum; # when the marginal product of labor (MPL) rises, the marginal cost of production

(MC) falls; # when the marginal product of labor (MPL) falls, the marginal cost of production

(MC) rises; and # when the marginal product of labor (MPL) is at its maximum, the marginal cost of

production (MC) is at its minimum. The mathematical proofs of the above inverse relationships between average product and marginal product of labor on the one hand and the average variable cost and marginal cost on the other hand are as follows. Given TVC = w.L, where w = the market wage rate (assumed fixed) and L = the quantity of labor input.

149

1. AVC =

TVC w.L = , where Q is the level of output Q Q L Q 1 = w. APL

⇒ AVC = w.

⇒ AVC = 2. MC =

w APL

∂ (TC ) ∂ (TVC ) = , ∂Q ∂Q

⇒ MC =

∂ ( w.L) ∂L = w. because w is a constant (fixed). ∂Q ∂Q = w.

1 MPL

⇒ MC =

w MPL

Below, the same set of relationships is shown graphically:

APL MPL 150 A

Check Your Progress 1. Why is the cost function a derived function? 2. Distinguish between/among: a. The short run total fixed cost, total variable cost and total cost. b. The short run average fixed cost, average variable cost and average total cost. c. Implicit and explicit costs 3. Discuss the relationship between each of the following pairs (in the short run).

151

a. MC and AVC b. MC and ATC c. MC and MPL d. AVC and APL

4. 5 LONG-RUN COSTS The long-run is a period of time of such length that all inputs are variable. It is a planning horizon in the sense that economic agents can plan ahead and choose many aspects of the “short-run” in which they will operate in the future. Thus, the long-run consists of all possible short-run situations among which an economic agent may choose. If a production technology is characterized by constant returns to scale (CRS), doubling output requires doubling of inputs, which implies doubling of total output (cost) for given factor prices. Hence, the long-run total cost curve in this case is a straight line through the origin. This implies that the long-run average and marginal cost curves are horizontal lines and are identical (i.e., LAC = LMC). LTC

LTC

LMC

LMC = LAC

O

Q

O

Q

Figure 4.8: The Long-Run Total, Average and Marginal Cost Curves under CRS If we consider the case where total cost first increases at a deceasing rate due to

increasing returns to scale (which implies economies of scale), and then increases at an increasing rate attributed to decreasing returns to scale after the optimum size, the long-

152

run total cost curve will look like the following. Consequently, the LAC and LMC curves will be U-shaped. LTC

LAC LTC LMC

O

Q

LMC

O

LAC

Q

Figure 4.9: The Long-Run Total, Average and Marginal Cost Curves

The range to the left of the minimum point of the LAC curve is called the range of economies of scale, which means output can be doubled for less than doubling of cost. The range to the right of the minimum point of the LAC curve is called the range of diseconomies of scale, because a doubling of output requires more than a doubling of cost. The traditional theory of the firm assumes that economies of scale exist only up to a certain plant size, which is known as the optimum plant size. With this plant size all possible economies of scale are fully exploited. If the firm expands production further than this optimum size, there are diseconomies of scale arising from managerial inefficiencies. It is argued that management becomes highly complex, managers are overworked and the decision making process becomes less efficient. When a firm is producing an output level along the falling part of the LAC curve, the LMC is less than the LAC. Conversely, when the LAC curve is rising, the LMC is greater

153

than the LAC. The two curves intersect at the point where the LAC curve achieves its minimum. Like the short run average cost (SAC) and short run marginal cost (SMC) curves, the LAC and the LMC curves are also U-shaped. But the reason behind the U-shape of the long run curves is different from the reason behind the U-shape of the short run curves. In the long-run, the source of the U-shape is increasing and decreasing returns to scale, rather than diminishing returns to a factor of production which is the source of the Ushape fro the short run.

4.6 THE RELATIONSHIP BETWEEN SHORT-RUN AND LONGRUN AVERAGE AND MARGINAL COSTS Assume that a firm is uncertain about the future demand for its product and is considering three alternatives plant sizes: Small, Medium and Large. The short-run average cost curves are SAC1, SAC2 and SAC3 as shown in the figure below. Cost ($)

SAC1 SAC2

AC1

SAC3

AC2

AC1* AC2*

O

Q1

Q1*

Q2

Q2*

Q

Run Average Costfurther Curvesthan andQthe, itLong Cost will Run installAverage the medium If the firmFigure expects4.10: that Short the demand will expand 1

plant, because with this plant outputs larger than Q1 are produced with a lower cost. For

154

instance, the average cost of producing Q1* units with the medium plant (AC1*) is less than the average cost of producing the same units with the small plant (AC1). Similar considerations apply for the decision of the firm once the level production passes Q2. For instance, the average cost of producing Q2* units with the large plant (AC2*) is less than the average cost of producing the same units with the medium plant (AC2). Thus, the firm follows the path which is drawn in bold in the figure above. This bold envelope is thus the long run average cost curve for the case of three plant sizes assumed. If we relax the assumption of the existence of only three plant sizes and assume that there is a very large (an infinite) number of plant sizes, we obtain a continuous curve, which is the planning LAC curve of the firm. Cost ($) SAC7 SAC1 SAC2

LAC

SAC6 SAC4

SAC5

SAC3 M

O

Q*

Q

Figure 4.11: The LAC Curve as an Envelope of Various SAC Curves

The LAC curve is the locus of points denoting the least cost ways of producing various levels of output. It is a planning curve because the firm decides what plant size to set up in order to produce optimally the expected level of output at minimum cost on the basis of this curve. The LAC curve is U-shaped and it is often called the envelop curve because it envelopes the short run curves.

155

Because there are economies of scale and diseconomies of scale in the long-run, the minimum points of the short run average cost curves (plants 1 up to 3, and 5 up to 7 in the figure above) do not lie on the long-run average cost curve. For example, a plant size of 2 operating at its minimum average cost is not efficient because a larger plant can take advantage of increasing returns to scale to produce the same level of output at a lower average cost. Each point of the LAC curve is a point of tangency with some corresponding SAC curve. The point of tangency occurs on the falling part of the SAC curves for points lying to the left of M, i.e., for the plant sizes such as 1, 2 and 3. Since the slope of the LAC is negative up to M, the slope of these SAC curves must also be negative, because at the point of tangency the two curves have the same slope. By the same logic, the points of tangency of the LAC curve and the SAC curves for outputs larger than Q* (to the right of M) occur on the rising part of the SAC curves. Only at the minimum point (M) of the LAC is the corresponding SAC also at a minimum. At the falling part of the LAC curve the plants are not worked to full capacity. To the rising part of the LAC curve the plants are overworked. Only at the minimum point M is the plant optimally utilized. The LMC is derived from the SMC curves but does not envelop them. The LMC is formed from points of intersections of the SMC curves with vertical lines drawn from the points of tangency of the corresponding SAC and the LAC curve. Figure 4.12 below illustrates how this is done.

SMC3 LMC

Cost ($) SMC1 a

LAC SAC1

SAC3 156

SAC2

SMC2

To the left of a, SAC1 is greater than LAC so that SAC1 declines at a faster rate than the LAC. As the larger (SAC1) is falling at a faster speed than the smaller (LAC), the two will be equalized at some point – at point a in the figure above. This implies the LMC is greater than SMC1 to the left of a. At a, LMC = SMC1 (the same amount of additional costs accrue to both the short-run and the long-run costs so that SAC1 = LAC). To the right of a, LMC < SMC1 (more incremental cost is added to the short-run cost than to the log-run cost). At the minimum point of the LAC, the LMC intersects the LAC. At this point, SAC = SMC = LAC = LMC.

Check Your Progress 1. Are the short run and the long run cost curves similar in shape? If so, do you see any difference between the two? 2. The long run average cost curve is an envelope curve. What does this mean? Explain. 3. Why don’t we have a long run average fixed cost?

157

4.7 DERIVATION OF COST FUNCTION FROM PRODUCTION FUNCTION Cost curves are derived functions in that they are derived from the production function. Costs are not incurred for their own sake but only to produce output. Graphically, the total cost curve is determined by the locus of points of tangency of successive isocost lines with the corresponding highest isoquants. Mathematically, the cost function can be derived as follows. As usual, we use the CobbDouglas production function: X = ALb K c Given this production function and the cost function C = wL + rK , we want to derive the cost function, that is, cost as function of output: C = f(X). We begin by solving the constrained output maximization problem: Maximize X = ALb K c subject to C = wL + rK Form the composite function:

Z = X − λ ( wL + rK − C ) Partially differentiate Z with respect to L, K, λ and equate each to zero. *

∂Z ∂X = − λw = 0 ∂L ∂L

Ö MPL = λw Ö λ=

*

MPL …………………………………………………………………… (1) w

∂Z ∂X = − λr = 0 ∂K ∂K

Ö MPK = λr Ö λ=

MPK …………………………………………………………………… (2) r

158

*

∂Z = wL + rK − C = 0 ∂λ

Ö wL + rK = C ……………………………………………………………… (3)

From equations (1) and (2) we understand that:

MPL MPK w MPL = or = r MPK w r

Using the Cob-Douglas production function given above, bALb K c b = X L L cALb K c c and similarly, MPL = cALb K c−1 = = X K K MPL = bALb−1K c =

Using the equilibrium condition and these marginal products, solve for K in terms of L, or for L in terms of K. Let us solve for L in terms of K. b X w L = c r X K ⇒

w bK = r cL

⇒ wcL = rbK rbK ⇒L= .................................................................................................................(4) wc Substitute this term for L into the production function and solve for K in terms of X:

rbK b c ) K wc rb ⇒ X = A( ) b K b + c wc X wc b ⇒ ( ) = K b+c A rb 1 X wc ⇒ [ ( ) b ] b + c = K .......... .......... .......... .......... .......... .......... .......... .......... ....(*) A rb X = A(

From equation (4) above, we know that L =

rbK . wc

159

1

rbK rb X wc b b+ c Then, L = = [ ( ) ] wc wc A rb 1

c

⇒L=(

rb b+c X b+c ) [ ] ..............................................................................(**) wc A

As a final step, substitute (*) and (**) into the isocost equation: C = wL + rK 1

c

1

rb X X wc C = {w( ) b+c [ ]b+c } + {r[ ( )b ]b+c } wc A A rb b c c −1 −b b −1 1 1−b 1 b b ⇒ C = [ w b +c r b+ c ( ) b +c A b +c X b +c ] + [ r b+c ( ) b +c w b+c A b +c X b +c ] c c b c c −1 −b b −1 1−b 1 b b ⇒ C = {[ w b+c r b+c ( ) b+c A b+c ] + [r b+c ( ) b+c w b+c A b+c ]}X b+c c c

1 −1 −b −1 b c c b 1−b b b b + ⇒ C = {v} X c ; where v = [ w b+c r b+c ( ) b+c A b+c ] + [r b+c ( ) b+c w b+c A b+c which is a constant c

c

Don’t worry if you find the above derivation cumbersome. A numerical example makes it 2 3

1 3

easier. Suppose we have a production function given by X = L K , w = 2 Birr per unit and r = 4 Birr per unit. Derive the cost function. Solution:

The steps that are involved to derive the cost function are: Step 1: Solve for L in terms of K or K in terms of L from the optimality −1

1

2 3 3 L K 2 3 w MPL .⇒ = condition = 4 1 23 −32 r MPK LK 3 −1

1

1 2L 3 K 3 ⇒ = 2 −2 2 L3 K 3 1 2 +

1 K3 3 ⇒ = 2 1 + 4 L3 3

160

1 K = 4 L ⇒ L = 4K ⇒

Step 2: Substitute the result from step 1 into the production function and solve for L and

K in terms of Q from the production function. 2 3

X =L K

1 3 2 3

⇒ X = (4 K ) K 2 3

⇒X =4 K

1 3

2 1 + 3 3

⇒ X = 3 16 K X ⇒K=3 16 ⇒ L = 4K = 4 3

X 16

−2

Because L = 4K, ⇒ L = 414 3 X ⇒ L = 3 4X

Step 3: Substitute the results from step 2 into the cost constraint. C = wL + rK

⇒ C = 2L + 4K ⇒ C = 2(3 4 ) X + 4( 3 ⇒ C = [2(3 4 ) + 4( 3 5

1 )X 16

1 )] X 16

2

⇒ C = [2 3 + 2 3 ] X .

4.8 DYNAMIC CHANGES IN COSTS – THE LEARNING CURVE A large firm may have a lower long run average cost than a smaller firm because of increasing returns to scale in production, which implies that growing firms with increasing returns to scale enjoy lower average costs over time.

161

But this may not be necessarily the case. In some firms, long-run average cost may decline overtime because workers and managers absorb new technological information as they become more experienced at their jobs. As management and labor gain experience with production, the firm’s marginal cost (MC) and average cost (AC) of producing a given level of output fall for four reasons: 1. As workers become more adapted to a given task, their speed increases. 2. Managers learn to schedule the production process more effectively. 3. Engineers who are initially cautious in their product designs may gain enough experience to be able to allow for tolerances in design that save cost without increasing defects. Better and more specialized tools and plant organization may also lower cost. 4. Suppliers of materials may learn how to process materials required more effectively and may pass on some of this advantage in the form of lower materials cost. As a consequence of this, a firm “learns” overtime as cumulative output increases. The graph (curve) that describes the relationship between a firm’s cumulative output and the

unit of output

Amount of inputs needed per

amount of inputs needed to produce each unit of output is known as the learning curve.

Learning Curve Cumulative output Figure 4.13: The Learning Curve

162

Overtime, a firm’s average cost of production can decline because of: a. Growth of sales when increasing returns are present (movement from A to B in the figure below), or b. The existence of learning curve/effect (movement from A to C in the figure). AC

A B AC1

C AC2

Q

O

Figure 4.14: Economies of Scale versus Learning Effect

Check Your Progress 1. Outline the steps to be followed for deriving the cost function from the production function 2. Discuss the reasons for which a firm that has been in business for long could experience low average unit cost of production. 3. What is the difference between economies of scale and learning effect?

