Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Managerial Economics & Business Strategy Chapter 3 Quantitative Demand Analysis

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

3-3 The Elasticity Concept  How responsive is variable “G” to a change in variable “S” If E G,S > 0, then S and G are directly related. If E G,S < 0, then S and G are inversely related. If E G,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 E G,S > 0, then S and G are directly related. If E G,S < 0, then S and G are inversely related. If E G,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 D Price Quantity D Price Quantity

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

3-8 Elasticity, Total Revenue and Linear Demand QQ P TR

3-9 Elasticity, Total Revenue and Linear Demand QQ P TR

3-10 Elasticity, Total Revenue and Linear Demand QQ P TR

3-11 Elasticity, Total Revenue and Linear Demand QQ P TR

3-12 Elasticity, Total Revenue and Linear Demand QQ P TR

3-13 Elasticity, Total Revenue and Linear Demand QQ P TR Elastic

3-14 Elasticity, Total Revenue and Linear Demand QQ P TR Inelastic Elastic Inelastic

3-15 Elasticity, Total Revenue and Linear Demand QQ P TR Inelastic Elastic Inelastic Unit elastic

3-16 Demand, Marginal Revenue (MR) and Elasticity  For a linear inverse demand function, MR(Q) = a + 2bQ, where b < 0.  When –MR > 0, demand is elastic; –MR = 0, demand is unit elastic; –MR < 0, demand is inelastic. Q P Inelastic Elastic Unit elastic MR

3-17 Total Revenue Test  TRT can help manage cash flows.  Should a company increase prices to boost cash flow or cut prices and make it up in volume?

3-18 TRT  If elasticity of Demand = -2.3  Cut prices by 10%  Will sales increase enough to increase revenues?  Qd will increase by 23%.  Since the % decrease in price is< % increase in Qd, TR will increase.

3-19 Factors Affecting the Own-Price Elasticity  Available Substitutes  Broad or narrowly defined categories  Time  Expenditure Share

3-20 Mid-Point Formula  For consistency when working from a function whether it is Demand or Supply an average approximation of elasticity is used.  Ep = Q2-Q1/[(Q2+Q1/2]/P2-P1/[(P2+P1/2]

3-21 Cross-Price Elasticity of Demand If E Q X,P Y > 0, then X and Y are substitutes. If E Q X,P Y < 0, then X and Y are complements.

3-22 Cross-Price Elasticity Examples  Transportation and recreation =  Food and Recreation = 0.15  Clothing and food = -0.18

3-23 Predicting Revenue Changes from Two Products Suppose that a firm sells two related goods. If the price of X changes, then total revenue will change by:

3-24 Example  Suppose a diner earns $5000/wk selling egg salad sandwiches and $3000/wk selling French fries. If own price elasticity for egg salad is -3.2 and cross price elasticity between egg salad and French fries is -0.5 what happens to the firms total revenue if it increased the price of egg salad sandwiches by 5%?

3-25 Solution  [5000 x (1+(-3.2)) +((3000 x (-0.5))] x +5%  [5000 x (-2.2) – (1500)) x +5%  [-550 – 75] = -$ 625

3-26 Income Elasticity If E Q X,M > 0, then X is a normal good. If E Q X,M < 0, then X is a inferior good.

3-27 Income Elasticities  Transportation 1.80  Food 0.80  Ground beef, non-fed -1.94

3-28 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!

3-29 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  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?

3-30 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.

3-31 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?

3-32 Answer: Calls Increase! Calls would increase by percent!

3-33 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  If competitors reduced their prices by 4 percent, what would happen to the demand for AT&T services?

3-34 Answer: AT&T’s Demand Falls! AT&T’s demand would fall by percent!

3-35 Interpreting Demand Functions  Mathematical representations of demand curves.  Example: –Law of demand holds (coefficient of P X is negative). –X and Y are substitutes (coefficient of P Y is positive). –X is an inferior good (coefficient of M is negative).

3-36 Linear Demand Functions and Elasticities  General Linear Demand Function and Elasticities: Own Price Elasticity Cross Price Elasticity Income Elasticity

3-37 Example of Linear Demand  Q d = P.  Own-Price Elasticity: (-2)P/Q.  If P=1, Q=8 (since = 8).  Own price elasticity at P=1, Q=8: (-2)(1)/8=

3-38 Log-Linear Demand  General Log-Linear Demand Function:

3-39 Example of Log-Linear Demand  ln(Q d ) = ln(P).  Own Price Elasticity: -2.

3-40 Graphical Representation of Linear and Log-Linear Demand P Q Q D D LinearLog Linear P

3-41 Regression Analysis  One use is for estimating demand functions.  Econometrics – statistical analysis of economic phenomena  Important terminology and concepts: –Least Squares Regression model: –Y = a + bX + e. –Least Squares Regression line: –Confidence Intervals. –t-statistic. –R-square or Coefficient of Determination. –F-statistic. –Causality versus Correlation

3-42 Regression Analysis  Standard error is a measure of how much each estimated coefficient would vary in regressions based on the same underlying true demand relation, but with different observations.  LSE are unbiased estimators of the true parameters whenever the errors have a zero mean and are iid.  If that is the case then C.I.s can be constructed

3-43 Evaluating Statistical Significance  Confidence intervals:  90% C.I.  a +/- 1 SE of the estimate  95% C.I.  a +/- 2 SE of the estimate  99% C.I.  a +/- 3 SE of the estimate  T statistic: ratio of the value of the parameter estimate to its SE.  When the absolute value of the t-statistic is >2 one can be 95% confident that the true value of the underlying parameter is not zero.

3-44 Evaluating Statistical Significance  R-squared – coefficient of determination. Fraction of the total variation in the dependent variable explained by the regression.  R 2 = Explained variation/total variation  R 2 = SS regression / SS total  Subjective measure of goodness of fit.  Remember! degrees of freedom  Adjusted R 2 better indicator of GOF.  AdjR 2 = 1 – (1 – R 2 ) [(n-1)/(n-k)]

3-45 Evaluating Statistical Significance  F statistic – alternative measure of GOF. Provides a measure of total variation explained by the regression relative to the total unexplained variation.  Larger the F-stat the better the overall fit of the regression line to the data.

3-46 An Example  Use a spreadsheet to estimate the following log-linear demand function.

3-47 Summary Output

3-48 Interpreting the Regression Output  The estimated log-linear demand function is: –ln(Q x ) = ln(P x ). –Own price elasticity: (inelastic).  How good is our estimate? –t-statistics of 5.29 and indicate that the estimated coefficients are statistically different from zero. –R-square of 0.17 indicates the ln(P X ) variable explains only 17 percent of the variation in ln(Q x ). –F-statistic significant at the 1 percent level.

3-49 Multiple Regression  MR – regressions of a dependent variable on multiple independent variables.  Caveat: beware of using regression indiscriminately.  Issues: Heteroskedacity, Multi-colinearity, etc.

3-50 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: –Demand functions. –Elasticities. –A host of other things, including cost functions.  Managers can quantify the impact of changes in prices, income, advertising, etc.