Chap_3_Solutions_Odd

Chap_3_Solutions_Odd - Chapter 3 Answers to Questions and...

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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. $0 $2 $4 $6 $8 $10 $12 $14 0 1 2 3 4 5 6 Quantity Price Demand MR Figure 3-1 Managerial Economics and Business Strategy, 4e Page 1
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2. 3. a. The own price elasticity of demand is simply the coefficient of ln P x , which is – 0.5. Since this number is less than one in absolute value, demand is inelastic. b. The cross-price elasticity of demand is simply the coefficient of ln P y , which is – 2.5. Since this number is negative, goods X and Y are complements. c. The income elasticity of demand is simply the coefficient of ln M , which is 1. Since this number is positive, good X is a normal good. d. The advertising elasticity of demand is simply the coefficient of ln A , which is 2. 4. 5. Using the cross price elasticity formula, 5 % 50 - = y P . Solving, we see that the price of good Y would have to decrease by 10 percent in order to increase the consumption of good X by 50 percent. 6. 7. Table 3-1 contains the answers to the regression output. SUMMARY OUTPUT Regression Statistics Multiple R 0.62 R Square 0.39 Adjusted R Square 0.37 Standard Error 190.90 Observations 100.00 ANOVA degrees of freedom SS MS F Significance F Regression 2.00 2,223,017.77 1,111,508.88 30.50 0.00 Residual 97.00 3,535,019.49 36,443.50 Total 99.00 5,758,037.26 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 187.15 534.71 0.35 0.73 -880.56 1,254.86 Price of X -4.32 0.69 6.26 0.00 -5.69 -2.96 Income 0.09 0.02 4.47 0.00 0.05 0.14 Table 3-1 a. 187.15 4.32 .09 d x x Q P M = - + . b. Only the coefficients for the Price of X and Income are statistically significant at the 5 percent level or better. c. The R -square is fairly low, indicating that the model explains only 39 percent of the total variation in demand for X. The adjusted R -square is only marginally lower (37 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, Page 2 Michael R. Baye
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however, suggests that the overall regression is statistically significant at better than the 5 percent level.
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