4.9 LESSON SUMMARY # The cost function is a derived function – derived from the production function. # In both the short and the long run, economists calculate implicit as well as explicit

costs of production. Implicit costs are those costs implied by the alternatives given up, and explicit costs are direct expenditure or bookkeeping costs. 163

# In the short run, as more and more units of the variable factor(s) are added to the

fixed factor, the firm may initially experience increasing returns to the variable factor and thus total costs of production rise slowly at lower levels of output. However, eventually the firm reaches a point (some higher level of output) at which total costs begin to increase at an increasing rate. Such increasing and diminishing returns to the variable factor of production (the law of variable proportions) account for the U- shape of the short-run average and marginal cost curves. # Except that we don’t have a fixed cost in the long run, the short and the long run

cost follow similar patterns. However, the U-shape of the long-run average and marginal cost curves is due to economies and diseconomies of large-scale production. # There a predictable relationship between short run cost functions and production

functions as well between short run and long run cost functions. # A large firm may have a lower long run average cost than a smaller firm because of

two reasons: because of increasing returns to scale (economies of scale) in production, and/or because of the learning effects (as workers and managers of a large firm could easily absorb new technological information as they become more experienced at their jobs).

4.10 REVIEW QUESTIONS I. Multiple Choice Questions

1. If we have a linear cost function of the firm C = a +bQ, then the average cost will: a.

remain constant as production expands.

b.

decrease continuously as production expands.

c.

increase with increases in output

d.

first increase and then decrease with increases in output.

2. When the marginal cost increases beyond its minimum, the average cost, a.

increases

164

b.

decreases

c.

remains constant

d.

first decreases and then increases

3. Which of the following is the general sequence? a.

Economies of scale begin when diseconomies end

b.

Diseconomies begin where economies end.

c.

Diseconomies end where economies begin

d.

Economies and diseconomies of scale go together

4. The cost that a firm incurs in purchasing or hiring any factor of production from outside the firm is referred to as: a.

explicit cost

b.

implicit cost

c.

variable cost

d.

fixed cost

5. An entrepreneur running a business earns $20,000 per year as his/her salary from the total receipts of the firm; the implicit cost of this entrepreneur is: a.

$20,000/year

b.

more than $20,000/year

c.

less than $20,000/year

d.

any of the above is possible

6. If only part of the labor force employed by a firm can be dismissed at any time and without pay, the total wages and salaries paid out by the firm must be considered: a.

a fixed cost

b.

variable cost

c.

partly fixed and partly variable cost

d.

any of the above

7. When the law of diminishing returns begins to operate, the TVC begins to: a.

fall at an increasing rate

b.

rise at a decreasing rate

c.

fall at a decreasing rate

d.

rise at an increasing rate

165

8. All the following curves are “U” shaped except: a.

the AVC curve

b.

the AFC curve

c.

the ATC curve

d.

the MC curve

9. MC is given by: a.

the slope of the TFC curve

b.

the slope of the TVC curve, but not by the slope of the TC curve

c.

the slope of the TC curve, but not by the slope of the TVC curve

d.

either by the slope of the TC curve or by the slope of the TVC curve

10. The MC curve reaches its minimum point before the AVC and the ATC curves do so. In addition, the MC curve intersects both the AVC and the AC curves at their lowest points. The above statements are both true: a.

always

b.

never

c.

often

d.

sometimes

11. At the point where a straight line from the origin is tangent to the TC curve, the ATC is: a.

at its minimum

b.

equal to MC

c.

equal to AVC plus AFC

d.

all of the above

12. The LAC curve is tangent to the SAC curve at the lowest point of the latter when the LAC curve is falling. This statement is true: a.

always

b.

never

c.

sometimes

d.

cannot say

13. If the LAC curve falls as output expands, this is due to: a.

economics of scale

166

b.

the law of diminishing returns

c.

diseconomies of scale

d.

any of the above

14. The LAC curve: a.

falls only when the LMC curve falls

b.

rises whenever the LMC curve rises

c.

goes through the lowest point of the LMC curve

d.

falls when LMC < LAC and rises when LMC > LAC

15. The short run total cost can never be less than the long run total cost. This statement is: a.

always true

b.

often true

c.

sometimes true

d.

never true

II. Discussion and Workout Questions

1. Distinguish between: (a) short-run and long-run costs, (b) explicit and implicit costs. 2. Explain the relationship between the marginal and average cost curves. Show the relationship between marginal cost, average variable cost and average total cost. 3. Explain why the average total cost and the average variable cost become closer and closer as output increases. 4. Show the circumstances when the marginal cost is constant throughout but the average cost is falling. (Hint: think of the geometric derivations of the two costs.) 5. Derive the long run average cost curve from the short run average cost curves. 6. Write a short note on the derivation of long run marginal cost curve. 7. Why is it that at the output where SAC = LAC, SMC also equals LMC? 8. Suppose the cost function is given as C = 135 + 75Q – 15Q2 + Q3. Prepare a cost schedule (table) showing the TFC, TVC, TC, AFC, AVC, MC, and ATC. Is this cost function a short run or a long run cost function? Why? Draw the cost curves on the basis of cost data obtained from the cost function.

167

CHAPTER FIVE PERFECT COMPETITION LESSON STRUCTURE 5.1 Introduction 5.2 Chapter Objectives 5.3 Characteristics of Pure and Perfect Competition 5.4 Market Equilibrium 5.4.1 Equilibrium in the Market Period 5.4.2 The Short Run Equilibrium of a Firm and Industry/Market 5.4.3 The Long Run Equilibrium 5.5 Perfect Competition and Consumers’ Welfare 5.6 Lesson Summary 5.7 Review Questions

5.1 INTRODUCTION The market in which an individual firm operates or sells its product (good or service) to consumers can be categorized broadly into perfect and imperfect market9. The type (or nature) of competition firms face from competitors, which in turn determines the degree of power of a firm over the price of its product, is the basis for categorizing markets into perfect and imperfect. While price competition is the only type of competition firms operating in perfectly competitive markets will face from competitors both price and nonprice competitions are common in imperfect markets. In short, Perfect Competition is a market structure characterized by complete absence of rivalry among individual firms.

9

Markets dominated by one firm (monopoly), very few firms (oligopoly), and relatively large numbers of firms selling closely substitutable products (monopolistic competition) are the three common types of imperfect markets in which firms use different means of deterring other firms from entering into the market or the means of influencing their market share. The later two are characterized by rivalry among individual firms.

168

In neoclassical economics and microeconomics, perfect competition describes a market in which no buyer or seller has market power or where all buyers and sellers are pricetakers; that is, perfect competition is a market structure in which firms treat price as a parameter. It is this distinction which differentiates perfectly competitive markets from imperfectly competitive ones. Perfectly competitive markets are characterized by allocative and productive efficiency. In general, a perfectly competitive market is characterized by the fact that no single firm has influence on the price of the product it sells. Because the conditions for perfect competition are very strict, there are few perfectly competitive markets in the real world.

5.2 CHAPTER OBJECTIVES After completing this chapter, you will be able to: # Distinguish between pure and perfect competition # Determine the short and long run equilibrium output and price of a competitive

firm and industry. # Describe why perfect competitive market is an ideal market in terms of ensuring

consumer welfare.

5.3 CHARACTERISTICS OF PURE AND PERFECT COMPETITION A perfectly competitive market has several distinguishing characteristics. The main features include: 1. Many Buyers and Many Sellers

There are many consumers with the willingness and ability to buy the product at a certain price and many producers with the willingness and ability to supply the product at a certain price. Since each firm supplies only small part of the total market supply any firm cannot affect the market price by altering (increasing or decreasing) its output.

169

2. Homogeneous Products

The industry or market is defined as group of firms supplying homogeneous products (goods or services). That is, products supplied by the different firms are exactly the same. Example, salt supplied by two sellers are identical to the extent that buyers are unable to differentiate which firm supplied which product. The assumption of large number of sellers and product homogeneity together imply that an individual firm operating in a perfectly competitive market is a price taker. Thus, a competitive firm faces a completely horizontal or perfectly elastic demand curve for its product indicating that it can sell any amount of output only at the ongoing market price ( P ). Moreover, the demand curve is also the average revenue (AR) and marginal revenue (MR) curve.

P

P = DD = AR = MR

P

O

Q

Figure 5.1: The Demand Curve Faced by a Firm under Perfectly Competitive Market

The reason for the equality of the ongoing market price ( P ) and the demand curve is that any firm receives, for any unit of output sells, the price which is determined by the intersection of market demand and market supply. This is depicted in Figure 5.2 below.

170

SS P

MC

−

−

P

P

EM

−

EF

P = DD = MC

DD QM

Q

(a) Industry/Market

Q

QF

(b) Firm

Figure 5.2: Determination of Equilibrium Price under Perfect Competition

Why do the relationships P = AR and P = MR hold? Let us show these mathematically. AR =

TR P .Q = Q Q

MR =

⇒ AR = P

dTR d (Q.P ) dQ = = P( ) dQ dQ dQ

⇒ MR = P

3. Free Entry/Exit

Unlike imperfect markets, entry into and exit from a business is not blocked in a perfectly competitive market. In other words, firms have freedom of movement or there is no barrier that restricts firms from entry into and/or exit out of a perfectly competitive market. 4. Firms Aim to Maximize Profit

The objective of firms in perfect competition is profit maximization. To this end firms operate (produce and sell) at a point where the marginal cost of production meets the marginal revenue from sales. More on this will be discussed in Section 5.4.

171

5. Absence of Government Intervention

This is to say there is no government regulation or intervention in the market in any way, say through imposing tariffs, granting subsidies, rationing, etc., which are considered as disturbances to the market. This notion is based on the argument of the classical economists led by Adam Smith who regard the government intervention as unnecessary. A market that fulfils only the above five characteristics is called pure competition. Pure competition and perfect competition are different for the later requires the fulfillment of the following additional characteristics/assumptions. 6. Perfect Mobility of Factors of Production

This implies that all factors of production, such as labor and raw materials, are free to move from one sector to another or from one firm to another. That is, workers can change their jobs without any restriction for labor is not unionized and the supply of raw materials is not monopolized either by one or few firms. This also implies full employment of resources. 7. Perfect Information for Both Consumers and Producers.

It is assumed that in a perfectively competitive market both sellers and buyers have complete information and knowledge of the market. The implication is that the current and future price of products, quality of products supplied by different firms, etc., are certainly known. In other words, information is costless: there is no uncertainty about future prices, and no non-price competition exists under a perfectly competitive market. Check Your Progress

1. Distinguish between pure competition and perfect competition.

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2. Discuss the implication of the notion that there is no barrier to entry and exit under perfect competition.

5.4 MARKET EQUILIBRIUM We will see the equilibrium of a perfectly competitive firm as well as that of industry under three different cases: the market period, the short run and the long run equilibria. 5.4.1 The Market Period Equilibrium

A market period refers to a very short period in which supply is absolutely fixed. For instance, the quantity of agricultural products available in the market cannot be increased instantly with demand as production is seasonal. Put it differently, though different levels of demand give rise to different prices, supply will remain the same for it cannot be increased until the next harvest. P

S

P3 P2

P1

D3 D2 D1 O

Q

QS

Figure 5.3: Market Period Equilibrium under Perfectly Competitive Market

From the above figure it is clear that different level of demand gives different equilibrium but equilibrium output remains the same. This implies that, at any market period demand alone determines the equilibrium price. A market period is thus different from short run

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and long run in which both the supply and demand conditions determine the equilibrium price and quantity. 5.4.2 The Short Run Equilibrium of a Firm and Industry/Market

The Short Run Equilibrium of a Firm

Shot run is a production period in which the amount of one or more of the inputs a firm uses is fixed or constant. In other words, in the short run, the quantity of output produced by a competitive firm can be increased (decreased) only by increasing (decreasing) the variable inputs. The short run equilibrium of a firm or an industry (a market) is thus the output level that maximizes profit or minimizes loss under such conditions. This profitmaximizing level of output and the profit level can be determined using any of the two approaches discussed below. 1. The Total Revenue – Total Cost (TR – TC) Approach

Using this approach, a firm is in equilibrium when total revenue less total cost is the maximum. That is, the firm maximizes profit when the difference between total revenue and total cost is the greatest. The following hypothetical example for a competitive firm clarifies how we determine the equilibrium output and maximum profit using the TR – TC approach. Example 1: Suppose the short run market price is $5. Moreover, the short run output (Q)

and associated total cost of a competitive firm as are shown in the table below. Q

0

1

2

3

4

5

6

7

8

9

10

11 12

TC10 15 17 18.5 19.5 20 22.25 24.75 27.48 32.48 38.88 46.66 55 65.28

10

Recall from Chapter Four that the total cost when output is equal to zero is the short run total fixed cost

174

Given the above information, we need to compute only TR (i.e., price multiplied by the level of output, Q) in order to determine the equilibrium output and maximum profit using the TR – TC approach. The profit/loss of the firm for each output level is computed by subtracting TC from TR and is shown in the last column of table 5.1. Other variables are computed for latter use.

TFC

TVC

TC (FC+VC)

0

0

-

-

15

-

15.00 -

$5

1

5

5

5

15

2.00

17.00 17.00 2.00

(12.00)

$5

2

10

5

5

15

3.50

18.50 9.25

1.50

(8.50)

$5

3

15

5

5

15

4.50

19.50 6.50

1.00

(4.50)

$5

4

20

5

5

15

5.00

20.00 5.00

0.50

0

$5

5

25

5

5

15

7.25

22.25 4.45

2.25

2.75

$5

6

30

5

5

15

9.75

24.75 4.13

2.50

5.25

$5

7

35

5

5

15

12.48 27.48 3.93

2.73

7.52

$5

8

40

5

5

15

17.48 32.48 4.06

5.00

7.52

$5

9

45

5

5

15

23.88 38.88 4.32

6.40

6.12

$5

10

50

5

5

15

31.66 46.66 4.67

7.78

3.34

$5

11

55

5

5

15

40.00 55.00 5.00

8.34

0

$5

12

60

5

5

15

49.20 64.20 5.35

9.20

(4.20)

$5

13

65

5

5

15

59.36 74.36 5.72

10.20 (9.36)

Note: The values of ATC (SAC) are rounded to two decimal places.

