Unit Iii Utility Analysis - Economics

UNIT – II UTILITY ANALYSIS Introduction: A consumer demands a good or a service. He demands a good because it gives him utility. Wants – satisfying capacity of a good is called utility. Meaning of Utility: The term utility in economics is used to denote that quality in a commodity or service by virtue of which our wants are satisfied. In other words, want – satisfying power of a good is called utility. Definitions: • According to Jevons, “Utility refers to abstract quality whereby an object serves our purpose. • In the words of Hibdon, “Utility is the quality of good to satisfy a want.” • According to Mrs. Robinson, “Utility is the quality in commodities that makes individuals wants to buy them”. Features: 1. Utility is Subjective: as it deals with the mental satisfaction of a man. A thing may have different utility to different persons. E.g. Liquor has utility for drunkard but for person who is teetotaller, it has no utility. 2. Utility is Relative: As a utility of a commodity never remains the same. It varies with time and place. E.g. Cooler has utility in summer not during winter season. 3. Utility is not essentially Useful: A commodity having utility need not be useful. E.g. Liquor and cigarette are not useful, but if these things satisfy the want of addict then they have utility for him. 4. Utility is independent of Morality: It has nothing to do with morality. Use of opium liquor may not be proper from moral point of view, but as these intoxicants satisfy wants of the opium – eaters, drunkards, they have utility. Concepts of Utility: 1) Initial Utility: The utility derived from the first unit of commodity is called initial utility. It is obtained from the consumption of the first unit of a commodity. It is always positive. 2) Total Utility: The aggregate of utility obtained from the consumption of different units of a commodity, is called Total utility. Tux = f (Qx) Tux = total utility of x is a function (f) of quantity of commodity x.

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3) Marginal Utility: The change that takes place in the total utility by the consumption of an additional unit of commodity is called marginal utility. MUnth = Tn – Tn-1 or MU = change TU/ change Q MUnth = Marginal utility of nth unit. Tn = total utility of n units. Tn-1 = total utility of n-1 units Change TU = change in total utility Change Q = change in the quantity of commodity Marginal utility can be: a) Positive Marginal Utility: If by consuming additional units of commodity, total utility goes on increasing, then marginal utility of these units will be positive. b) Zero Marginal Utility: If the consumption of additional unit of commodity causes no change in the total utility, it means the marginal utility of additional unit is zero. c) Negative Marginal Utility: If the consumption of an additional unit of a commodity causes fall in total utility, it means the marginal utility is negative. Relation between Total Utility and Marginal Utility: Total utility is the summation of the marginal utilities of different units of a commodity. TU =

MU

Total utility is summation of Marginal utility Table: Quantity 0 1 2 3 4 5 6

Total Utility 0 8 14 18 20 20 18

Marginal Utility 8–0=8 14 – 8 = 6 18 – 14 = 4 20 – 18 = 2 20 – 20 = 0 18 – 20 = -2

Description Initial Utility Positive Utility Zero Utility Negative Utility

Table shows that: a) As more and more units of commodity is consumed, the marginal utility derived from each successive unit goes on diminishing. But the total utility increases up to a limit.

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b) Marginal utility of the first four units being positive, the total utility goes on increasing. Thus as long as the marginal utility of the commodity remains positive, total utility goes on increasing. c) Marginal utility of the fifth unit is zero. In this situation total utility (20) will be maximum. This situation also represents point of saturation. d) Marginal utility of the sixth unit is negative. As a result of it, total utility of six units of the commodity falls from 20 to 18 units. Total Utility Curve [A] Y

OY – Axis Utility, OX – Axis Quantity

O

Figure A • TU represents Total utility • It slopes upwards upto point F means TU is rising upto the consumption of 4 unit. • From point F to G TU is constant • Point G represents maximum total utility. • After point G, TU slopes downwards, meaning there by utility becomes negative and total utility begins to fall.

