Managerial Economics Business Strategy Chapter 3 Quantitative Demand

Managerial Economics & Business Strategy Chapter 3 Quantitative Demand Analysis Mc. Graw-Hill/Irwin Michael R. Baye, Managerial Economics and Business Strategy Copyright © 2008 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

3 -2 Overview I. The Elasticity Concept n n Own Price Elasticity and Total Revenue Cross-Price Elasticity Income Elasticity II. Demand Functions n n Linear Log-Linear III. Regression Analysis

3 -3 The Elasticity Concept • How responsive is variable “G” to a change in variable “S” If EG, S > 0, then S and G are directly related. If EG, S < 0, then S and G are inversely related. If EG, S = 0, then S and G are unrelated.

3 -4 The Elasticity Concept Using Calculus • An alternative way to measure the elasticity of a function G = f(S) is If EG, S > 0, then S and G are directly related. If EG, S < 0, then S and G are inversely related. If EG, S = 0, then S and G are unrelated.

3 -5 Own Price Elasticity of Demand • Negative according to the “law of demand. ” Elastic: Inelastic: Unitary:

3 -6 Perfectly Elastic & Inelastic Demand Price D D Quantity

3 -7 Own-Price Elasticity and Total Revenue • Elastic n Increase (a decrease) in price leads to a decrease (an increase) in total revenue. • Inelastic n Increase (a decrease) in price leads to an increase (a decrease) in total revenue. • Unitary n Total revenue is maximized at the point where demand is unitary elastic.

3 -8 Elasticity, Total Revenue and Linear Demand P 100 TR 0 10 20 30 40 50 Q

3 -9 Elasticity, Total Revenue and Linear Demand P 100 TR 80 800 0 10 20 30 40 50 Q

3 -10 Elasticity, Total Revenue and Linear Demand P 100 TR 80 1200 60 800 0 10 20 30 40 50 Q

3 -11 Elasticity, Total Revenue and Linear Demand P 100 TR 80 1200 60 40 800 0 10 20 30 40 50 Q

3 -12 Elasticity, Total Revenue and Linear Demand P 100 TR 80 1200 60 40 800 20 0 10 20 30 40 50 Q

3 -13 Elasticity, Total Revenue and Linear Demand P 100 TR Elastic 80 1200 60 40 800 20 0 10 20 30 40 50 Q 0 10 20 Elastic 30 40 50 Q

3 -14 Elasticity, Total Revenue and Linear Demand P 100 TR Elastic 80 1200 60 Inelastic 40 800 20 0 10 20 30 40 50 Q 0 10 Elastic 20 30 40 Inelastic 50 Q

3 -15 Elasticity, Total Revenue and Linear Demand P 100 TR Elastic 80 Unit elastic 1200 60 Inelastic 40 800 20 0 10 20 30 40 50 Q 0 10 Elastic 20 30 40 Inelastic 50 Q

3 -16 Demand, Marginal Revenue (MR) and Elasticity P 100 Elastic 80 • For a linear inverse demand function, MR(Q) = a + 2 b. Q, where b < 0. • When Unit elastic 60 Inelastic 40 n 20 n 0 10 20 40 MR 50 Q n MR > 0, demand is elastic; MR = 0, demand is unit elastic; MR < 0, demand is inelastic.

Factors Affecting Own Price Elasticity n 3 -17 Available Substitutes • The more substitutes available for the good, the more elastic the demand. n Time • Demand tends to be more inelastic in the short term than in the long term. • Time allows consumers to seek out available substitutes. n Expenditure Share • Goods that comprise a small share of consumer’s budgets tend to be more inelastic than goods for which consumers spend a large portion of their incomes.

3 -18 Cross Price Elasticity of Demand If EQ X, PY > 0, then X and Y are substitutes. < 0, then X and Y are complements.

3 -19 Predicting Revenue Changes from Two Products Suppose that a firm sells to related goods. If the price of X changes, then total revenue will change by:

3 -20 Income Elasticity If EQ X, M > 0, then X is a normal good. < 0, then X is a inferior good.

3 -21 Uses of Elasticities • • • Pricing. Managing cash flows. Impact of changes in competitors’ prices. Impact of economic booms and recessions. Impact of advertising campaigns. And lots more!

Example 1: Pricing and Cash Flows • According to an FTC Report by Michael Ward, AT&T’s own price elasticity of demand for long distance services is -8. 64. • AT&T needs to boost revenues in order to meet it’s marketing goals. • To accomplish this goal, should AT&T raise or lower it’s price? 3 -22

3 -23 Answer: Lower price! • Since demand is elastic, a reduction in price will increase quantity demanded by a greater percentage than the price decline, resulting in more revenues for AT&T.

Example 2: Quantifying the Change • If AT&T lowered price by 3 percent, what would happen to the volume of long distance telephone calls routed through AT&T? 3 -24

Answer • Calls would increase by 25. 92 percent! 3 -25

Example 3: Impact of a change in a competitor’s price • According to an FTC Report by Michael Ward, AT&T’s cross price elasticity of demand for long distance services is 9. 06. • If competitors reduced their prices by 4 percent, what would happen to the demand for AT&T services? 3 -26

Answer • AT&T’s demand would fall by 36. 24 percent! 3 -27

3 -28 Interpreting Demand Functions • Mathematical representations of demand curves. • Example: n n n Law of demand holds (coefficient of PX is negative). X and Y are substitutes (coefficient of PY is positive). X is an inferior good (coefficient of M is negative).

3 -29 Linear Demand Functions and Elasticities • General Linear Demand Function and Elasticities: Own Price Elasticity Cross Price Elasticity Income Elasticity

3 -30 Example of Linear Demand • • Qd = 10 - 2 P. Own-Price Elasticity: (-2)P/Q. If P=1, Q=8 (since 10 - 2 = 8). Own price elasticity at P=1, Q=8: (-2)(1)/8= - 0. 25.

3 -31 Log-Linear Demand • General Log-Linear Demand Function:

3 -32 Example of Log-Linear Demand • ln(Qd) = 10 - 2 ln(P). • Own Price Elasticity: -2.

Graphical Representation of Linear and Log-Linear Demand P 3 -33 P D Linear D Q Log Linear Q

3 -34 Regression Analysis • One use is for estimating demand functions. • Important terminology and concepts: n n n Least Squares Regression model: Y = a + b. X + e. Least Squares Regression line: Confidence Intervals. t-statistic. R-square or Coefficient of Determination. F-statistic.

3 -35 An Example • Use a spreadsheet to estimate the following log-linear demand function.

3 -36 Summary Output

3 -37 Interpreting the Regression Output • The estimated log-linear demand function is: n n ln(Qx) = 7. 58 - 0. 84 ln(Px). Own price elasticity: -0. 84 (inelastic). • How good is our estimate? n n n t-statistics of 5. 29 and -2. 80 indicate that the estimated coefficients are statistically different from zero. R-square of 0. 17 indicates the ln(PX) variable explains only 17 percent of the variation in ln(Qx). F-statistic significant at the 1 percent level.

Conclusion • Elasticities are tools you can use to quantify the impact of changes in prices, income, and advertising on sales and revenues. • Given market or survey data, regression analysis can be used to estimate: n n n Demand functions. Elasticities. A host of other things, including cost functions. • Managers can quantify the impact of changes in prices, income, advertising, etc. 3 -38