175

(TR –TC)

M (∆TR/∆Q)

Profit/Loss

AR (TR/Q)

$5

ATC (TC/Q)

TR (P.Q)

(15.00)

Output (Q)

-

Price (P)

MC (∆TC/∆Q)

Table 5.1: Determination of Equilibrium of a Firm Using the TR – TC Approach

From Table 5.1 it is clear that the firm obtains normal (zero) profit or is at its break even point when it produces 4 or 11 units of output. Moreover, the firm obtains maximum profit when it produces either 7 or 8 units of output. The most important points in the total revenue – total cost approach are depicted graphically as follows. TC

TR

B

55.00

T

40.00 The maximum profit = 7.52 T

32.48 A

20.00 15.00

T O

4

7 8

11

Q

Figure 5.4: Profit Maximization of a Firm Depicted Using the TR – TC Approach

The profit (loss) of a firm is represented by the positive (negative) distance between the total revenue (TR) and total cost (TC) curves. In the above figure, first the TC curve lies above the TR curve until exactly 4 units of output is produced at point A implying that profit is negative (there was loss) prior to this point. Secondly, the intersection of the total revenue and total cost curves at point A implies that the firm has reached its breakeven point (no loss and no gain or obtains zero profit). Thirdly, the firm achieves economic (positive) profit at any level of production between point A and B. In this region, profit increases gradually, reaches maximum towards the middle, and declines gradually after 8 units of output is produced. Once again, the firm breaks even at point B when it produces exactly 11 units of output. Finally, profit becomes negative beyond point B.

176

Therefore, profit maximizing level of output is achieved at a point where the positive distance between the total revenue and total cost curves is the longest. At this point, the slope of the total cost, the MC (see the TT line which is tangent to the TC curve) is equal to the slope of the total revenue curve, the MR. In other words, the short run equilibrium of the firm is achieved when 8 units if output is produced. 2. The Marginal Approach

The total revenue – total cost approach indicates only the amount of profit (or loss) at different levels of production. In the above example, for instance, both 7 and 8 units of output generate 7.52 units of profit and the TR – TC approach doesn’t tell us why we choose 8 as a profit maximizing level of output (and why not 7). Hence, it does not help for analytical interpretation of business behavior. In this regard, the marginal approach is a useful analytical tool at least for the following reasons. The first reason is that the short run equilibrium output (profit maximizing level of output) and the associated profit can be clearly determined by equating marginal revenue to marginal cost, i.e., MR = MC . Graphically: MC

MR MC ATC 5.00

ATC

P = MR

Profit

4.06

0.50 4

EQ = 8

Q

Figure 5.5: Short Run Equilibrium of a Firm Depicted Using the Marginal Approach

177

The amount of profit (π ) at any level of output could be calculated using:

π = ( P − ATC )Q . This is derived from the TR-TC approach as follows: π = TR − TC

π = P.Q − ATC.Q π = ( P − ATC )Q . Thus, if P > ATC , there is excess profit; if P = ATC the firm gets normal (zero) profit; and, if P < ATC the firm incurs loss. For instance, at the equilibrium output (EQ) profit is,

π = (5 − 4.06)8 , which is π = (0.94)8 = 7.52 . The second reason is that comparing the value of MR and MC to the left and right of short run equilibrium output (EQ) has an important implication for a firm’s decision on whether to expand or reduce output. For example, to the left of EQ (for any output level less than 8), the MR ( = P) exceeds the MC, indicating that the sale of a unit of output would increase total revenue more than total cost since price is greater than unit cost (ATC) of production. Therefore, it pays for the firm to expand production. On the other hand, MR is lower than MC to the right of the equilibrium output implying that the firm should reduce its production. Alternatively, the short run equilibrium of a firm can also be derived mathematically from the given level of market price and total cost function of a firm. Example 2:

Suppose the market (per unit) price a firm faces is $10 and its cost function is given by: TC = Q 2 + 1 . Calculate the profit maximizing level of output and the maximum profit.

In this case, MC =

dTC TC Q 2 + 1 = = 2Q and ATC = . dQ Q Q

Equating the market price to the MC will give the equilibrium output. That is,

178

P = MC

10 = 2Q . Thus, the output level that maximizes profit is: Q = 5 . Substituting this output level into the TC and ATC equations gives the values 26 and 5.2, respectively. Furthermore, the profit of the firm obtains is:

π = TR − TC

π = PQ − (Q 2 + 1) = PQ − Q 2 − 1 ⇒ π = 10(5) − (52 + 1) = 50 − 26 = 24 .

The same result can also be obtained using: π = ( P − ATC )Q .

π = (10 − 5.2)5 = (4.8)5 = 24 .

Check Your Progress 1. A perfectly competitive firm is faced with the following output and total cost schedule. Q

0 1

2

TC 9 20 30

3

4

5

6

7

8

9

10

32

39

47

60

67

77

90

109

If the market price is Birr 13, a. Compute a table that shows the short run equilibrium of the firm using the TR – TC and marginal approaches. b. What is the equilibrium output of the firm? c. Using the marginal approach, show the profit level graphically. 2. Assume a two product firm is operating in a perfectly competitive market. The market prices of its products are $12 and $18, respectively. Furthermore, the production cost of the firm is given by TC = 2Q12 + Q1Q2 + 2Q22 . Based on this information: a. Find the short run equilibrium outputs, Q1 and Q2 , that in combination maximize profit. b. Calculate the total profit of the firm. c. Show graphically the profit the firm earns from each market separately. 179

So far we have seen two reasons for the usefulness of the marginal approach. Thirdly, this approach will provide the basis weather to shutdown a loss making firm or not. This can be illustrated with the help of the figure below. P MC

ATC

AVC

E1

P1

A

D F

B

H P2 P3 G P4 P5

MR1

C

E2

MR2

E3

MR3

K E5

MR4

E4

MR5

Q O q5 q4 q3 q2 q1 Figure 5.6: Short Run Equ ilibria of a Firm for Different Market Prices

In the above figure, five short run equilibrium points are established at different market prices. The equilibria are established at points where P = MR = MC . As a result, the quantity of output produced by a firm as well as its profit or loss varies. For example, when the ongoing market price is P1 , the short run equilibrium is at point E1 . At this price, the total amount of output produced by a firm operating in a perfectly competitive market is Oq1 . On the other hand, the unit cost (ATC) of producing one unit of output is given by the distance OF or q1C .Since P1 > ATC (q1C ) , the area P1 E1CF indicates the excess profit the firm obtains. Suppose the market price declines from P1 to P2 . In this case, the short run equilibrium is established at point E 2 and Oq 2 amount of output is supplied. Since, price OP2 is equal to unit cost q 2 E 2 , the firm is in its breakeven point; that is it earns normal (zero)

180

profit. However, for any price level below P2 , the firm will incur loss or will earn negative profit as the market price will be less than ATC. An interesting question one might ask is that, should a loss making firm close down? The answer to this question is that one should observe whether the market price is greater than or equal to the AVC at that equilibrium output in order to decide whether to close down or not. That is, a loss making firm should stay in business by continuing production as far as the market price is greater than the AVC. This is because not all fixed costs incurred are lost if the market price is greater than AVC. In other words, since all fixed costs will be lost if the firm discontinues production, the firm will lose less by staying in business and covering some part of the fixed costs. However, a loss making firm should shut down when the market price becomes less than the minimum of AVC. Recall from earlier discussion in Chapter Four that, graphically, AVC will be at its minimum when it is crossed by the MC curve from below. Therefore, the point where thee minimum AVC is equal to MC is called the shutdown point. The reason as to why it is a sensible strategy for a loss making firm to stay in business and shutdown when the market price is greater than and less than the AVC respectively can be justified by considering the situations at market price P3 and P4 in Figure 5.6 above. First, consider the situation when the market price declines from P2 to P3 . When the ongoing market price is P3 , the short run equilibrium is established at E3 and hence the firm produces Oq3 amount of output. At this level of production, the cost of producing one unit of output (ATC) is given by OH or q3 B . Since P3 < q3 B , or P3 < OH , the area P3 E3 BH indicates the loss incurred by this competitive firm.

Besides, # Total cost, which is equal to output multiplied by ATC, is Oq3 BH . # AVC is OG or q3 K . This implies that, total variable cost (TVC) is Oq3 KG .

181

# The difference between total cost and total variable cost gives us the total fixed

cost (TFC), which is equal to KBHG . # But the market price is greater than average variable cost, i.e. OP3 (= q3 E3 ) > q3 K

Therefore, if the firm decides not to produce Oq3 amount of output it will lose the whole of TFC given by area KBHG . However, by deciding to stay in business it will lose only P3 E3 BH , which is less than KBHG . This is because it has covered the part of the TFC

given by the area KE 3 P3G . Profit maximizing firms may in the short run continue to operate even though they are losing money. This is the case particularly for firms that own great deal of capital and therefore high fixed costs, because it is often less costly to continue producing at a loss than to shutdown and still be forced to bear the high fixed cost. However, a loss making firm should shutdown as soon as the market price falls below P4 . Because, when it produces Oq 4 amount of output at E 4 , the firm will lose all of its

TFC amounting to E 4 ADP4 ; and, as soon as the price falls short of P4 , it won’t even cover its variable cost if it decides to produce. The market price ( P4 ) that is equal to the minimum of the AVC ( q 4 E 4 ) and the MC is the dividing line between the decision to shut down and to continue operation. When the market price is below P4 , the firm should shut down since it will lose only its fixed cost by shutting down. If it were to produce at the point where MC equals the very low market price, it would lose more than fixed cost. Therefore, it is a wise decision to shutdown the business.

The Short Run Market/Industry Equilibrium

The short run industry supply curve is the horizontal summation of the short run supply curves of individual firms. The short run supply curve of an individual firm is derived from the intersection of its MC curve with its successive demand (MR) curves. It is part of the MC curve above the intersection of the MC and the AVC curve. As the market price increases gradually we expect that each higher demand curve (price line) cuts the 182

MC curve at a point to the right of the previous intersection. This indicates that quantity supplied by firms will increase as price increases. MC

P

The Supply Curve of a Firm

ATC AVC

P3 P2

P1 q1

q2 q3

q1

Q

q2 q3

Q

Figure 5.7: The Supply Curve of a Perfectly Competitive Firm

Therefore, the industry supply curve is simply the horizontal summation of the individual firms’ supply curves. Given the industry supply curve, the short run industry equilibrium will be obtained after determining the industry demand curve which is downward sloping. Assuming that there are 100 identical firms in the industry, the short run equilibrium will be as shown in the figure below. The Industry Supply Curve

P

P3 Market Demand Curve

100*q3

Q

Figure 5.8: The Short Rum Equilibrium an Industry 5.4.3 The Long Run Equilibrium

183

Unlike the short run, the long run is a period of time in which a firm can vary/change the amounts of all of its inputs. Since all inputs are variable in the long run, a firm has the option of adjusting its output through adjusting its plant size to achieve maximum profit. It is also possible some businesses can be liquidated /shutdown/ entirely if profit prospect is poor. The resources are thus transferred into more profitable investment areas/endeavors. Similarly, new firms will enter into the industry if profit prospect is attractive or are greater than profits elsewhere. Hence, adjustment of the number of firms in the industry in response to profit motives is the key element in establishing the long run equilibrium.

The Long Run Equilibrium of a Firm

In the long run, firms are in equilibrium when they have adjusted their plant size so as to produce at the minimum of the long run average cost (LAC) curve. At this point the LAC will be tangent to the demand curve defined by the market price. Therefore, the equality: LMC = SMC = SAC = LAC = P = MR is the long run equilibrium condition of a

competitive firm. The implication is that competitive firms will earn only normal profit in the long run. SMC

LMC SAC

LAC

DD = MR

P

Lq

Q

Figure 5.9: The Long Run Equilibrium of a Firm

Assume for simplicity that there are 100 identical firms that are supplying the same amount of output in the short run. Further assume that the business they engaged in is

184

profitable. The short run market/industry supply is thus 100 multiplied by the supply of each firm or simply 100(q1) indicated on the industry supply curve,

∑q

1

. As mentioned

earlier, we can now expect that the short run excess profit enjoyed by the firms in the industry will attract new firms into the industry.

∑q

1

SMC

A

P1 D P2

∑q

2

D ES

MR1 B

Firm C

SAC

EL

MR2

Market D

180(q q2 q1 of Long Run equilibrium100(q Figure 5.10: Derivation of Firms from the 1) 2) Short Run

Equilibrium

As shown in Figure 5.10, the individual firms are in the short run equilibrium when each supplies q1 units of output. It cannot be the long run equilibrium because each firm in the industry earns excess profit shown by area ABDP1 in the first graph as P1 > ATC . Each time new firms (attracted by the excess profit) enter into the market, the market supply curve will shift to the right. The entry of firms will continue until the industry supply curve shifts to

∑q

2

, the market price falls to P2, each firm produces q2, and firms in the

business obtain normal profit. At this point, suppose 80 new firms have entered into the market. Therefore, the long run industry equilibrium output will be 180(q2).

The Long Run Equilibrium of the Industry/Market

The industry is in the long run equilibrium when a price level reaches a point where all firms are in equilibrium. That is, when all firms produce at the minimum point of the LAC curve or when LMC = SMC = SAC = LAC = P = MR , and each firm just makes a

185 SAC

normal profit. With all firms in the industry being in equilibrium and with no entry and exit, then the industry supply curve remains stable and given the demand curve, the price will be the long run equilibrium price.

Figure 5.11: The Long Run Equilibrium of the Industry

Therefore, the difference between the short run and long run equilibrium is that although demand equals supply in both cases, the long run equilibrium is defined at a point where demand is equal to supply and no excess profit is obtained. Check Your Progress 1) Referring to Figure 5.10 above, what is the price elasticity of supply if an individual

firm supplied 18 units of output when P1 was $6 and 12 units when the market price falls to P2 = $3? 2) Based on the price and output information in question 1, calculate the elasticity of

market demand? 3) Do you expect any of the 180 firms to exit out of the business at P2? Why or why

not?

5.5 PERFECT COMPETITION AND CONSUMERS WELFARE

186

Perfect competition is regarded as the most ideal market from the point of view of resource allocation; resource utilization; resource employment; and consumers’ welfare. When the long run equilibrium is achieved, the economy operates at the maximum economic efficiency. This is because: # individual firms operate at the optimal plant sizes and produce optimal level of

output, # consumers buy different units of each output at the price equal to the minimum

attainable average cost per unit (P = LAC). This implies that each consumer buys those quantity of goods at which the marginal rate of substitution (MRS) between any two goods is equal to the price ratio of the two goods. Put differently, the marginal utility of the consumed good (MU) equals the price (P) at competitive equilibrium, which in turn equals the marginal cost (MC) of producing the good. The discussion in the following three steps show that, if MU = P = MC , allocation is efficient or optimal. 1. P = MU : Consumers choose to purchase a good up to the amount corresponding to P = MU . As a result, every person is gaining utils of satisfaction from the last unit of the good consumed as good as what he/she pays. Since the prices of goods are the lowest, consumers’ welfare is maximized. 2. P = MC : The equilibrium condition of a perfectly competitive firm is given by P = MC. From the viewpoint of laborers, workers are supplying their sweaty

labor up to the point where the utils of satisfaction lost by working that last bit of time needed to produce the last unit of the good (output price/value) exactly equals the firm’s MC of producing the last unit of the good supplied11. 3. Putting these two equations together, we see that MU = MC . This means that the utils gained from the last unit of good consumed exactly equals the utils lost for sweaty labor required to produce that last unit. It is exactly this condition – the marginal gains of society from the last unit consumed equal the marginal costs of

11

The MC (of the firm) is the price/wage paid to the laborer for the cost they incur in terms of the utility of leisure forgone and the disutility of the sweaty labor needed to produce the last unit of the good.