X

Marginal Utility Curve [B] Y

O

X

Figure B • MU represents Marginal Utility • It slopes downwards from left to right; MU of successive units goes on diminishing. • Upto fourth unit of commodity, MU goes on diminishing but TU goes on increasing. • At the fifth unit MU curve touches OX – axis, MU utility is zero and TU is maximum. • After fifth unit MU curve intersects Ox – axis and slopes downward. Means that

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Can utility be measured? It can be attempted to measure by two methods: 1. Measurement in terms of Money: In order to measure the utility in terms of money, it is estimated what amount of money a man is willing to pay for a thing. 2. Measurement in terms of Units: Prof. Fisher has used the term, “Util”, as a unit for the measurement of utility. In this method utility is expressed in Utils. Criticism of the Measurement of Utility: It has been criticized by Prof. Samuelson as the value of money keeps changing. Therefore utility cannot be measured definitely in the terms of money. Laws of Utility Analysis: Utility has two main laws:

Law of Diminishing Marginal Utility

Law of Equi – Marginal Utility

LAW OF DIMINISHING MARGINAL UTILITY Law of Diminishing Marginal Utility is the foundation stone of utility analysis. All of us experience this law in our daily life. If you buy pen at any given time, then as the number with you is increasing, the marginal utility from each successive pen will go on decreasing. It is the reality of man’s life which is referred to in economics as Law of Diminishing Marginal Utility. Definitions: • According to Marshall, “The additional benefit which a person derives from a given stock of a thing diminishes with every increase in the stock that he already has.” •

According to Chapman, “The more we have of a thing, the less we want additional increments of it or more we want not to have additional increments of it.”

•

According to Samuelson, “As the amount consumed of good increases, the marginal utility of a good tends to decrease.”

It is clear from the above definitions that at a given time when we go on consuming additional units of a commodity, the marginal utility from each successive unit of that commodity, other things being equal, goes on diminishing in relation to the preceding unit. It is this diminishing tendency of the marginal utility that has been enshrined in the law of diminishing marginal utility.

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Assumptions: 1. Utility can be measured in the Cardinal number system. 2. Marginal Utility of money remains constant. 3. Marginal Utility of every commodity is independent. 4. Every unit of the commodity being used is of same quality and size. 5. There is a continuous consumption of commodity 6. Suitable quantity of a commodity is consumed. 7. There is no change in the income of consumer. 8. There is no change in the price of commodity and its substitutes. 9. There is no change in the tastes, character, fashion, and habits of consumer. Explanation: The law can be explained with the help of the table and figure below: Table No. of Ice Cream Cups Marginal Utility First 4 Second 3 Third 2 Fourth 1 Fifth 0 Sixth -1 Y

Table Shows: • The table shows that first cup of ice cream yields 4utils of marginal utility. • The second cup of ice cream will yield less marginal utility than the first one i.e. 3utils. • Third cup will yield still less MU, say 2utils. • Fourth cup will yield just 1utils of MU. At this stage want may be fully satisfied. • Thus fifth cup will yield zero MU. If you are forced to take sixth cup of ice cream it may upset system and yields negative utility say, -1 util.

A

4

+Ve

3 Point of Saturation 2 1 Zero MU C O

X 1

-1

2

3

4

5

6 B

In the Figure: • OX axis – Ice Cream(Quantity) • OY axis – Marginal Utility(MU) • AB is Marginal Utility Curve (MUC) • It slopes downward from left to right (negative slope) indicating first cup of ice cream 4 utils, second 3 utils, third 2 utils and fourth 1util of marginal utility. Fifth cup of ice – cream yields zero marginal utility. • AB curve touches OX – axis at point C that represents fifth cup of ice cream. • sixth cup of ice cream yields negative marginal utility and so AB curve goes below OX – axis. 5

Exceptions: Law does not apply under the following situations: 1. Curious and rare things Law does not apply to rare or curious things like persons who collect old and rare coins, postage stamps as increasing marginal utility as the stock of these rare articles goes on increasing. They are always keen to obtain more and more units of such things. 2. Misers It seems law does not apply to misers who are out to acquire more and more of wealth. Their desire for money seems to be insatiable. 3. Good book or poem It is said that by reading a good book or listening to a melodious song and a beautiful poem again and again one gets more utility than before. 4. Drunkards It can be said that when a drunkard takes a liquor and intoxicant than as he takes more and more pegs of liquor his desire to have more of it goes on increasing. 5. Initial units When the initial units of a commodity in used in less then appropriate quantity, then the marginal utility from the additional units goes on increasing. In short, Prof Taussig has rightly said that the tendency of law of diminishing marginal utility is so widely relevant that it would not be wrong to call it as universal law. Causes of its application: 1. Commodities are imperfect substitutes. According to this law it applies because commodities are imperfect substitutes. In other word one commodity cannot always be used for other commodity. Example tea in place of coffee or vice versa. 2. Satiability of particular wants Another cause of its application is that there is hardly any particular want which cannot be fully satisfied. As before arriving at saturation point total utility increases at a diminishing rate and at saturation point is no increase in it. 3. Alternative uses Each commodity has many alternative uses. Some uses are more important while others are less. Example every consumer gives first priority to the most important use. If we have to give little quantity of milk, it will be used for feeding the infant only, but if we have large quantity of milk then after feeding the infant rest can be used for making tea for elders or for making curd etc. Importance of the law 1. Basis of the law of consumption Law of diminishing marginal utility is the basis of all law of consumption. There are three laws of consumption: a) Law of equi marginal utility According to this law a consumer does not spend all his income on one commodity. In order to get the maximum

