Chapter 3 Quantitative Demand Analysis


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1 Managerial Economics & Business Strategy Chapter 3 uantitative Demand Analysis McGrawHill/Irwin Copyright 2010 by the McGrawHill Companies, Inc. All rights reserved.
2 Overview I. The Elasticity Concept Own Price Elasticity Elasticity and Total Revenue CrossPrice Elasticity Income Elasticity II. Demand Functions Linear LogLinear III. Regression Analysis 32
3 The Elasticity Concept How responsive is variable G to a change in variable S E G, S % G = % 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. 33
4 The Elasticity Concept Using Calculus An alternative way to measure the elasticity of a function G = f(s) is E = G, S dg ds S G 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. 34
5 Own Price Elasticity of Demand E, P % = % P d Negative according to the law of demand. Elastic: Inelastic: Unitary: E, P >1 E, P <1 E, P =1 35
6 Perfectly Elastic & Inelastic Demand Price Price D D Perfectly Elastic (, = ) E P uantity Perfectly Inelastic ( E, P = uantity 0) 36
7 Elastic OwnPrice Elasticity and Total Revenue 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. 37
8 Elasticity, Total Revenue and Linear Demand P 100 TR
9 Elasticity, Total Revenue and Linear Demand P 100 TR
10 Elasticity, Total Revenue and Linear Demand P 100 TR
11 Elasticity, Total Revenue and Linear Demand P 100 TR
12 Elasticity, Total Revenue and Linear Demand P 100 TR
13 Elasticity, Total Revenue and Linear Demand P Elastic TR Elastic 313
14 Elasticity, Total Revenue and Linear Demand P Elastic TR Inelastic Elastic Inelastic 314
15 Elasticity, Total Revenue and Linear Demand P Elastic Unit elastic TR Unit elastic Inelastic Elastic Inelastic 315
16 Demand, Marginal Revenue (MR) and Elasticity P Elastic Unit elastic Inelastic MR For a linear inverse demand function, MR() = a + 2b, where b < 0. When MR > 0, demand is elastic; MR = 0, demand is unit elastic; MR < 0, demand is inelastic. 316
17 Factors Affecting the OwnPrice Elasticity Available Substitutes The more substitutes available for the good, the more elastic the demand. Time Demand tends to be more inelastic in the short term than in the long term. Time allows consumers to seek out available substitutes. 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. 317
18 CrossPrice Elasticity of Demand E, P Y % = % P Y d If E,P Y > 0, then and Y are substitutes. If E,P Y < 0, then and Y are complements. 318
19 Predicting Revenue Changes from Two Products Suppose that a firm sells to related goods. If the price of changes, then total revenue will change by: R = ( R ( ) ) 1 + E, P + RY E, P % P Y 319
20 Income Elasticity E, M % = % M d If E,M > 0, then is a normal good. If E,M < 0, then is a inferior good. 320
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! 321
22 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? 322
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. 323
24 Example 2: uantifying 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? 324
25 Answer: Calls Increase! Calls would increase by percent! E, P % 8.64 = 3% 3% % = 8.64 = ( 8.64) d d = = 25.92% % % P % d d 325
26 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? 326
27 Answer: AT&T s Demand Falls! AT&T s demand would fall by percent! E, P Y % 9.06 = 4% 4% 9.06 = % = 9.06 = d d % % P % = 36.24% d d Y 327
28 Interpreting Demand Functions Mathematical representations of demand curves. Example: d = 10 2P + 3P 2M Y Law of demand holds (coefficient of P is negative). and Y are substitutes (coefficient of P Y is positive). is an inferior good (coefficient of M is negative). 328
29 Linear Demand Functions and Elasticities General Linear Demand Function and Elasticities: d = 0 α + α P + α P + α M + Y Y M α H H P E, P = α Own Price Elasticity E, P Y = α Y P Cross Price Elasticity Y E M, M = α M Income Elasticity 329
30 Example of Linear Demand d = 102P. OwnPrice Elasticity: (2)P/. If P=1, =8 (since 102 = 8). Own price elasticity at P=1, =8: (2)(1)/8=
31 LogLinear Demand General LogLinear Demand Function: ln = β + β ln P + β ln P + β ln M + β ln H d 0 Y Y M H Own Price Elasticity : Cross Price Elasticity : Income Elasticity : β β β Y M 331
32 Example of LogLinear Demand ln( d ) = 102 ln(p). Own Price Elasticity:
33 Graphical Representation of Linear and LogLinear Demand P P D D Linear Log Linear 333
34 Regression Analysis One use is for estimating demand functions. Important terminology and concepts: Least Squares Regression model: Y = a + b + e. Least Squares Regression line: Confidence Intervals. tstatistic. Yˆ = aˆ + b ˆ Rsquare or Coefficient of Determination. Fstatistic. 334
35 An Example Use a spreadsheet to estimate the following loglinear demand function. ln = β + β ln P + e x 0 x x 335
36 Summary Output Regression Statistics Multiple R 0.41 R Square 0.17 Adjusted R Square 0.15 Standard Error 0.68 Observations ANOVA df SS M S F Significance F Regression Residual Total Coefficients Standard Error t Stat Pvalue Lower 95% Upper 95% Intercept ln(p)
37 Interpreting the Regression Output The estimated loglinear demand function is: ln( x ) = ln(p x ). Own price elasticity: (inelastic). How good is our estimate? tstatistics of 5.29 and indicate that the estimated coefficients are statistically different from zero. Rsquare of 0.17 indicates the ln(p ) variable explains only 17 percent of the variation in ln( x ). Fstatistic significant at the 1 percent level. 337
38 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. 338
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