187

society for that last unit produced – which guarantees that a competitive equilibrium is efficient. Hence, both the allocation and utilization of resources are optimal under perfect competition. To the contrary of this quality of perfect competition, as we will see in subsequent chapters, the imperfect markets (monopoly, monopolistic competition, and oligopoly) fall short of reaching such an efficient and welfare-maxima equilibrium.

5.6 LESSON SUMMARY # A perfectly competitive firm is the one that can sell an amount of output it wants at

the ongoing market price. Competitive firms are assumed to maximize their profit (or minimize losses). To maximize profits, the competitive firm will choose that output level at which price equals marginal cost of production, i.e., P = MC . Diagrammatically, the competitive firm’s equilibrium will come where the rising MC curve intersects its horizontal demand curve. # Variable (or avoidable) costs must be taken into account in determining firm’s

short-run decision to shutdown or to continue operation. Below some critical price (the shutdown point), the firm’s revenue will not even cover the variable cost that could be saved completely if it shuts down. Rather than end up losing more than fixed costs by operating, it would be better if the firm shuts down and produce nothing when price falls below the shutdown price. # The rising part of the MC curve of each firm above the shutdown price is its supply

curve. To obtain the supply curve of a group of independent competitive firms, we add horizontally their separate supply curves. Hence, the supply curve of an industry represents the marginal cost curve for the competitive industry as a whole. # In the long run when firms are free to enter and leave the industry and where no one

firm has any particular advantage of skill or location, competitors will compete and eat away any excess profits earned by existing firms in the industry. So as free entry

188

means P cannot persist above the breakeven point and free exit means P cannot fall below that point, all firms just earn normal profit in long-run equilibrium. # The analysis of competitive markets shed light on the efficient organization of a

society. Productive and allocative efficiency occur when there is no way of recognizing production and distribution such that anyone’s satisfaction or profit can be improved without hurting others. A different way of defining efficiency (in production and consumption) is to say that it is a situation where no single individual/firm is made better off without making other(s) worse off. # Under ideal conditions, a competitive economy attains allocative efficiency. This

occurs because of three step conditions: (a) First, when consumers buy goods in market, they buy that amount for which the marginal utility just equals the price. (b) Secondly, competitive producers choose to supply goods where the marginal cost is just equal to price. (c) Since, MU = P and MC = P , it follows that MU = MC . Thus, the social cost of producing a good under competition just equals its marginal utility.

5.7 REVIEW QUESTIONS I. Discussion Questions

1. Why a competitive firm is a price taker? 2. What is the difference between market period (momentary run) and short run? 3. What is the profit maximizing (or loss minimizing) condition of a competitive firm? 4. Does a firm is in its short run equilibrium necessarily mean that the firm enjoys excess profit? 5. Interpret this dialogue. A) “How can competitive profits be zero in the long run? Who will work for nothing?” B) It is only the excess profits that are wiped out by competition. Managers get paid for their work; owners get a normal return on capital in competitive long run equilibrium – no more, no less.” 6. Under what condition should perfectly competitive firm supply goods at a loss? 7. What are the three conditions for the efficiency of perfect competition?

189

II. Workout Questions

1. Suppose the market price a competitive firm faces in the short-run is Birr 10. Moreover, its fixed cost is Birr 40. The output level ( Q ) and the corresponding variable costs ( TVC ) are as given in the table below. Q

0

5

10

15

20

25

30

35

40

45

50

VC

0

30

60

80

120

170

225

287

340

410

520

(A) Compute the TR, MR, TC, ATC, AVC, and profit or loss of the firm at each

level of production and present the results in a table similar to Table 5.1. (B) What will be the short run equilibrium output? (C) Show the short run equilibrium and profit levels graphically using the marginal

approach (D) Derive the short run supply curve of the firm from your graph in (C) and

interpret the implication of the lowest point from which the supply curve begins. (E) Calculate the producer’s surplus at the equilibrium. (F) Calculate the elasticity of demand at the equilibrium price and output.

2. Suppose there were 80 identical firms operating in the industry in the short run. Price was Birr 10. Further assume that the short run profit the existing competitive firms enjoy attracts 80 more firms to enter the industry. The increase in output following the entry of the new firms has also dampened market price from Birr 10 to Birr 8. (A) What will be the long run equilibrium output of a firm and the industry? (B) How much profit do firms in the industry enjoy? What is the implication of the

profit? (C) Derive the short run and long run supply curves of the industry. (D) What happens to the consumers’ surplus?

3. Suppose the short run market price a competitive firm faces is Birr 9 and the total cost of the firm is: TC = 200 + Q + 0.02Q 2 . Answer the questions that follow. 190

(A) Calculate the short run equilibrium output and profit of the firm. (B) Derive the MC, ATC, and AVC and calculate the values at the short run

equilibrium output. (C) Calculate the producers’ surplus at the equilibrium output. (D) Find the output level that will make the profit of the firm zero.

191

CHAPTER SIX PURE MONOPOLY LESSON STRUCTURE 6.1

Introduction

6.2

Chapter Objectives

6.3

The Characteristic Features of Pure Monopoly

6.4

Origins of Monopoly Power

6.5

The Short Run Equilibrium of a Pure Monopolist

6.6

The Long Run Equilibrium of a Pure Monopolist

6.7

Price Discrimination

6.8

A Multi-Plant Monopolist

6.9

The Social Cost of Monopoly

6.10 Lesson Summary 6.11 Review Questions

6.1 INTRODUCTION Monopoly is a market structure in which there is only one supplier in the market (industry). Since there is only one firm in the market, the demand and supply curves of a monopoly are also the industry demand and supply curves. When there is only one firm in the market, the firm is unlikely to take the market price as given. Instead, the monopolist would recognize its influence over the market price and choose that level of price and output that will maximize its overall profit. Of course, a monopoly firm cannot choose price and output independently. Because, for any price, the monopoly will sell only what the market will bear. If it chooses high price, consumers will demand small quantity. In other words, the demand behavior of consumers will constrain the monopolist’s choice of price and quantity. 192

6.2 CHAPTER OBJECTIVES After learning this chapter, you will be able to: # compare and contrast a purely monopolistic market to that of perfect competition; # identify the sources of monopoly power; # examine the equilibrium conditions for a single plant and multi-plant monopolist; # examine price discriminations applied by monopoly firms; and, # figure out the social cost of monopoly power.

6.3 THE CHARACTERISTIC FEATURES OF PURE MONOPOLY The main features characterizing pure monopoly are: 1. The existence of a single seller and many buyers in the market. 2. The product or service of a monopolist is unique or does not have close substitutes. 3. A monopolist is a price-maker for its product/service. 4. Entry to and exit out of the market are difficult (if not impossible). This is because since the fixed cost (for potential entrants) will be larger while the marginal and average costs for the existing monopolist will be smaller, this serves as a barrier for new entrants. Such a situation is referred to as natural monopoly. Some other sources of monopoly power will be discussed in Section 6.4. As a result of these features, price will be higher and output will be lower than competitive market. Moreover, a monopolist operates at a point where P(= AR) is greater than MC . This is regarded as the inefficiency of monopoly in terms of resource allocation and maximizing social welfare. The price of a monopolist is derived from the profit maximization equation as follows.

π = TR − TC = PQ − TC ------------------------------------------------------- (1) The equilibrium of a monopoly is MR = MC which is similar to the equilibrium condition of perfectly competitive market discussed in Chapter Five. 193

We know that MC =

dTC . And, MR is derived as follows: dQ MR =

dTR dPQ = ---------------------------------------------- (2) dQ dQ

Since monopoly price is not constant as in the case of perfectly competitive market, price cannot be equal to MR for a monopolist. Using the product rule of differentiation the MR is:

MR =

PdQ QdP QdP + = P+ ------------------------------- (3) dQ dQ dQ

Alternatively, equation (3) can also be written as: ⎡ QdP ⎤ MR = P ⎢1 + ⎥ --------------------------------------------- (4) ⎣ PdQ ⎦

Recall that the price elasticity of demand (ε P ) =

QdP dQ P . . Hence, the expression in dP Q PdQ

equation (4) is the reciprocal of price elasticity of demand. Thus, the above equation can be written as: ⎡ 1⎤ MR = P ⎢1 + ⎥ ------------------------------------------------ (5) ⎣ εP ⎦

In equation (5), the one in the right hand side of the bracket, i.e., L =

1

εP

is known as the

Lerner Index, which measures the degree of the monopoly power. The formula indicates

that monopoly power is the reciprocal of the price elasticity of demand. Or, it implies that the extent to which the monopolist can influence the price of its product depends upon the elasticity of demand for its product. That is, the lower the price elasticity of demand the greater the monopoly power to increase price, and vice-versa.

194

Since the price elasticity of demand for normal goods is always negative12, equation (5) can also be written as: ⎡ 1 ⎤ MR = P ⎢1 − ⎥ -------------------------------------------- (6) ⎣ /εP /⎦

The above equation will be used to obtain either the monopolist’s price, its MR , or its price elasticity of demand ( ε p ) when any two of the three variables are known. You ⎡ ∆Q P ⎤ should note that, this formula is more relevant than the usual ⎢ . ⎥ in terms of ⎣ ∆P Q ⎦

yielding accurate ε P value for the monopolist’s product unlike when discrete price and output values of a monopolist are given. Finally, the equilibrium condition of a monopoly, MR = MC , is given by: ⎡ 1 P ⎢1 − ⎣ /εP

⎤ ⎥ = MC -------------------------------------------- (7) /⎦

We can also use the elasticity formula to express the optimal pricing policy of a monopolist. The optimal price of a monopolist is: P=

MC ----------------------------------------------- (8) ⎡ 1 ⎤ ⎥ ⎢1 − ⎣ /εP /⎦

Equation (8) indicates that the market price of a monopolist is a markup over its marginal cost; where the amount of the markup also depends on the elasticity of demand. The markup is: 1 ⎡ 1 ⎤ ⎢1 − ⎥ ⎣ /εP /⎦

12

---------------------------------------------------- (9)

Recall that the price elasticity of demand for normal goods is always negative due to the law of demand, which postulates an inverse relationship between price and quantity demanded. Moreover, since the importance of elasticity is to understand the magnitude of responsiveness of consumers to changes in price, it is conventional to use absolute value in order to make it a positive value.

195

Since a monopolist will always operate where the elasticity of demand for its product is elastic due to barriers to entry, we know that / ε P / is greater than unity. Hence, the markup is also greater than one. That is, since / ε P / > 1, 1−

1 /εp /

1 /εp /

< 1. It follows that

– the denominator of equation (9) – is between zero and one. Finally, 1 divided

by a number between 0 and 1 (for instance, 0.5) is greater than one.

6.4 ORIGINS OF MONOPOLY POWER There are several factors that lead to the origin of monopoly power. There are barriers to entry and exit. The four types of barriers are: 1. The minimum efficiency scale (MES); 2. Exclusive (special) knowledge of low cost production or technology; 3. A control over strategic raw materials; and 4. Government may grant a firm an exclusive right to serve the market for a particular product or service. 1) The Minimum Efficiency Scale (MES): MES refers to the level of output that minimizes average cost relative to the market size or market demand. The shape of ATC or MES, which is determined by the technology of production, is an important factor that determines whether a market will operate competitively or monopolistically. If the MES of a technology is very small it means that the technology of production is cheaper. Hence, the smaller the MES relative to the size of the market, the easier will it be for other firms to enter into the market and hence we might expect that competitive condition will prevail and vice versa. Consider the following graphs where the ATC curves and the demand curves of two monopolists with different capacities but facing similar market size in two separate markets/areas are depicted.

196

P

P

ATC

ATC

MC

MC

P*

P*

O

MES

QM

O

Q

A Monopolist with Small MES

MES QM

Q

A Monopoly with Large MES

Figure 6.1: Comparison of MES under Pure Monopoly

In the first graph of Figure 6.1, there is a room for other firms to enter into the market, each charging a price close to P* and operating at a relatively small scale since the MES is less than the market demand, QM. In the second graph, only one firm can make positive profit and the firm will be a monopolist. This is because, the incumbent firm (or the firm already in the market) in the latter case has enough cost advantage to be able to discourage other firms from entering into the industry as compared to the monopolist in the first market. Therefore, we would expect that the first market might operate as a competitive market and the second would operate as a monopolist. Technology may be such expensive that relatively large firms can invest and produce at a lower cost. Another reason is, the size of the market may not allow the existence of more than a single large plant size monopoly. Once a monopoly power is established entry will be difficult because any new entrant must be able to produce at a relatively low cost compared to the already established monopoly. This is likely to result in loss for these potential firms, as it likely corresponds to a price level below the shut-down price. Examples include electricity, telecommunication, and other utilities in our country.

197

Macroeconomic policy of a country can influence the size of the market. If a country follows non-restrictive foreign trade policy, domestic firms may face competition from foreign firms and hence the domestic firms’ power to influence price will be much less. A good example is the competition the Ethiopian Airlines (EAL) faces from foreign Airlines (Airways) in international flights or transporting citizens and foreigners to the outside world. The implication is that if the EAL sets higher fares for international flights, people would prefer to travel through other countries Airlines or Airways and hence EAL would lose its market share. Conversely, if a country follows restrictive trade policy in the sense to protect domestic firms from foreign competitors so that the market size is limited to the citizens of its own country, then monopolistic practices are more likely to take hold. Hence, if monopoly arises due to large MES relative to the market size and it is not feasible to increase the size of the market and/or if there is no threat from foreign firms, then the industry is liable to some form of regulation or government intervention. In practice, both regulation of monopoly power and government intervention are costly. Thus, from society point of view, the question should be weather the deadweight loss of monopoly exceeds the cost of regulation or not. In developing countries, the deadweight loss of monopoly is greater than the cost of regulation. Therefore, in most developing countries, public provision of essential public services and utilities for development is preferred to leaving them in the hand of monopolists.

