Case Problem

Case Problem Set A Gary operates an automobile detailing business in a mid-sized town in Pennsylvania. An automobile detailer restores a car to the level of cleanliness and perfection that it had when it was new. His fastidious nature, attention to detail, and ability to effectively manage employees have helped to make his business profitable, but he believes that more information about the market would allow him to operate more efficiently. He uses regression analysis to estimate the demand function for his business and gets the following result: QX = 235 - 3PX + 40A - 20U + 8PW The number of detailing jobs he gets per month (QX) depends on the price he charges per job (PX), his monthly advertising expenditures (A) measured in $1,000s, the regional percentage unemployment rate (U), and the average price charged by local car wash businesses (PW) for a standard wash and wax. Use the estimated demand function given above to solve Problems 1 through 8. 1. Is automobile detailing a normal good or an inferior good? How can you tell? 2. Is a wash and wax at the local car wash a complement or a substitute for automobile detailing? How can you tell? 3. Gary is currently charging $65 per detailing job and spending $3,500 per month on advertising. The regional unemployment rate is 7.5% and the average price of a wash and wax at a local car wash is $15. How many detailing jobs per month can Gary expect under these conditions. 4. Derive the demand curve for detailing jobs under current conditions. Calculate the values needed to fill in the demand schedule below and then plot the schedule on the graph provided.

4. Derive the demand curve for detailing jobs under current conditions. Calculate the values needed to fill in the demand schedule below and then plot the schedule on the graph provided.

PX 15

105

95

85

75

65

55

45

35

25

QX

Chapter 3: Problem 4 120 100

Price

80 60 40 20 0 0

50

100

150

200

250

300

Quantity

5.

Calculate the point price elasticity of demand under current conditions. Is it elastic or inelastic? Also calculate marginal revenue. If the marginal cost of a detailing job is equal to $12, should Gary increase price, lower price, or hold price constant?

350

6.

Calculate the point advertising elasticity of demand (%QX/%A) under current conditions. Is it elastic or inelastic? How many additional detailing jobs would result if Gary spent an additional $1,000 on advertising? How much additional revenue will be generated, under current conditions, if an additional $1,000 is spent on advertising?

7.

Assume that Gary increases his advertising expenditures to $4,500 while all other conditions remain unchanged. Derive the new demand curve for detailing jobs. Calculate the values needed to fill in the demand schedule that follows and then plot this schedule on the same axes you used for Problem 4. How does an increase in advertising expenditures influence the demand curve? How would an increase in the price charged for a detailing job influence the demand curve?

PX 15

105

95

85

75

65

55

45

35

25

QX

8.

Assume that Gary increases his advertising expenditures to $4,500 and raises his price to $70 and that all other conditions remain unchanged. Calculate the point price elasticity of demand and use it to calculate marginal revenue. If the marginal cost of a detailing job is equal to $12, should Gary increase price, lower price, or hold price constant?