Baye Solutions - Ch 3 PDF

Preview

Summary

Download Baye Solutions - Ch 3 PDF

Description

Chapter 03 - Quantitative Demand Analysis

Chapter 3: Answers to Questions and Problems 1. a. When P = $12, R = ($12)(1) = $12. When P = $10, R = ($10)(2) = $20. Thus, the price decrease results in an $8 increase in total revenue, so demand is elastic over this range of prices. b. When P = $4, R = ($4)(5) = $20. When P = $2, R = ($2)(6) = $12. Thus, the price decrease results in an $8 decrease total revenue, so demand is inelastic over this range of prices. c. Recall that total revenue is maximized at the point where demand is unitary elastic. We also know that marginal revenue is zero at this point. For a linear demand curve, marginal revenue lies halfway between the demand curve and the vertical axis. In this case, marginal revenue is a line starting at a price of $14 and intersecting the quantity axis at a value of Q = 3.5. Thus, marginal revenue is 0 at 3.5 units, which corresponds to a price of $7 as shown below.

Price $14 $12 $10 $8 $6 $4 $2 Demand $0 0

1

2

3

MR 4

5

6 Quantity

Figure 3-1 2. a. At the given prices, quantity demanded is 750 units: Qdx =1,200−3 ( 140 ) −0.1( 300 )=750 . Substituting the relevant information into Px 140 =−0.56 . Since this is less the elasticity formula gives: EQ ,P =−3 =−3 Qx 750 than one in absolute value, demand is inelastic at this price. If the firm charged a lower price, total x

x

3-1 © 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

Chapter 03 - Quantitative Demand Analysis

revenue would decrease. b. At the given prices, quantity demanded is 450 units: Qdx =1,200−3 ( 240 ) −0.1( 300 )=450 . Substituting the relevant information into Px 240 =−1.6 . Since this is the elasticity formula gives: EQ ,P =−3 =−3 Qx 750 greater than one in absolute value, demand is elastic at this price. If the firm increased its price, total revenue would decrease. c. At the given prices, quantity demanded is 750 units, as shown in part a. Substituting the relevant information into the elasticity formula gives: P 300 =−0.04 . Since this number is negative, goods X EQ ,P =−0.1 z =−0.1 750 Qx and Z are complements. x

x

x

z

3. a. The own price elasticity of demand is simply the coefficient of ln Px, which is – 1.5. Since this number is more than one in absolute value, demand is elastic. b. The cross-price elasticity of demand is simply the coefficient of ln Py, which is 2. Since this number is positive, goods X and Y are substitutes. c. The income elasticity of demand is simply the coefficient of ln M, which is -0.5. Since this number is negative, good X is an inferior good. d. The advertising elasticity of demand is simply the coefficient of ln A, which is 1. 4. % ΔQ dx =−3 . −5 Solving, we see that the quantity demanded of good X will increase by 15 percent if the price of good X decreases by 5 percent. % ΔQ dx b. Use the cross-price elasticity of demand formula to write =−4 . 8 Solving, we see that the demand for X will decrease by 32 percent if the price of good Y increases by 8 percent. % ΔQ dx c. Use the formula for the advertising elasticity of demand to write =2 . −4 Solving, we see that the demand for good X will decrease by 8 percent if advertising decreases by 4 percent. d % ΔQ x d. Use the income elasticity of demand formula to write =1 . Solving, we 4 see that the demand of good X will increase by 4 percent if income increases by 4 percent. a. Use the own price elasticity of demand formula to write

20 5. Using the cross price elasticity formula, % ΔP =4 . Solving, we see that the price of y good Y would have to increase by 5 percent in order to increase the consumption of good X by 20 percent. 3-2 © 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

Chapter 03 - Quantitative Demand Analysis

6. Using the change in revenue formula for two products, Δ R=[ $ 40,000 ( 1−1.5) + $ 90,000 (−1.8 ) ] ( 0.02 )=−$ 3,640 . Thus, a 2 percent increase in the price of good X would cause revenues from both goods to decrease by $3,640. 7. Table 3-1 contains the answers to the regression output. SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations

0.38 0.14 0.13 20.77 150

Analysis of Variance Degrees of Freedom Regression Residual Total

Intercept Price of X Income (‘000s)

2 147 149

Sum of Squares 10,398.87 63,408.62 73,807.49

Coefficients 58.87 -1.64 1.11

Standard Error 15.33 0.85 0.24

Mean Square 5199.43 431.35

F 12.05

Significance F 0.00

t Stat 3.84 -1.93 4.64

P-value 0.00 0.06 0.00

Lower 95% 28.59 -3.31 0.63

Upper 95% 89.15 0.04 1.56

Table 3-1 a. Qdx =58.87−1.64 P x + 1.11 M . b. Only the coefficients for the Intercept and Income are statistically significant at the 5 percent level or better. c. The R-square is quite low, indicating that the model explains only 14 percent of the total variation in demand for X. The adjusted R-square is only marginally lower (13 percent), suggesting that the R-square is not the result of an excessive number of estimated coefficients relative to the sample size. The F-statistic,

3-3 © 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

Chapter 03 - Quantitative Demand Analysis

however, suggests that the overall regression is statistically significant at better than the 5 percent level. 8. The approximate 95 percent confidence interval for a is ^a ± 2 σ ^a=22 ± 5 . Thus, you can be 95 percent confident that a is within the range of 17 and 27. The approximate 95 percent confidence interval for b is ^b ± 2 σ ^b=−1.8 ± 1.4 . Thus, you can be 95 percent confident that b is within the range of –3.2 and –0.4. 9. a. The t statistics are as follows:

t ^a=

8.27 −2.14 =−5.22 ; and =1.55 ; t ^b= 0.41 5.32

0.36 =1.64 . 0.22 b. Since |t ^a|2

^a , is not statistically different from

^b , is statistically different from |t ^c|...