2) A control over strategic raw materials:

If a firm has exclusive control over a given raw material, the firm can become a monopoly.

3) Exclusive (special) knowledge of low cost production or technology:

A firm may develop or invent a unique product or technique of production and steps to keep this from being copied by competitors by having patent right or copy right. Thus, patent right or copy right will give a firm an exclusive right to produce a certain

198

commodity or to use a certain production technology and as a result the firm becomes a monopoly. A monopolist established due to the above factors, will have enough cost advantage to be able to discourage other firms from entering into the industry. The incumbent firm (or the firm already in the market) may also, under certain conditions, threaten potential entrants that it will cut prices if they attempt to enter into the industry.

4) Government may grant a firm an exclusive right to serve the market for a particular product or service:

A monopoly established due to the right given by the government to serve solely a given market or geographical area within its jurisdiction is called franchise. The best example of such a monopoly in Ethiopia is the National Lottery.

Check Your Progress 1. What are the differences between a perfectly competitive firm and a pure monopolist? 2. Discuss the different sources of monopoly power.

6.5 SHORT RUN EQUILIBRIUM OF A PURE MONOPOLIST The short run cost functions confronting a monopolist are identical with those faced by a competitive firm. That is, the short run MC, AVC, and ATC are all U-shaped while AFC is hyperbola. Wide U-shape of ATC, as in the case of the monopolist in the second market in Figure 6.1, implies that the capacity of the plant installed is very high. Unlike perfectly competitive market, however, a unique supply curve cannot be derived from the MC curve of a monopolist. This is because since entry to and exit from the market is difficult, the price of a monopolist cannot reach the minimum point of AVC (or , MC = AVC ) . The probability that monopoly price will be equal or below the 199

minimum of AVC depends on the strategy of the incumbent monopolist to discourage potential entrants by reducing its price. As mentioned under Section 6.3, the profit maximization rule is the same in both perfect competition and monopoly markets. Accordingly, a monopolist will choose to produce output level for which MR = MC in order to maximize profit. Moreover, price is equal to average revenue ( P = AR ) in both markets. Nevertheless, the marginal revenue of a monopolist at any unit of output/production is always less than its price ( MR < P ) unlike that of price-taker competitive firms where marginal revenue is equal to the ongoing market price ( MR = P ). In order to understand the short run equilibrium price and output of a monopolist it is important to derive the relationship between demand, price, and average and marginal revenue curves. The relationship can be best explained mathematically. To this end, recall that there is an inverse relationship between price and quantity demand for normal goods. This law of demand implies that the demand function for normal goods is downward sloping. If we assume a linear demand function (for simplicity), we would have a demand function of the form: Q = α − βP; where alpha (α ) and beta ( β ) are constant numbers. From this demand function, the following important points and relationships can be derived: 1) The slope of the demand function:

dQ = −β dP

2) The price elasticity of demand: ε P =

dQ P P . = −β . dP Q Q

3) The inverse demand function: Q = α − βP ⇒ Q − α = − βP. Rearranging this gives:

P=

α 1 α 1 − Q , setting = a; = b we get β β β β

P = a − bQ . From this a is the vertical intercept and − b is the slope. 4) Total revenue: TR = P.Q

TR = (a − bQ)Q TR = aQ − bQ 2 200

5) Average revenue: AR =

TR aQ − bQ 2 = = a − bQ = P Q Q

6) Marginal revenue: MR =

dTR = a − 2bQ ; where a is the vertical intercept (the level dQ

of MR when output is equal to zero) and − 2b is the slope of the MR curve. From equation (6) above, it is also clear that the MR of a monopolist is a downward sloping straight line with the same vertical intercept13 as the price equation or inverse demand function but with a slope which is twice steeper. That is, the slope of the price equation in equation (3) is − b and that of the MR in equation (6) is − 2b . Furthermore, elasticity of demand will be unitary and that of the TR will be at its maximum when MR = 0. [See Figure 6.2]. P, MR, TR

/εp / >1

TR

/εp / =1

P*

/εp / <1 DD

Q

MR=0

Figure 6.2: The Relationship among Demand, ε p , MR, and TR under Monopoly

You should also note that a monopolist would always operate in the short run in the region where the price elasticity of demand in elastic. This implies that a monopolist will not set a price that will make elasticity of demand inelastic ( / ε P / < 1 ) (i.e., below P * in the above figure), unless it has a strategy of deterring potential firms from entering into the market (by reducing price below P * ). The reason is that the MR of a monopolist (the 13

Note that the values of price and MR in equations (3) and (6) corresponding to Q = 0, give the vertical intercept equal to a , and this is the only point at which P = MR for a pure monopolist.

201

additional revenue accrued to the monopolist due to sale of an additional unit of output) will be negative when the price elasticity of demand is less than one (or inelastic). With the short run profit maximization condition of a monopoly firm at hand, we can now determine the short run equilibrium price and output as well as the profit of a monopolist. To do so, we need to have information on either (1) a serious of output sold (quantity demanded for its product) and price per unit of output (or in short unit price) charged by a monopolist of our concern or (2) the market demand function it faces for its product and its total cost function, representing the plant capacity installed, to meet the current and future demand. The main procedures one should follow in order to determine the monopolist’s short run equilibrium price, output, and profit depending on the type of information provided are illustrated using two examples for normal goods. Example 1: Suppose we have information only about the amount of output supplied by a

hypothetical ABC monopolist and the unit price consumers are charged per output demanded (as shown in columns 1 and 2 of Table 6.1). Having this information, the short run equilibrium output and price of the monopolist as well as its profit associated to each amount of output sold are determined as shown in the same table (Table 6.1). Table 6.1: The Short Run Equilibrium of a Monopolist Qd

Price(P)

TR

MR

TC

ATC

MC

Profit

5

24.80

124.00

-

214.50

42.90

-

-90.50

13

23.20

301.60

22.20

228.90

17.61

1.80

72.70

23

21.20

487.60

18.60

264.90

11.52

3.60

222.70

36

18.60

669.60

14.00

341.60

9.49

5.90

328.00

50

15.80

790.00

8.60

462.00

9.24

8.60

328.00

60

13.80

828.00

3.80

572.00

9.53

11.00

256.00

66

12.60

831.60

0.60

647.46

9.81

12.58

184.14

72

11.40

820.80

-0.18

730.40

10.14

13.82

90.40

202

From the table above, the maximum profit is 328. The monopolist achieves this profit when the demand for its product is either 36 or 50 units. Despite this, the monopolist will supply 50 units of output in stead of 36 since the short run profit maximization condition or the equality of its marginal revenue and marginal cost ( MR = MC = 8.6 ) holds only at this output level. Accordingly, the short run equilibrium price is Birr 15.8. Furthermore, the equilibrium output, price, and profit of the monopolist can be depicted graphically using the marginal approach as follows. Profit

P, MC, ATC

ATC MC

15.8 9.24

E

8.60

50

Q

After determining price, the marginal revenue and marginal cost of the monopolist, we can also calculate the price elasticity of demand using equation (6) of Section 6.3. That is, price elasticity of demand is calculated as follows: ⎡ 1 ⎤ MR = P ⎢1 − ⎥. ⎣ /εP /⎦

Substituting the values of MR and P , we get: ⎡ 1 ⎤ 8.6 = 15.8⎢1 − ⎥. ⎣ /εP /⎦

Rearranging this gives: 8.6 = 15.8[ ⇒ 8.6 =

/ ε P /− 1 ]. /εP /

15.8 / ε P / − 15.8 /εP /

⇒ 8.6 / ε P / = 15.8 / ε P / − 15.8 ⇒ 8.6 / ε P / − 15.8 / ε P / = −15.8

203

⇒ −7.2 / ε P / = −15.8.

Finally, we get the price elasticity of demand: /εP / =

. − 15.8 = 2.19 4 ≈ 2.2. − 7.2

This implies that the price elasticity of demand for the product of this hypothetical monopoly is elastic. The value can be interpreted as: As a result of one percent increase in the price of the monopolist’s product, consumers will decrease their consumption by about 2.2 percent, and vice-versa14. As mentioned earlier, we also know that the monopolist’s price is always greater than the MC of producing an additional unit of output. The issue is thus to know by how much the

price of the monopolist is markup over its MC ? The markup can be determined using equation (9) of Section 6.3 as follows: Markup =

=

1 ⎡ 1 ⎢1 − ⎣ /εP

⎤ ⎥ /⎦

1 ⎡ ⎤ ⎢ 2.19 4− 1⎥ ⎢ 2.19 4. ⎥ ⎣ ⎦ .

=

=

1 ⎡ 1 ⎤ ⎢1 − . ⎥ ⎢⎣ 2.19 4 ⎥⎦ 1 ⎡ ⎤ ⎢ 1.19 4 ⎥ ⎢ 2.19 4. ⎥ ⎣ ⎦ .

=

1 = 1.84 0.544303798

Example 2: Unlike the above example, suppose that we now have information only about

the market demand function a hypothetical XYZ monopolist faces for its product and its

total cost function. Suppose the demand and cost functions are Q = 60 − 0.5 P and TC = 48 + 3Q 2 , respectively. The steps involved in order to obtain the short run output, price, and profit of the monopolist are given below. Solution:

(A) The steps involved to find the short run equilibrium output and price levels are: 14

Note that the accuracy of this value of / ε P / can be verified by substituting this value into equation (6) to obtain MR = 8.6 or into equation (7) to obtain MC = 8.6 .

204

1st: Find the inverse demand function.

Q = 60 − 0.5 P

⇒ Q − 60 = −0.5P ⇒P=

60 Q − = 120 − 2Q 0.5 0.5

2nd: Find TR.

TR = PQ TR = (120 − 2Q)Q = 120Q − 2Q 2 3rd: Find MR.

MR =

dTR = 120 − 4Q dQ

4th: Find MC. MC =

dTC d (48 + 3Q 2 ) = = 6Q dQ dQ

5th: Equate MR to MC.

⇒ 120 − 4Q = 6Q ⇒ 120 = 6Q + 4Q ⇒ 120 = 10Q ⇒ Q = 12. 6th: Substitute Q = 12 into the inverse demand function to obtain price.

P = 120 − 2Q = 120 − 2(12) = 96 Therefore, the short run equilibrium output and price of the monopolist are 12 and 96 respectively. (B) The profit of the monopolist is calculated as:

π = TR − TC

π = [120Q − 2Q 2 ] − [48 + 3Q 2 ] . Substituting Q = 12 , we get:

π = [120(12) − 2(12) 2 ] − [48 + 3(12) 2 ] = [1440 − 2(144)] − [48 + 3(144)]

205

= [1440 − 288)] − [48 + 432] = 1152 − 480 = 772.

(C) In order to show the equilibrium price, output, and profit graphically we need to follow the following steps. 1st: Find the value of MR and MC at the equilibrium output, Q = 12

MR =

dTR = 120 − 4Q dQ

MC =

MR = 120 − 4(12) = 72

dTC = 6Q dQ

MC = 6(12) = 72

2nd: Find ATC at Q = 12 ATC =

TC 48 + 3Q 2 = Q Q

ATC =

48 + 3(12) 2 48 + 432 480 = = = 40. 12 12 12

3rd : Graphic solution:

P, MR, MC, ATC

MC 96

72

ATC

E

40

12

30

206

Q

Check Your Progress On the basis on the information given in Example 2 above, answer the questions below. 1. Calculate the price elasticity of demand and the markup at the short run equilibrium output and price of the monopolist XYZ. 2. What will be the value of the price elasticity of demand when MR is 40 and price is 80? 3. What level of output makes the MR zero? What will be the price level and TR at this output level? How about the elasticity of demand?

6.6 THE LONG RUN EQUILIBRIUM OF A PURE MONOPOLIST In the long run, the monopolist will have time to expand its plant size or to use the existing plant optimally to produce output that will maximize profit. Hence, if the monopolist earns excess profit in the short run with the existing plant(s), it must determine weather a plant of different size will earn larger profit in the long run or not. Since entry is blocked, it is not necessary or a must for a monopolist to operate at optimal scale. In other words, there is nothing that induces to install additional plant size so as to operate at the minimum of LAC (where LAC will be equal to the LMC) and obtain normal profit if not its own strategy. The LMC is the change in total cost associated with the change in output when all factors including the plant scale vary or when the plant size itself is changed (in the long run). To understand how the long run marginal cost (LMC) and long run average cost (LAC) behave, assume that a monopolist has installed two plant sizes in the short run in order to meet the current and future demand for its product. Furthermore, assume that the change in quantity demanded to a change in price is constant. Given the relevant information in Table 6.2 below, Table 6.3 helps us compute the LMC and LAC.