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satisfaction the consumers spends his income in such a way that the last unit of money spent on different commodities yield equal marginal utility. b) Law of demand According to this law a consumer will demand more units of a commodity at low price. c) Concept of consumer surplus According to this concept unit prior to the marginal unity yield more utility. This surplus utility is called consumer surplus. 2. Variety in production and consumption It is because of the operation of the law of diminishing marginal utility that variety in production and consumption is found. Continuous consumption of one commodity will yield less and less marginal utility to the consumers. So every prudent consumer stops the consumption of that good after a particular limit and shift to other commodity. 3. Difference between value in use and value in exchange According to Adam Smith goods having more value in use command low price and those having more value in exchange command high price. It can be explained on the basis of diminishing marginal utility as there is abundant supply of water air etc and the same can be used in large quantity, consequently there marginal utility falls rapidly and so is the price. Thus goods having more value in use have less marginal utility. 4. Price determination Price of every commodity is determined by its demand and supply. Demand for a commodity depends upon its marginal utility. The consumer buys more units only when the price per unit falls. 5. Basis of progressive taxation Progressive taxation system refers to that system of taxation under which rate of taxation increases as the income of person increases. It is so because with increase in income marginal utility of money goes on diminishing. 6. Advantage to the consumer According to this law, in order to get maximum satisfaction from the consumption of a good a consumer should buy only that many units of it whose marginal utility is equal to its price. 7. Basis of redistribution According to this law the fundamental reason of redistribution of income is that marginal utility of money to the rich is less then to poor. So it wealth is redistributed in favor of poor, total welfare of society would increase. Derivation of demand curve with the help of law of diminishing marginal utility: The price that consumer pays for a commodity is equal to its Marginal utility. According to law of diminishing marginal utility, as a consumer goes on purchasing more and more units of a commodity its marginal utility goes on diminishing. As such consumer will buy more units of commodity only when its price goes down. When marginal utility is

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expressed in terms of money, in that case, positive part of marginal utility curve will be the demand curve. Y

[A]

Y

M

[B] D

Diminishing MU M1

P1

Demand Curve

Price M2

P2

M3

P3 D

O

Q1 Q2 Q3 U X O Q1 Q2 Q3 X Quantity Quantity When marginal utility is shown on OY – axis then the curve obtained will be marginal utility curve. In case, price is shown on OX – axis then the curve obtained will be called demand curve as is indicated in figure above. Figure A represents marginal utility curve. Figure B represents demand curve. This DD demand curve has been drawn with the help of marginal utility curve.(MU) Criticism: 1. Cardinal measurement of utility is not possible. The assumption of the law that marginal utility can be measured in cardinal numbers is not correct. In the absence of cardinal measurement one cannot calculate diminishing marginal utility. 2. Marginal utility of money is not constant. According to this law money is taken as the measure of utility. But the marginal utility of money itself never remains constant as money cannot be reliable. 3. Every commodity is not an independent commodity. No commodity is independent, as the marginal utility of one commodity has no effect on the consumption of other commodities. It is very difficult to make precise estimate of marginal utility. 4. Marginal utility cannot be estimated in all conditions Marginal utility of only those commodities can be estimated which are divisible, but in real life many commodities are not divisible. Example, 5. Unrealistic assumption This law is based on many unrealistic assumptions. It is applicable only when the tastes, habits, fashion, income etc. of the consumer remains constant. But in actual life all these are ever changing.

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LAW OF EQUI – MARGINAL UTILITY Law of equi – marginal utility is the second important law of utility analysis. This law point out of how a consumer can get maximum satisfaction out of his given expenditure on different goods. This law concerning the expenditure of the consumer was propounded in 19th century by a French engineer Gossen. Dr Marshall has called it law of Equi Marginal Utility. It states that in order to get maximum satisfaction, consumer should spend his limited income on different commodities in such a way that the last rupee spent on each commodity yield him equal marginal utility. Left witch refer to it as the general principal for maximization of consumer satisfaction. In simple words it is called as law of maximum satisfaction. Definitions: • According to Dr. Marshall, “If a person has a thing which he can put to several uses, he will distribute it among these uses in such a way that it has the same marginal utility in all.” •

According to Prof. Lipsey “The household maximizing utility will so allocate its expenditure between commodities that the last penny spent on each is equal.”

