Wiki #1 - Elasticity Of Demand & Marginal Revenue

Elasticity of Demand including Marginal Revenue and the Relationship with Elasticity of Demand Section 1, Topic 11, Sept. 19, 2007 Steve Jackson Price Elasticity of Demand Price elasticity of demand is defined as the ratio of the relative (or percent) change in the quantity demanded to the relative change in price. Own price elasticity of demand is use to help determine the quantitative impact of price increases and cuts on the firm’s sales and revenues. It is defined by the following equation: EQx,Px = %∆Q x %∆Px Example: What is the own price elasticity of demand if a 50% increase in price results in a 17% decrease in quantity sold? EQx,Px = %∆Q x %∆Px

=

- 17% 50%

=

-0.33

Another way to express the price elasticity of demand is found by the following equation: EQ, P = Q 2 – Q 1 P2 – P1

x

P1 Q1

This equation is useful when the actual changes in quantity demanded and changes in price are given. Example: What is the own price of elasticity of demand if 20 units are sold at a price of $30, and 10 units are sold at a price of $35? =

-3.00

EQ, P = Q 2 – Q 1 P2 – P1

x

P1 Q1

= (10 – 20) (35 – 30)

x 30 20

There are two aspects of the own price elasticity of demand that are important to accentuate: (1) whether it is positive or negative, and (2) whether the absolute value is greater or less than 1. The sign is important to determine the correct increase or decrease in quantity demanded or price. The absolute value is important to determine the degree of elasticity in the relationship. The following rules are important to remember:

inelastic

| EQx,Px| > 1

Demand is elastic

| EQx,Px| < 1

Demand is

| EQx,Px| = 1

Demand is unitary elastic

The quantity demanded of a good is responsive to a change in the price when demand is elastic; relatively unresponsive to a change in price when demand is inelastic. Unitary elastic means that a change in the price of a good will have the same change in quantity demanded. Demand, Elasticity, Marginal Revenue, and Total Revenue To understand the relationship between demand, elasticity, marginal revenue, and total revenue, we will need some further definitions. A basic principle in economics is that total revenue is equal to the quantity multiplied by the price (TR = P x Q). Example: If unit price is $25 and the number of units sold is 30, then what is the total revenue? TR = P x Q = $25 x 30 = $750 Marginal revenue (MR) is the change in total revenue generated by one additional unit of product; therefore, by this definition, MR is the slope of the TR curve. By using calculus methods and taking the derivative with respect to Q in the TR equation, the formula for MR is: MR = P [(1 + E) / E] Example: What is the marginal revenue when price is equal to $30 and the price elasticity of demand is -3? MR = P [(1 + E) / E] = $30 [(1 + (-3)) / (-3)] = $20 The relationship between demand, elasticity, marginal revenue and total revenue can be seen in the table and figures below. This table and figures are from “Managerial Economics and Business Strategy,” by Baye, and have been further expanded from the text by adding the marginal revenue column into the data table and figures. Adding marginal revenue to the figures aids in visually showing the relationship between demand, elasticity, marginal revenue, and total revenue.

From the figures, the following table summarizes price changes and its affect on demand, price elasticity, marginal revenue, and total revenue:

Application of Elasticity of Demand and Marginal Revenue Price elasticity of demand and marginal revenue can be used by firms to estimate and predict the effect of a change in price on total revenue. By knowing the value of the marginal revenue, total revenue can be estimated if sales changes. Institutions such as grocery stores, department stores, entertainment, etc., can use the price elasticity of demand and its relationship to marginal and total revenue to determine the effect of prices changes on revenue and sales. Example Multiple Choice Questions 1. The price of a firm’s product increases from $4 to $7 and the quantity demanded of the product declines from 800,000 to 450,000. The price elasticity of demand for the good is equal to a. b. c. d.

-2 -1 -0.58 0.58

2. The price elasticity of demand for a firm’s product is equal to -1.6. The firm currently sells 3,000 units per day at a price of $3. If the firm increases its product price by 20% then it can expect to sell approximately a. b. c. d.

2,040 units 3,960 units 1,400 units 1,860 units

3. If the price elasticity of demand for a firm’s product is -3 and the product’s price is $6, then marginal revenue is equal to a. b. c. d.

$1 $2 $3 $4

4. Which of the following will occur if a company increases the price of a product when demand is elastic? a. marginal revenue increases b. total revenue decreases c. quantity demanded decreases d. all of the above 5. Which of the following will occur if a company decreases the price of a product when the price elasticity of demand is equal to -0.6? a. b. c. d.

marginal revenue increases quantity demanded increases total revenue decreases both b. and c.

Answers to Multiple Choice Questions 1. The solution is found by using the price elasticity of demand equation as follows: E = [(Q2 – Q1) / (P2 – P1)] x (P1 / Q1) = [ (450,000 – 800,000) / (7 – 4) ] x (4 / 800,000) E = - 0.58 2. The solution is found by using the price elasticity of demand equation as in question 1: -1.6 = [ (Q2 – 3,000) / (3.6 – 3) ] x (3 / 3,000) Solving for Q2,

Q2 = 2,040 units

3. Using the marginal revenue equation with price and price elasticity of demand given: MR = P x [ (1 + E) / E ] = 6 x [ (1 + (-3)) / (-3) ] = $4 4. As found in the figures and tables provided, an increase in price with elastic demand results in a marginal revenue increase, total revenue decrease, and quantity demanded decrease. The correct answer is d. all of the above. 5. When price elasticity is -0.6, then demand is inelastic. A price decrease will result in a marginal revenue decrease, quantity demanded increase, and total revenue decrease. The correct answer is d. both b. and c. References: http://www.tutor2u.net/economics/revision-notes/as-markets-price-elasticityof-demand.html http://ingrimayne.com/econ/elasticity/RevEtDemand.html http://en.wikipedia.org/wiki/Marginal_revenue

http://en.wikipedia.org/wiki/Price_elasticity_of_demand http://www.netmba.com/econ/micro/demand/elasticity/price/ http://www.mackinac.org/article.aspx?ID=1247 Baye, Michael R., "Managerial Economics and Business Strategy", McGrawHill Irwin, 5th Edition. 2006.