207

Table 6.2: Information for Deriving LMC Q

MR

TC1

TC2

0

-

1

34.5

11

14.25

2

33.5

14

15.00

3

32.5

19

16.25

4

31.5

26

18.00

Table 6.3: Determination of the LMC from Short Run and Long Run Plants

Q P

TR

MR

TC1

11.00 14.25

1

34.5 34.5

-

2

34.0 68.0

TC2

SAC1 SAC2 SMC1 SMC2 LMC LAC

Profit

11.00

14.25

-

-

-

11.00 23.5

33.5 14.00 15.00

7.00

7.25

3

0.75

3

7.00

54.0

3

33.5 100.5 32.5 32.50 16.25

6.33

5.42

5

1.25

2.25

5.42

84.25

4

33.0 132.0 31.5 31.50 18.00

6.50

4.50

7

1.75

1.75

4.50

114.0

The problem of the monopolist is which of the two plants should be used in the short and long run in order to maximize profit. If the monopolist wants to produce only one unit of output in the long run, then the best choice would be to use plant one. This is because SAC1 < SAC 2 or TC1 < TC 2 . If the monopolist wants to produce two units of output, it should also choose to use the first plant. Since the first plant is chosen to produce the first and second units, the SMC of the first plant will also be the LMC up to the second unit of output. However, the monopolist has to choose plant 2 if it wants to produce 3 units of output for SAC 2 < SAC1 or TC 2 < TC1 . In this case, the LMC of the monopolist will be the

difference between the total costs of a plant chosen to produce 3 units output (plant 2) and 2 units of output (plant 1). As indicated in the eleventh column of the third row of Table 6.3, this will be equal to 2.25, which is TC2 (16.25) less TC1 (14). Furthermore,

208

since the plant 2 is the one to be chosen to produce 4 units of output, the LMC will be 1.75 (the SMC of the plant 2). As indicated in Figure 6.3, the optimal plant of the monopolist in the long run is plant 2 whose SAC 2 is tangent to the LAC curve and the long run equilibrium is established at point E 2 where MR = SMC2 = LMC. The corresponding unit price is P4. It is thus clear from Figure 6.3 that the monopolist’s point of optimal operation is on the falling part of LAC. To the contrary, producing 4 units of output in the long run (or equilibrium point E 2 ) is not optimal from the viewpoint of the society for the monopolist is not operating at the minimum point of the LAC (envelop) curve. This is because producing 5 units at point E3 where the LAC is at its minimum and where LAC = LMC = SMC2 = p (similar to the case of a competitive firm in the long run) will

increase the output of the monopolist and reduce selling price thereby eliminating the excess profit that could be enjoyed by producing 4 units of output and implying a normal (zero) profit. This implies that since there is output restriction or since the monopoly firm does not produce at its full capacity, price is greater than MC in pure monopoly in the long run. This situation, which arises due to restriction of output, is called the Deadweight Loss (DWL) of pure monopoly. This will be discussed in detail under a latter section. Nevertheless, the monopolist may prefer to produce at point E3 only if there are firms planning to enter into the market and hence the monopolist wants to discourage them or block entry by reducing price.

209

SAC1 SMC1

P1 P2

LMC SMC2

SAC2

LAC

P3 P4

E1 E3

E2

DD MR

1

2

3

4

5

Q

Figure 6.3: The Long Run Equilibrium of a Pure Monopolist

Given the information in the table below, we can obtain the monopolist’s price if the price elasticity of demand is given for any level of output. Once the monopolist’s price is known, we can also determine the total revenue and the associated profit (or loss) for both the short run and long run. Q

MR

TC1

TC2

0

-

-

-

1

18

12

17.5

2

12.5

22.8

23.8

3

4

30

26.7

4

3.6

45

30.3

For example, let us calculate the price and short and long run profit (or loss) of the .

monopolist if the price elasticity of demand of producing 4 units of output is 1. 6 . 210

Solution:

1st: Find the unit price of the monopolist when selling 4 units of output ( P4 ) .

MR4 = P4 (1 −

1 /εP /

)

3.6 = P4 (1 −

1 .

)

1. 6

3.6 = P4 (1 − 0.625) 3.6 = P4 (0.375) 3 .6 0.375 . P4 = 9.6 P4 =

2nd: Find the profit of the monopolist when selling 4 units of output. Since, plant 2 is used to produce 4 units of output we should consider the total cost15 of the second plant to calculate profit (π 4 ) .

π 4 = TRQ 4 − TC Q 42 π 4 = PQ − 30.3

π 4 = Q4 ( P4 − SACQ 42 ) OR

π 4 = 9.6(4) − 30.3 π 4 = 38.4 − 30.3 = 8.1

π 4 = 4(9.6 −

π 4 = 4(2.025) = 8.1

3rd: Find P3 , P2 , and P1 sequentially

MR4 =

TR4 − TR3 P4Q4 − P3Q3 = Q4 − Q3 Q4 − Q3

3.6 =

38.4 − P3 (3) 4−3

3.6 = 38.1 − P3 (3) − 34.5 = −3P3

P3 =

15

30.3 ) 4

34.5 = 11.5 3

The subscript at the end of the total cost indicates the plant used.

211

MR3 =

TR3 − TR2 P3Q3 − P2 Q2 = Q3 − Q2 Q3 − Q2

4=

11.5(3) − P2 (2) 3−2

4 = 34.5 − P2 (2) 4 − 34.5 = −2 P2

P2 = MR2 =

30.5 = 15.25 2

TR2 − TR1 P2 Q2 − P1Q1 = Q2 − Q1 Q2 − Q1

12.5 =

15.25(2) − P1 (1) 2 −1

12.5 − 30.5 = − P1 P1 = 18

4th: Find profit by considering the total cost of a plant used to produce each level of output.

π 3 = TRQ 3 − TC Q 32 π 3 = PQ − 26.7 π 3 = 11.5(3) − 26.7 = 7.8 π 2 = TRQ 2 − TC Q 21 π 2 = PQ − 12.5 π 2 = 15.25(2) − 22.8 = 7.7

π 1 = TRQ1 − TC Q11 π 1 = PQ − 12 π 1 = 18(1) − 12 = 6 Therefore, from the above profit figures we can conclude that the short run equilibrium level of output of the monopolist is 2 units for it yields higher profit as compared to producing and selling one unit of output (7.7 > 6). In the long run, however, as the profit

212

level from producing and selling 4 units of output (8.1) is greater than that of producing and selling any other level of output (1, or 2, or 3), the monopolist will produce and sell 4 units of output and thus operates at a point where MR = SMC2 = LMC = 3.6.

Check Your Progress 1. Can a pure monopolist earn a positive economic profit in the long run? Why or why not? Discuss. 2. Is the long run profit-maximizing condition (rule) of a monopolist the same as the short run one?

6.7 PRICE DISCRIMINATION 6.7.1 Definition and Necessary Conditions

Price discrimination is the practice of selling a certain product or service of a given quality at different prices to different consumers for reasons unrelated to costs. It involves charging different prices for the same or different quantities of a given quality of a product or service to different class of buyers, and/or in different markets based on elasticity of demand. Price discrimination is workable when the following three conditions are realized: (A) Monopoly power: The seller must be a monopolist or at least possess some degree of

monopoly power over the commodity or service. That is, it must have some ability to control the production of the good or service and its price. (B) Market segregation: The seller must be able to segregate buyers into separate classes

where each group has a different willingness or ability to pay for the product or service. This segregation of buyers is based on the difference in elasticity of demand. (C) No resale: The monopolist must be able to separate (or segment) the two or more

markets and keep them separate so that it is impossible for one buyer to resale the product to another. 213

6.7.2 Types of Price Discrimination

Economists usually consider three types of price discriminations. These are: first, second, and third degree price discriminations. First degree (perfect) price discrimination: This means that the monopolist sells

different units of output at different prices and prices may differ from person to person. This means that the monopolist sells each unit of output to that individual who values it most highly at the maximum price that he/she is willing to pay for it. This turns out that perfect price discrimination produces an efficient level of output. To prove this, note that a perfectly price discrimination monopolist must produce an output level where price is equal to the marginal cost ( P = MC ) . If price is grater than the MC, then it would mean that there is someone who is willing to pay more than what it costs to produce an extra unit of output; so, why not produce that extra unit and sell to that person? However, perfect price discrimination is an idealized concept as the word “perfect” might suggest. But it is interesting theoretically since it gives us an example of a resource allocation mechanism (other than perfectly competitive market) where Pareto efficiency is achieved. By Pareto efficiency, we refer to the situation where all the possibilities of making someone better off without making others worse off have already been carried out. There are few real life examples of perfect price discrimination. A small town doctor who charges different prices to his/her patients based on their ability to pay is one of the closest examples of perfect price discrimination. Other examples include, the prevailing differential prices to different classes or ranks of train transportation; international air transportation (the payment for economic and business class are different though two people fly in the same airplane); cinema hall; football match etc. For example, the prices can be differentiated as first class or rank ticket-Birr 60, second rank-Birr 40; and third rank-Birr 30 to watch a football match in a stadium; a movie in a cinema hall, or to travel through train.

214

Second degree (non-linear) price discrimination: This means that a monopolist sells

different units of output for different prices; but every individual who buys the same amount of output pays the same price. In other words, price differs across the quantity of goods consumed or depending how much is bought but not across people like first degree price discrimination. The most common examples of this type of price discrimination are the practice of charging different prices for consumption at different bands (blocks) and bulk discounts in public utilities.

For example, the price of electricity often depends on how much is consumed. Suppose an electricity supplier charges consumers a progressive rate across bands say for the first 50KWH each at a price of 0.2730 cents; for the next 50 KWH each at 0.2921 cents; and the next 100KWH each at 0.4508 cents. In this case, the payment/ bill of the household who consumed 200 KWH a month is: Bill = [(50 x0.2730) + (50 x0.2921) + (100 x0.4508)] = 13.6 + 14.605 + 45.08 = 73.335 The above example indicates that the price charged by the hypothetical electricity supplier is progressive in a sense price per unit increases as consumption increases from one band to another. That is, any output or service consumed within the next higher consumption band will cost higher price and hence the decision to consume more depends on the willingness and ability to pay of the consumer. Contrary to the example above, sometimes monopolists offer discounts for bulk purchases, in most cases across blocks. The price charged by such type of monopolist is regressive because price per unit decreases as consumption increases from one block to another. In this case, consumers who purchase large quantities of the monopolist’s product or service may face a price equal to MC at some level of purchase. From the viewpoint of social welfare, since there is consumption at a price greater than MC (at least for some consumers), there are some ways to make some consumers in the market better off without making others worse off. That is, not all the possibilities to

215

maximize social welfare are exhausted. Hence, second degree (non-linear) price discrimination is Pareto inefficient. Third degree price discrimination: This occurs when a monopolist charges different

prices for the same commodity in different markets; but every unit of output sold in a given market is sold at the same price. For this to happen markets must be kept separate (no resale) and the elasticity of demand of these two or more markets must be different. Third degree price discrimination is the most common form of price discrimination. An example of charging different prices in different markets is found in international trade when a nation sells its commodity abroad at a lower price than in its domestic market. This is referred to as dumping. The reason for dumping is that the demand for a monopolist product is more elastic abroad because substitutes are available from other nations whereas there can be import restriction in domestic market making the domestic demand less elastic. The key issue of third degree price discrimination is: “How does a monopolist determine the optimal price to charge in each market?” The answer is based on the conditions/assumptions that consumers in each market are not able to resale the good in another market, and that there are different elasticities of demand in the two (or more) markets. To illustrate this with an example, assume that a monopolist sells its product only in two markets. Furthermore, let p1 (q1 ) and p2 (q2 ) be the inverse demand functions of market 1(domestic) and market 2 (abroad), respectively. In addition, let c(q1 + q2 ) be the cost of producing the output. Thus, the profit maximization problem of the monopolist is: Max p1 (q1 )q1 + p 2 (q 2 )q 2 − c(q1 + q 2 ) ---------------------------------------- (1) q1 ,q2

The optimal solution must have: MR1 (q1 ) = MC (q1 + q 2 ) – Equilibrium in market 1 -------------------------- (2a) MR2 (q 2 ) = MC (q1 + q 2 ) – Equilibrium in market 2 ------------------------- (2b)

216

Equations 2a and 2b say that the MC of producing an additional unit of output must be equal to the MR in each market. If the MR in market 1 exceeds MC, it pays to expand output sale in market 1 and vice versa. Using the standard elasticity of demand formula for MR, we can write the profit maximization condition as: ⎡ ⎤ 1 p1 (q1 ) ⎢1 − ⎥ = MC (q1 + q2 ) ⎣ / ε P (q1 ) / ⎦ ⎡ ⎤ 1 p2 (q2 ) ⎢1 − ⎥ = MC (q1 + q2 ) ⎣ / ε P ( q2 ) / ⎦ ⎡ ⎤ ⎡ ⎤ 1 1 These two conditions imply that: p1 (q1 ) ⎢1 − ⎥ ⎥ = p2 (q2 ) ⎢1 − ⎣ / ε P ( q2 ) / ⎦ ⎣ / ε P (q1 ) / ⎦

⎡ ⎤ 1 ⎢1 − ⎥ p1 (q1 ) ⎣ / ε P (q2 ) / ⎦ ------------------------------------------------------------- (3) ⇒ = p2 ( q2 ) ⎡ ⎤ 1 ⎢1 − ⎥ ⎣ / ε P (q1 ) / ⎦

If price in the first market is greater than price in the second market ( p1 > p 2 ) , then each side of equation (3) must be greater than 1 and thus we must have: ⎡ ⎤ ⎡ 1 1 ⎤ ⎥ ------------------------------------------------ (4) ⎢1 − ⎥ < ⎢1 − ⎣ / ε P (q1 ) / ⎦ ⎢⎣ / ε p (q2 ) ⎥⎦ This implies that, 1 1 -------------------------------------------------- (5) > / ε P (q1 ) / / ε p (q2 )

Therefore, / ε p (q1 ) < / ε p (q2 ) / ---------------------------------------------------------- (6) Equation (6) says that the market with a lower elasticity of demand (price insensitive) must have the higher price while the price sensitive market will have lower price. The validity of this argument is illustrated with the help of a numerical example below. Example: Suppose the demand functions a monopolist faces in market 1 and market 2

are q1 = 55 − p1 and q 2 = 70 − 2 p 2 , respectively. Furthermore, assume that its cost function is TC = 5Q + 20 . With this information at hand let us:

217

1) determine q1 , q 2 , p1 , and p 2 that maximize the profit of the monopolist; 2) calculate the profit of the monopolist from selling its product in the two markets; 3) determine the price elasticities of demand in the two markets; and 4) show the outputs and prices of the two markets using the back-to-back diagram Solution:

From the given cost function, the common marginal cost is: MC = 1.

Outputs and prices of the monopolist (a) For market 1

1st: Find the inverse demand function. q1 = 55 − p1 p1 = 55 − q1

2nd: Find TR1 = p1 q1 TR1 = (55 − q1 )q1

= 55q1 − q12 3rd: Find MR1 =

dTR1 dq1

MR1 = 55 − 2q1 4 : Equate MR to MC. th

MR1 = MC 55 − 2q1 = 5 − 2q1 = 5 − 55 − 2q1 = −50

q1 =

50 = 25 2

5th: Substitute q1 = 25 in the inverse demand function. p1 = 55 − q1 = 55 − 25 = 30

(b) For market 2

218

dTC = 5. dQ

1st: Find the inverse demand function q 2 = 70 − 2 p 2 q 2 − 70 = −2 p 2 p2 =

70 q 2 − = 35 − 0.5q 2 2 2

2nd: Find TR. TR2 = p 2 q 2 TR2 = (35 − 0.5q 2 )q 2

=35q2-0.5q22 3rd: Find MR. MR2 =

dTR2 dq 2

MR2 = 35 − q 2

4th: Equate MR to MC. MR2 = MC 35 − q 2 = 5

− q 2 = 5 − 35 q 2 = 30

5th: Substitute q 2 = 30 in the inverse demand function. p 2 = 35 − 0.5q 2 p 2 = 35 − 0.5(30) p 2 = 35 − 15 = 20

2.