•

According to Samuelson “A consumer gets maximum satisfaction when the ratio of marginal utilities of all commodities and their price is equal.” MU1

MU2 =

P1

MU3 =

P2

P3

If the prices of the commodities are equal, then maximum satisfaction to the consumer can be indicated in the following equation: MU1 = MU2 = MU3 In the above equation MU1, MU2, MU3 refers to marginal utility of the first, second, third commodity and P1, P2, P3 refers to the price of all commodity. Assumptions: 1. Cardinal measurement of utility is possible. 2. Consumer is rational that he wants maximum satisfaction from his income. 3. Income of consumer is constant. 4. Marginal utility of money remains constant. 5. Price of the commodity remains constant. 6. Commodity is divisible into small units. 7. The consumption takes place at a given period of time.

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Explanation: The law can be explained with the help of table and figure below: Rupee Spent 1st 2nd 3rd 4th 5th Y

Table MU of Mangoes 12 10 8 6 4

MU of Mangoes [A]

MU of Milk 10 8 6 4 2

Y

MU of Milk [B]

12

12

10

10

8

Utility

8

6

6

4

4` O

1

2

3

4

5

X

Equi – Marginal Utility Line

O

1

2

3

4

5

X

In the figure above: • OY axis – Marginal Utility, OX – Units of Rupees • The figure indicates that if the income of the consumer is Rs. 5, he will spend Rs. 3 on mangoes and Rs. 2 on milk because third rupee spent on mangoes and second rupee spend on milk yield equal marginal utility i.e. 8utils. • Line adjoins the figure represents equal marginal utility derived from the last rupee spent on both the goods. • By distributing his income on mangoes and milk in this manner the consumer gets total utility of 48 utils. • It will be the maximum total utility derived by the consumer out of his expenditure of Rs.5. • It is by spending his income the consumer in this manner that the consumer will get maximum satisfaction.

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Y 12

MU of Mangoes

Y 12

10

10

8

A

4 D 1 • • • •

2 3 Rupees

E

8

6

O

MU of Milk

4

B

6

Gain C

4

5

F

Loss G

H X

O

1

2 3 4 Rupees

5

X

If the consumer spends his income on mangoes a milk in any other manner, then his total utility will be less than the maximum; as in figure above. OX axis – Rupees OY axis – M. Utility It is evident from the figure that by spending one rupee on mangoes the consumer gains 6utils of marginal utility as shown by ABCD area. Similarly by spending one rupee less on milk, the consumer loses 8utils of marginal utility as shown by EFGH area.

Importance of the law: 1. Consumption Every consumer wants to get maximum satisfaction from his limited means. He spends that last unit of money in a way to get maximum satisfaction. 2. Production Every producer aims at earning maximum profit. A producer must go on substituting various factors until marginal productivity of each factor is equal. 3. Exchange It implies replacing of goods giving less utility with goods giving more utility. Acting upon the law every person will go on substituting goods giving more utility for the ones giving less utility, till the marginal utility of all becomes equal. 4. Distribution It refers to the distribution of national income among the factors of production that is land labor, capital etc. it is done in such a way that in the long run every factor gets share out of national income according to its marginal utility. 5. Public finance The law also has importance in this sphere of public finance, that revenue and expenditure of the sate. It is insured that the marginal benefit of every type of expenditure should be equal. 6. Distribution of income between saving and consumption According to this law income should be distributed between consumption and saving that the last unit of