The profit of the monopolist:

From the above solution the monopolist will sell 25 units of output in market 1 and 30 in market 2. The price of a unit of output in market 1 is Birr 30 while it is Birr 20 in the second market. Thus, total profit will be

π = (TR1 + TR2 ) − TC = [(q1 p1 + q 2 p 2 ) − (5Q + 20)]

Since Q = q1 + q 2 the profit equation is also

219

π = [(q1 p1 + q2 p2 ) − (5(q1 + q2 ) + 20)] = [(25 x30) + (30 x 20) − (5(25 + 30) + 20)]

= 750 + 600 − (5(55) + 20) = 1350 − (275 + 20) = 1350 − 295 = 1055

3.

Price elasticity of demand Market 1 q1 = 55 − p1

Slope:

dq1 = −1 dp1

/ ε p1 / =

dq1 p1 x dp1 q1

/ ε p1 / = − 1x / ε p1 / = −

30 25

30 = − 1.2 = 1.2 25

Market 2 q 2 = 70 − 2q 2

Slope:

dq 2 = −2 dp 2

/ ε p2 / =

dq2 p2 x dp2 q2

/ ε p2 / = − 2x / ε p2 / = −

20 30

. 40 = − 1.3 3 = 1.33 30

220

The above result tells us that demand is more elastic in market 2 as compared to market 1. Therefore, as described in equation 4 to 6 earlier in this section, the monopolist charges lower price in market 2 compared to market 1. 4.

Back to back diagram

The relationship between output and prices in the two markets can be represented using what is known as the Back to back diagram as follows. P

P1=30 P2=20

MC = 5 DD1 q1

MR1

MR2 q1=25

DD2

q2=30

Market 1

q2

Market 2

Figure 6.4: The Back to Back Diagram of Third Degree Price Discrimination

From the above figure, it is clear that the market with lower elasticity of demand (market1) has higher price. This implies that the monopolist will charge high price in the market in which quantity purchased is less responsive to price changes16.

16

For further reading on this topic, see Koutsoyiannis, A. (1998). “Modern Microeconomics”. 2nd edition, pp 197.

221

6.8 A MULTI-PLANT MONOPOLIST So far it has been assumed that a monopolist owns and produces by means of only one plant. Nevertheless, it is also possible for a monopolist to install more than one plant and hence cost conditions may differ from one plant to another. Such a monopolist is called a multi-plant monopolist. The problem of such a monopolist is the allocation of production among the different plants (say, between plant 1 and plant 2 in the case of two plants). The monopolist’s profit maximization rule is equating MR MC. However, we have only one marginal revenue function and many marginal cost functions for a multi-plant monopolist. For the case of a monopolist with two plants, we have: MC1 = The marginal cost function of plant 1 MC 2 = The marginal cost function of plant 2 MC = Common or the multi-plant marginal cost function

The profit maximization rule of this multi-plant monopolist is depicted in Figure 6.5. MC1

MC

MC2

DD MR O

q1

q2 Q O

Q* = q1+q2

Each Plant

Q

Multi-plant

Figure 6.5: Short Run Equilibrium of a Multi-Plant Monopolist

Example: Given the price and MC figures of two plants for each level of output,

determine the MR, the common MC, and the total output a multi-plant monopolist should produce, and also find how much should be produced by each plant. 222

Table 6.4: The Short Run Equilibrium of a Multi-Plant Monopolist

Q

P

MR

MC1

MC2

MC

1

5.00

5.00

1.92

2.04

1.92

2

4.50

4.00

2.00

2.14

2.00

3

4.10

3.30

2.08

2.24

2.04

4

3.80

2.90

2.16

2.34

2.08

5

3.55

2.55

2.24

2.44

2.14

6

3.35

2.35

2.32

2.54

2.16

7

3.20

2.30

2.40

2.64

2.24

8

3.08

2.24

2.48

2.74

2.24

9

2.98

2.18

2.56

2.84

2.32

10

2.89

2.08

2.64

2.94

2.34

The common MC is obtained by arranging the MC figures in ascending order. The profit maximizing level of output the multi-plant monopolist will produce is 8 units of output. It is at this level of output that the MR will be equal to the common MC. Once the total output to produce is determined, the monopolist will produce 5 units using plant 1 and 3 units using plant 2. This is because profit is maximized when MR = MC1 = MC2 = MC. Mathematical Example:

Suppose a monopolist faces a linear demand function Q = 200 − 2 P for its product. Let, the cost functions of the two plants be: TC1 = 10q1 and TC 2 = 0.25q 22 , respectively. Given the above information, find q1 , q 2 , P and the profit of the multi-plant monopolist.

223

Solution:

1st: Find the inverse demand function, TR, and MR: Inverse demand function Q = 200 − 2 P

Q − 200 = −2 P P = 100 − 0.5Q ; Where Q = q1 +q2 Total revenue

TR = PQ TR = (100 − 0.5Q)Q = 100Q − 0.5Q 2 Marginal revenue MR =

dTR dQ

= 100 − Q 2nd: Find the marginal cost of the two plants; MC1 and MC 2 MC1 =

dTC1 d (10q1 ) = = 10 dq1 dq1

dTC 2 d (0.25q22 ) MC2 = = = 0.5q2 dq2 dq2 3rd: Equate the MR to the two MCs ( MR = MC11 and MR = MC 2 ) MR = MC1

100 − Q = 10 100 − (q1 + q 2 ) = 10 100 − q1 − q 2 = 10 ------------------------------------------------------------- (1)

MR = MC 2 100 − Q = 0.5q 2 100 − (q1 + q 2 ) = 0.5q 2

224

100 − q1 − q 2 = 0.5q 2 ------------------------------------------------------- (2)

4th: Solve the two equations in step 3 using simultaneous equation procedures to obtain the output levels to be produced by each plant. ⎧100 − q1 − q2 = 10 ⎨ ⎩[100 − q1 − q2 = 0.5q2 ](× − 1) ⎧100 − q1 − q2 = 10 ⇒⎨ ⎩− 100 + q1 + q2 = −0.5q2 ⇒ 10 − 0.5q2 = 0

⇒ q2 =

10 = 20 . 0.5

Substituting this output level into one of the two equations we found under step 3, we get the optimal output that should be produced using plant 1. Let us substitute q 2 = 20 into the first equation17. 100 − q1 − q 2 = 10 100 − q1 − 20 = 10 80 − q1 = 10

q1 = 80 − 10 = 70

5th: Calculate the market price by substituting Q = q1 + q 2 = 20 + 70 = 90 into the inverse demand function derived from the market demand in step one. P = 100 − 0.5Q P = 100 − 0.5(90) P = 100 − 45 = 55

6th: Finally, calculate the profit of the multi-plant monopolist using the total revenue – total cost approach. It can be calculated in two ways: either by substituting total output (Q) into the total revenue function or obtaining total revenue by multiplying price and total output (Q) as follows:

π = TR − (TC1 + TC 2 ) 17

After obtaining q1 and q2 you should check whether substituting them into both equations will satisfy the equality. Do this before proceeding to the next step!

225

= (100Q − 0.5Q 2 ) − (10q1 + 0.25q22 ) = [100(90) − 0.5(90) 2 ] − [10(70) + 0.25(20) 2 ]

= [9000 − 4050] − [700 + 100] = [4950 − 800] = 4150

OR

π = PQ − (TC1 + TC 2 ) = (55 × 90) − (10q1 + 0.25q22 ) = 4950 − [10(70) + 0.25(20) 2 ] = 4150

6.9 THE SOCIAL COST OF MONOPOLY Is the existence of a monopolist evil? The answer to this question depends on the pricing decision of the monopolist. If the monopolist charges a single price, the answer is “YES”! If the monopolist charges different prices based on the willingness to pay (WTP) [or if the monopolist sells each unit at the maximum price consumers are willing to pay], i.e., if the monopolist can exercise the first degree price discrimination, the answer to the above question would be “NO”! That is, a monopolist exercising the first degree price discrimination produces a Pareto efficient outcome as it expands output to the level where P = MC. If the monopolist exercises the second or the third degree price discrimination (block pricing, bulk discount, market segregation based on differences in price elasticity of demand), the outcome is Pareto inefficient though the inefficiency is minimal. To sum up, the existence of a monopolist charging a single price is evil; that of a second or third degree price discriminator is less evil; and that of a first degree price discriminator is consistent with social welfare maximization (just like a perfect competitor). We have seen in Chapter Five that a remarkable outcome of a perfectly competitive market is an efficient resource allocation, which results in a maximum social welfare and maximum employment. This is because the equilibrium of a competitive firm is at the

226

equality of price and the MC of producing the good which implies that the marginal utility (MU ) of goods consumed is also equal to the price ( p ) charged. Hence, if P = MC (i.e., allocation efficiency) and MU = P (i.e., maximization of consumers’

welfare), then MU = MC = P 18. An alternative way to understand the efficiency of the competitive market is through using the concepts of consumers’ surplus (CS) and producers’ surplus (PS). Consumers’ surplus is the difference between what consumers are willing to pay for

different levels of quantity demanded (proportional DD curve; see DDP in the figure below)19 and what they actually paid to consume QE amount of output (prorata DD curve; see DD A in the figure below). In Figure 6.6, it is shown by the area to the left of the perceived DD curve and above the equilibrium price or (prorata DD curve) or simply by area PE EP1 . In other words, it represents money not spent by consumers who have the willingness to pay a price higher than the equilibrium price or it is the savings of the consumers from buying QE at equilibrium price PE .

P

P MC=SS

P1

CS

P1

E

CS DDA

PE

MC=SS

PS

PE

PS DDP

DDP

D

QE

Linear Demand and Supply Curves

18 19

E

QE

Non-Linear Demand and Supply Curves

Refer back to Chapter Two on how the equality of P = MU is derived based on the ordinalist argument. The perceived demand curve can be linear or non-linear. Because determining CS and PS from nonlinear demand and supply functions requires some advanced knowledge in integral calculus, which is beyond the scope of the course, we restrict ourselves to the discussion of consumers and producers surpluses using linear demand and supply functions for the mathematical example in this section.

227

Figure 6.6: Consumers’ Surplus and Producers’ Surplus

The MC of producing a good represents the supply curve. Equating the MC or the supply curve that passes through point E to demand (as in the above graphs) gives the producers’ surplus (PS). Producers’ surplus is the area above the MC curve but below the equilibrium

price ( PE ). The PS indicates the difference between the market price (what competitive firms charge per unit) and the MC (what competitive firms actually incur for producing different quantities of output). Put differently, it is the money that suppliers receive solely because of selling each unit of output (below QE) at a price above what they incur to produce that unit. In Figure 6.6, it is shown by the area PE ED. These being the CS and PS in a perfectly competitive market, the social cost of monopoly arises due to the fact that a monopolist operates inefficiently as compared to perfect competition in the sense that price under monopoly ( PM ) is greater than price under perfect competition ( PC ) or PM > PC and the monopolist’s optimum level of output (QM ) is less than output under perfect competition (QC ) or QM < QC . This is because unlike the competitive firms that equate P = MC in order to determine equilibrium output and price, which in turn always makes P = MR , a monopolist determines its equilibrium output and price by equating MR = MC and hence its price is greater than both marginal revenue and marginal cost.20 As a result, some part of the CS and PS in a perfectly competitive market are lost when the market is monopolized by a single firm. These losses in consumers’ and producers’ surpluses due to monopoly power are known as the social cost or the Dead Weight Loss (DWL) of monopoly. Consider the graph below.

20

Note that P > MC implies that the value of the good measured in terms of market price is greater than the social cost measured in terms of MC.

228

P

MC

F PM

A

PC

B

EC

DDC=MRC=MC

EM

DDM D MRM QM

QC

Q

Figure 6.7: The social Cost (Dead Weight Loss) of Monopoly

The above graph shows the change in the CS and PS when the market is changed from competitive to monopoly or from monopoly to competitive. Consider the first case. As the market changes from perfect competition to monopoly, the CS goes down by area PC EC APM [area ABEC since they lose some surplus from the reduction in the units that were used to be sold under perfect competition by QC − QM ; and area PC BAPM since consumers are now getting all the units they buy at a higher price]. Alternatively, we can consider what happens when a monopolist is replaced by a perfectly competitive firm. As the market changes from monopoly to perfect competition, the CS goes up by area PC EC APM [area PC BAPM since consumers are now getting all the units they used to buy under monopoly at a lower price; and area ABEC since they now gain some surplus from the additional units (QC − QM ) that are now sold in the market]. Let us continue our discussion with the first approach – where a perfect competitor is replaced by a pure monopolist.

229

The PS, on the other hand, goes up by area PC BAPM due to the higher price on the units that were already being sold; and goes down by EM BEC due to the loss from the decline in the level output as the firm is not selling (QC − QM ) now. The area PC BAPM is just a transfer from the consumers to the monopolist, and hence one side of the market (the producer) is made better off while the other side (consumers) is made worse off; but, the total surplus does not change as a result of this transfer. However, the areas ABEC and EM BEC represent the Dead Weight Loss (DWL) due to monopoly behavior. The DWL provides a measure of how much worse off people are paying the monopolist’s price than paying the completive price. The DWL due to monopoly like that of the DWL due to tax increase measures the value of the lost output by valuing each unit of lost output at a price that people are willing to pay for a unit. In other words, as we move from competitive to monopoly output, the sum of the distance between the demand curve and the MC curve generates (gives) the value of the lost output (QC − QM ) due to monopoly behavior. The total area between the two curves (area AEM EC ) is the DWL when moving from competitive to monopoly output. Clearly, an economy is performing well when it generates much to the consumer surplus and an inefficient situation is one in which the maximum amount of consumers’ surplus is squeezed out of the system. Numerical Example:

Assume that there is a tendency of moving from competitive to monopoly output. If the demand and total cost functions are Q = 100 – 2P and TC = 14Q + 2Q2 respectively, A. Determine PC, QC, PM, and QM. B. Show the equilibrium Q and P you obtained in (A) above graphically. C. Calculate the CS and PS under competitive and monopoly market structures. 230

D. Calculate the part of CS transferred to the monopolist due to inefficiency of monopoly. E. Calculate the social cost (net loss or DWL) of monopoly. Solution:

A. Equilibrium Q and P: (i) In perfectly competitive market: P = MC 50 – 0.5Q = 14 + 4Q 50 – 14 = 4Q + 0.5Q 36 = 4.5Q QC = 8 PC = 50 – 0.5Q

OR

PC = 14 + 4Q

= 50 – 0.5(8)

= 14 + 4(8)

= 50 – 4

= 14 + 32

PC = 46

PC = 46

(ii) In monopoly market: TR = P.Q = (50 – 0.5Q).Q = 50Q – 0.5Q2 MR =

∂TR = 50 − Q ∂Q

MC =

∂TC = 14 + 4Q ∂Q

Equate MR to MC: MR = MC 50 – Q = 14 + 4Q 50 – 14 = 4Q + Q 36 = 5Q

QM = 36/5 = 7.2 PM = 50 – 0.5Q = 50 – 0.5(7.2)

231

= 50 – 3.6 PM = 46.4

B. Graphical presentation of the results under (A)

C.