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money spent on present consumption should yield the same utility as the last unit of money kept in the form of saving. Such a distribution is called optimum allocation. 7. Optimum distribution of commodities Optimum distribution of commodities refers to that distribution, a slight change whereof may diminish the total utility enjoyed by society as a whole. Optimum distribution becomes possible when a commodity is distributed among different persons in such a way that marginal utility derives from each person becomes equal. 8. Distribution of assets: This law helps people distribute their assets in different forms like bank deposits, bonds, stock, share etc. According to this law, investment should be made in different form of assets in such a way that last unit of money invested in each form should yield equal marginal utility. Criticism of the Law: 1. Consumers are not fully rational The assumption that consumers are not fully rational is not correct. Some consumers are idle by nature, and so to satisfy their habits and customs, they sometimes buy goods yielding less utility. Consequently they do not get maximum satisfaction. 2. Consumer is not calculating. The law is based on wrong assumption that while spending his income a consumer constantly calculates the utility derived by him out of each rupee spent. In actual life one hardly comes across such a calculating consumer. So the application of this law is practically difficult. 3. Shortage of goods If goods giving more utility are not available in the market, the consumption will have to consume goods yielding less utility. 4. Influence of Fashion, Customs and Habits Actual expenditure of every consumer is influenced by fashion, customs, and habits. Under their influence, many a time consumer buys more of such goods which give less utility. 5. Ignorance of the Consumer Consumer is ignorant about many things concerning consumption. He is ignorant about right price of goods, less expensive substitute, different uses of goods. The consumer fails to spend his income in a manner that may yield him maximum satisfaction. 6. Indivisibility of Goods The law does not apply to those goods which can not be divided into small parts e.g. Car, LCD etc. 7. Constant Incomes and price Income of consumer is limited as such he can not increase his satisfaction beyond a particular limit. Likewise, prices being constant, he will get only as much of satisfaction as the amount of goods that he can buy with his limited income.

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8. Indefinite Budget period The budget period of consumer is not definite. Budget periods refer to that period in which a consumer has to spend his income of different uses. It may be a month or an year. Goods like TV Set, Refrigerator are bought in one budget period, but they continue to yield utility over many budget periods. 9. Cardinal measurement of utility is not possible Utility can not be measured in cardinal number system. How can a consumer say he would get 12utils of utility from first mango and 10utils from second. Unless the marginal utility is estimated application of the law remains dubious. 10. Change in the marginal utility of money In actual life marginal utility of money may increase or decrease. When a consumer buys more goods, he is left with less amount of money. Smaller the amount of money higher is its marginal utility. As a result of it application of the law will become pretty difficult. 11. Complementary goods The law does not apply to complimentary goods because they are used in fixed proportion. By using less of one commodity, use of other can not be increased. In short, Chapman has rightly said about this law, “We are not, of course, compel to distribute our income according to the law of substitution or Equi-marginal expenditure, as a stone thrown in the air is compelled, in a sense to fall back to the earth but as a matter of fact, we do so in a certain rough fashion because we are reasonable”. Criticism of utility analysis: Economists like Edge worth, Pareto, Hicks, Allen, and Samuelson etc. have criticized utility analysis on the following grounds: 1. Utility is subjective As it relates to man’s psychology. It is not possible to objective about it. But the analysis of consumer’s demand based on it is objective. 2. Cardinal measurement of Utility is not possible Utility cannot be measured in cardinal number system like 1,2,3 because, utility derived from different goods can neither be added or subtracted. 3. Every commodity is not an independent commodity It means that utility of a commodity is very much dependent upon the utility of other commodities. No commodity is independent commodity. 4. Marginal utility cannot be estimated in all conditions It can only be measured with commodities that can be measured which are divisible. 5. Marginal utility of money does not remain constant. As the quantity of money with a person increases, its marginal utility diminishes and as the quantity of money decreases, its marginal utility increases.

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6. Too many assumptions. Practicability of any theory depends on its practical assumptions. Many assumptions like Cardinal number system, independent commodities etc. are unrealistic and impracticable. 7. No division of price effect between income effect and substitution effect As it does not indicate that when as a result of change in price, demand changes, how much of this changed demand is due to change in real income(Income effect), and how much due to substitution of good for the expensive one (Substitution effect). 8. consumer is regarded as computer According to this analysis while spending his money, consumer always compares the amount of gain he will have by way of utility of the commodity purchased with the loss that he will have to suffer by the way of sacrifice of the money spent. But in real life none of us is calculating. 9. Utility analysis breaks down in an under – developed planned economy Utility analysis is based on the assumption that the taste of consumer remain unchanged. it may also be so for a short period only but in long period, consumer’s taste undergo a change. In a planned economy long – term plans are formulated keeping in view a fact that in the long run demand of consumer will change with change in taste. 10. It does not explain giffen’s paradox. As it has no answer to explain as to why demand curve of many inferior goods slopes upward (positive slope) from left to right. In other words, why demand extend with rise in price and why does demand contacts with fall in price. In short, although utility analysis is based on many unrealistic and impractical assumptions, yet being the first theory seeking to determine consumer’s equilibrium, it will continue to occupy an important place. It is worth mentioning that indifference analysis and revealed preference analysis have their genesis in the scathing criticism of cardinal utility analysis.

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