Consumers’ and producers’ surplus: (i) Under perfect competition: 1 (50 − 46)(8) 2 1 ⇒ CS = (4)(8) = 16. 2 CS =

1 (46 − 14)(8) 2 1 ⇒ PS = (32)(8) = 128. 2 PS =

(ii) Under monopoly: 1 (50 − 46.4)(7.2) 2 1 ⇒ CS = (3.6)(7.2) = 12.96. 2 CS =

232

1 (42.8 − 14)(7.2) + (46.4 − 42.8)(7.2) 2 1 ⇒ PS = (28.8)(7.2) + (3.6)(7.2) 2 ⇒ PS = 103.68 + 25.92 = 129.6 PS =

D. The amount of surplus transferred from consumers to the monopolist: (PM – PC) x QM = (46.4 – 46) x 7.2 = 0.4 x 7.2 = 2.88 E. DWL due to monopoly Method (i) The DWL is represented by the shaded area in the figure under (B) above. The area of 1 (46.4 − 42.8)(8 − 7.2) 2 the triangle shaded is: 1 ⇒ DWL = (3.6)(0.8) = 1.44 2 DWL =

Method (ii) Alternatively, DWL is the (negative) net change in consumers’ and producers’ surpluses. Changes in CS = CS under monopoly – CS under perfect competition. That is, ∆CS = 12.96 − 16 = −3.04 (LOSS!)

Changes in PS = PS under monopoly – PS under perfect competition. That is, ∆PS = 129.6 − 128 = 1.6 (GAIN!)

Thus, the net change (NCh) in consumers’ and producers surpluses is: NCh = ∆CS + ∆PS ⇒ NCh = −3.04 + 1.6 = −1.44

The net change is negative – indicating an overall loss to the economy: ⇒ DWL = 1.44

Method (iii) DWL = CS not transfered toProducers + PS Lost

DWL =

1 1 ( PM − PC )(QC − QM ) + ( PC − MC at QM )(QC − QM ) 2 2

233

DWL =

1 1 (46.4 − 46)(8 − 7.2) + (46 − 42.8)(8 − 7.2) 2 2

1 1 (0.4)(0.8) + (3.2)(0.8) 2 2 ⇒ DWL = 0.16 + 1.28 = 1.44 DWL =

Conceptually, all the three methods are the same.

Check Your Progress 1. What are the necessary conditions for the practicability of price discrimination? 2. Is there any relationship between the prices a monopolist engaged in third degree price discrimination charges and the price elasticities of demand in the segregated markets? Discuss. 3. Differentiate between the concepts of price discrimination and multi-plant monopolist. 4. How do you compare the social welfare aspects of perfectly competitive and monopoly market structures?

6.10 LESSON SUMMARY # When a single firm produces all the output in a given industry then we have an

imperfect market structure called monopoly, which is the exact opposite of perfect competition. Unlike a competitive firm a monopolist is a price maker. As a result, a monopolist faces a downward sloping demand curve. # Economies of scale or decreasing average costs are the major sources of imperfect

competition in pure monopoly. When the minimum efficient size of plant is larger relative to the national or regional market, the cost conditions of the monopolist produce barriers to entry and hence monopoly power emerges. In addition to declining costs, other forces leading to market imperfections such as legal

234

restrictions in the form of patents or government regulations are also barriers to entry/competition. # There is a spectrum between perfect competition and natural monopoly. Natural

monopoly occurs when average costs are falling for successive units of output so that the industry requires a single most efficient firm. Few industries come close to this condition today - perhaps local utilities like telephone, water, electricity etc. # From a monopolist's demand curve, we can easily derive its total revenue. From the

schedule or curve of total revenue, we can easily derive its marginal revenue – the extra revenue resulting from the sale of an extra unit of output. For a monopolist, marginal revenue will fall short of price ( MR < P ) because of the loss on all previous units of output that will result when it is forced to drop price in order to sell an extra unit of output. # A monopolist will find maximum profit position where the last unit it sells brings in

extra revenue just equal to its extra cost. This same MR = MC result can be shown graphically by the intersection of MR and MC curves. Regardless of whether a monopolist is a single plant or multi-plant monopolist the equality of marginal revenue and marginal cost must hold at the equilibrium. # A monopolist may sell its product or service of a given quality to different

consumers at different prices for reasons unrelated to costs. Such a practice is called price discrimination. The three necessary conditions that must be fulfilled for price discrimination to take place are: (a) monopoly power; (b) market segmentation; and (c) there should no be resale of products from one market to another. The basis for price discrimination are consumers’ ability to pay (first degree or perfect price discrimination); quantity of output consumed (second or non-linear price discrimination); and elasticity of demand (third degree price discrimination). # Exercise of monopoly power also leads to economic waste when price rises above

marginal cost. This is because a monopolist produces where MR equal MC and consequently produces less output than where MC equals price (less than the point of allocation efficiency). In other words, a monopolist does not produce the optimal level of output where the social cost (as measured by MC ) is equal to the value of the good to consumers or social welfare (as measured by P = MU ). Rather, the

235

monopolist is keeping its output a little in short supply. It does not produce up to the point of P = MC because to do so would require lowering price to all consumers, which would make the monopolist lose some profit. So, society does not get as much of the monopolist’s output as it wants in terms of the good’s marginal cost and marginal value to consumers. The losses in consumers' and producers' surpluses due to monopoly power are known as the social cost or the Dead weight Losses (DWL) of monopoly.

6.11 REVIEW QUESTIONS I. True or False Questions with Justification(s).

1. The lower the value of the MR of a monopolist the higher will be the degree of its monopoly power. 2. The lower the value of the price elasticity of demand for a monopolist product the higher will be the markup. 3. We can derive the short run supply curve for a monopolist, provided that the minimum AVC is known. II. Discussion Questions

1. How many price discriminations are there under pure monopoly? What are they? 2. Does the difference in payment by spectators for the same movie or football match in a stadium represent an example of price discrimination? Why or why not? 3. Why is that it is meaningless to ask what price will a monopolist charge for its product? 4. What kind of economic and technological conditions are conducive to the emergence of monopoly power? 5. Why a monopolist is better off with price discrimination than without? Under what conditions is it feasible for a monopolist to practice price discrimination?

236

III: Workout Questions

1.

Suppose a hypothetical monopolist facing a linear demand function operates at an output level where the elasticity of demand is negative 3. If the government imposes a quantity tax of Birr 6 per unit, how much will be the new selling price of the monopolist?

2. Given the demand function a single plant monopolist faces and its cost function as: Q = 10 P −3 and TC = 2Q , respectively, A. Determine the short run optimal output, price, and profit of this monopolist. B. Calculate elasticity and mark up price at the equilibrium output and price. C. Show your results in (A) and (B) graphically using the marginal approach. D. Based on your graph in (C), do you think there is a room for entry into the market in which this existing monopoly operates? Why or why not? 3. Advanced: Suppose a multi-monopolist has marginal cost functions MC1 = 20 + 2q1 , and MC 2 = 10 + 5q 2 .

Where, MC1 is the marginal cost of the first plant and MC 2 is the marginal cost of the second plant. Besides, q1 and q 2 represent output to be produced using the first and second plants, respectively. If the monopolist is maximizing its short run profit by producing 5 units of output in the first plant, then: A. What is the monopolist's profit maximizing level of output in the second plant? Show the steps how you have determined q 2 . B. Prepare a schedule similar to 6.3 for both marginal costs for 1 up to 10 output levels and show how you determine the total short run output of the monopolist. 4. Assume that a monopolist has identified two markets such that the inverse demand functions for its product in the two markets are: P1 = 92 − 2q1 , and P2 = 70 − q 2 .

Its total cost function is: TC = 100 + 40Q + 2Q 2 ; Where Q = q1 + q 2 .

237

A.

How much output will the monopolist sell and what price will it charge in the two markets with price discrimination and without price discrimination?

B.

Show the short run optimal outputs and prices in the two markets with price discrimination using back-to-back diagram.

C.

Find the amount of profit the monopolists will earn with price discrimination. What is total profit if the monopolist does not discriminate between the two markets?

D.

Based on the profit figures you obtained in “C” above, are you then convinced that a monopolist is always better off with price discrimination than without? Why or why not?

E.

In which market is the elasticity of demand higher? What is its implication?

F.

Calculate the mark up at the short run equilibrium when the monopolist discriminates. In which market is it higher? Why?

G.

Show that a monopolist charges a price higher than its marginal cost in the two markets.

5. Assuming that the monopolist in Question 4 above has evolved from perfect competition to monopoly. A.

What is the restricted amount of output due to monopoly power?

B.

Calculate the consumers’ and producers’ surplus under perfect competition and monopoly.

C.

What is the surplus transferred from consumers to the monopolist?

D.

Calculate the net social cost (or Dead weight loss-DWL) due to monopoly power or behavior.

E.

Show first, the output and price levels under perfect competition graphically and then shade or label with number (i) consumers’ and monopoly surplus; (ii) surplus transferred to the monopolist; and (iii) the net DWL.

6. If the marginal cost functions of a monopolist were those given for the two plants in Question 3, but if it faces the total market demand function in Question 4, A.

How much output should the multi-plant monopolist produce in each plant?

B.

What will be the price the monopolist charges?

C.

Calculate the monopolist’s profit assuming that TFC of each plant is 30 Birr.

238

REFERENCES )

Dwivedi, D.N. (1997). Microeconomic Theory. 3rd ed. Vikas Publishing House Pvt P

P

Ltd, New Delhi. )

Ferguson, C.E. and Gould J.P. (1989). Microeconomic Theory. 6th ed. Irwin Publications.

)

Henderson, M. and Quandt E. (1980). Microeconomic Theory: A Mathematical Approach. 3rd edition. McGraw Hill. P

P

)

Koutsoyiannis, A. (1981). Modern Microeconomics. 2nd edition. St Martins Pr.

)

Mansfield, E. (1988). Microeconomics: Theory and Applications. Shorter sixth edition. W.W. Norton & Company: New York, London.

)

Pindyck, R. S. and D.L. Rubinfeld (1991). Microeconomics. 8th ed. Macmillan.

)

Salvatore, D. (2003). Microeconomics: Theory and Applications. 4th ed. Oxford University Press, New York.

)

Varian, Hal R. (2002). Intermediate Microeconomics: A Modern Approach. 6th ed. W.W. Norton and Company.

239

ANSWERS TO SELECTED REVIEW QUESTIONS CHAPTER ONE

Part II

because

Part I

1. True

utility from the gamble

1. a

2. True

(= 1600) is exactly the

2. d

3. False

same

3. e

4. False

utility from the safe

4. d

5. False

source (U = 4m = 4*400

5. c

Part III

= 1600).

6. a

4.

d. risk-neutral

7. a

a. Expected income =

8. d

Birr 12,000; Expected

CHAPTER THREE

Part II

utility =10.8 utils.

Part I

1. True

b. She is risk-averse.

1. b

2. False

Because, the expected

2. c

utility from gambling

3. d

CHAPTER TWO

(10.8) < the utility from

4. c

Part I

the

5. a

1. c

income (11).

6. a

2. d

5. X* = 320; Y* = 80

7. b

3. c

6. ε pd = − 1 . Demand 3

8. a

4. c 5. b 6. d 7. d 8. d 9. c 10. a 11. a 12. a

safe

source

of

is price inelastic at the point.

9. c 10. b 11. b

7. a. Birr 400. b. 1600 utils. c. She is indifferent

between buying and not buying the share. This is

240

12. d 13. c 14. a

as

the

her

expected

current

CHAPTER FOUR

At equilibrium, MC* = 9;

(F) Markup in market 1

Part I

ATC* = 6; AVC* = 5.

= 20/17; Markup in

1. b

(C) PS = 800

market 2 = 69/68. It is

2. d

Q = 200 ± 100 3.

higher

3. b

⇒ Q ≈ 26.8; Q ≈ 373.2

because consumers in

4. a

market

in 1

market are

1 less

5. d

CHAPTER SIX

sensitive

6. c

Part I

changes.

7. d

1. True

5. (A) output declines by

8. b

2. True

1 unit (from 8 to 7).

9. d

3. False

(B) *Under perfect

10. a

Part III

competition:

11. d

1.

CS = 21.33; PS = 128

12. b

2. (A) Q* = 10/27; P* =

*Under monopoly:

13. a

3; Π* = 10/27

CS =16.33; PS = 130.67.

14. d

(B) / ε pd / = 3;

15. a

Markup = 3/2 = 1.5

CHAPTER FIVE

Part II 1. (B) Q* = 25. (E) PS = ? (F) / ε pd / = ∞ 2.

3.

Π* = 600.

(A) *With price

discrimination: q1 = 6; p1 = 80; q2 = 1; p2 = 69. * Without price Q = 7; P = 72.67. (B) *With price

(B) MC = 1 + 0.04Q;

discrimination: Π* =171

ATC = (200/Q) + 1

* Without price

+ 0.02Q; AVC = 1 + 0.02Q.

price

(C) CS transferred to

producer = 4.67. (D) DWL = 2.33 6.

4.

discrimination:

3. (A) Q* = 200;

to

discrimination: Π* = 130.67

241

(A) q1 = 410/29 = 14.14;

q2 = 222/29 = 7.66 (B) P = 5464/87 = 62.8. (C) Π = 602.68