ECON 661: Managerial Economics

Please answer all questions. You must show all your steps and calculations. You are expected to fully apply or use the methods and techniques you have learned in the chapters.

1. Market researchers at Chrysler estimated the demand for their new Chrysler Crossfire sports

cars as follows:

QC = 1,050,000 - 95PC + 14.25M + 60PBMW + 25PP

Where QC is the quantity of Chrysler Crossfires sold annually, PC is the price of a Chrysler

Crossfire, M is average household income, PBMW is the price of BMW’s 330i sports sedan,

and PP is the price of Porsche’s Boxster S sports car. The marketing team at Chrysler planned

to price the Crossfire at $32,000. They predicted that average household income would be

$75,000 for buyers in the market for their sports sedan. The current prices for BMW’s 330i

and Porsche’s Boxster S was $34,000 and $50,000, respectively. Use this information to

answer the following questions. (25 points)

a. What was the predicted yearly annual sales of the Chrysler Crossfire?

b. What was the income elasticity of demand for the Chrysler Crossfire? What does your

computed income elasticity say about Crossfire? If average household income was predicted to fall the next year by 2.5 percent (other factors remaining the same), would sales rise or fall? By how much (express your answer in percentage terms)?

c. What was the price elasticity of demand for the Chrysler Crossfire:

d. What was the cross-price elasticity of demand for Chrysler Crossfires

(i). With respect to changes in the price of the BMW 330i?

(ii). With respect to changes in the price of the Porche’s Boxster S?

e. In part d, which of the two cross-price elasticities is larger in absolute value? Why do you suppose one is larger than the other?

2. A private-garage owner is currently charging his customers $1.75 per hour. But he is

considering changing the way he prices parkers in an attempt to increase profit. He has

identified two distinct market segments for his business: short-term parkers and

all-day parkers with respective demand curves (functions) of QS = 600 - 200PS and QA = 400

– 200PA. Here PS and PA are the hourly rates charged to short-term and all-day parkers,

respectively, and QS and QA are the number of cars parked at respective prices. The cost

associated with adding extra cars in the garage is negligible ( thus, maximizing revenues also

maximizes profit).

a. Is the owner maximizing revenue (profit) by charging $1.75 per hour? (10 pts)

b. What price should he charge each group if he wants to maximize revenue (profit). What will

be the total revenue collected in each market? (10 points)

c. Show if total revenue (profit) will indeed increase if different prices (discovered in

b) are charged. (5 points)

3. The table below provides partial information on the market for children’s toys. The data

represents quarterly sales (in millions) of toys over the period 1995 – 2004. (t = 1, 2, 3,...40)

Quarterly Sales over 1995 – 2004 (in millions)

Year Quarter Sales

1995 1 133

2 135

3 140

4 181

1996 1 141

2 170

3 172

4 186

1997 1 143

2 148

3 150

4 194

1998 1 154

2 156

3 158

4 196

1999 1 153

2 161

3 193

4 204

2000 1 158

2 169

3 171

4 209

2001 1 172

2 207

3 209

4 214

2002 1 183

2 212

3 184

4 219

2003 1 181

2 190

3 222

4 227

2004 1 199

2 228

3 230

4 229

a. Firms in the industry are concerned about sales. They would like to know if there is an

upward trend in sales of children’s toys. Use the data above to estimate the quarterly trend in

sales using a linear trend model of the form: Qt = a + bt. Does your statistical analysis

indicate a trend? If so, is it an upward or downward trend and how great is it? (use the 5

percent level of significance to test for statistical significance)? (12 pts)

b. A follow manager points out that there might be a seasonal variation in the data and

suggested that you tested for statistically significant seasonal pattern. How would you adjust

your statistical model to account for seasonal variation in children’s toys sales. Describe your

model completely. Then estimate the adjusted model using the data provided. Does the data

indicate a statistically significant seasonal pattern in sales (use the 5 percent level of

significance)? If so, explain the nature of the variation. (15 pts)

c. Comparing your estimates of the trend in sales in parts a and b, which estimate is

likely to be more accurate? Why? (10 pts)

d. Using the estimated forecast equation from part b, forecast the industry’s sales for the next

quarter (winter 2005). ( 5 pts)

4. Use the information in the table to answer the questions below. (8 pts) (see attachemnt)

The amount of total output produced from various combinations of labor and capital.

a. If the capital stock is fixed at one unit, how much does the third unit of labor add to total output?

b. If the capital stock is fixed at one unit, diminishing returns begin with the

c. If the capital stock is fixed at four units and there are three units of labor, what is the average product of

labor?

d. If labor is fixed at three units, how much does the second unit of capital add to total output?

Please answer all questions. You must show all your steps and calculations. You are expected to fully apply or use the methods and techniques you have learned in the chapters.

1. Market researchers at Chrysler estimated the demand for their new Chrysler Crossfire sports

cars as follows:

QC = 1,050,000 - 95PC + 14.25M + 60PBMW + 25PP

Where QC is the quantity of Chrysler Crossfires sold annually, PC is the price of a Chrysler

Crossfire, M is average household income, PBMW is the price of BMW’s 330i sports sedan,

and PP is the price of Porsche’s Boxster S sports car. The marketing team at Chrysler planned

to price the Crossfire at $32,000. They predicted that average household income would be

$75,000 for buyers in the market for their sports sedan. The current prices for BMW’s 330i

and Porsche’s Boxster S was $34,000 and $50,000, respectively. Use this information to

answer the following questions. (25 points)

a. What was the predicted yearly annual sales of the Chrysler Crossfire?

b. What was the income elasticity of demand for the Chrysler Crossfire? What does your

computed income elasticity say about Crossfire? If average household income was predicted to fall the next year by 2.5 percent (other factors remaining the same), would sales rise or fall? By how much (express your answer in percentage terms)?

c. What was the price elasticity of demand for the Chrysler Crossfire:

d. What was the cross-price elasticity of demand for Chrysler Crossfires

(i). With respect to changes in the price of the BMW 330i?

(ii). With respect to changes in the price of the Porche’s Boxster S?

e. In part d, which of the two cross-price elasticities is larger in absolute value? Why do you suppose one is larger than the other?

2. A private-garage owner is currently charging his customers $1.75 per hour. But he is

considering changing the way he prices parkers in an attempt to increase profit. He has

identified two distinct market segments for his business: short-term parkers and

all-day parkers with respective demand curves (functions) of QS = 600 - 200PS and QA = 400

– 200PA. Here PS and PA are the hourly rates charged to short-term and all-day parkers,

respectively, and QS and QA are the number of cars parked at respective prices. The cost

associated with adding extra cars in the garage is negligible ( thus, maximizing revenues also

maximizes profit).

a. Is the owner maximizing revenue (profit) by charging $1.75 per hour? (10 pts)

b. What price should he charge each group if he wants to maximize revenue (profit). What will

be the total revenue collected in each market? (10 points)

c. Show if total revenue (profit) will indeed increase if different prices (discovered in

b) are charged. (5 points)

3. The table below provides partial information on the market for children’s toys. The data

represents quarterly sales (in millions) of toys over the period 1995 – 2004. (t = 1, 2, 3,...40)

Quarterly Sales over 1995 – 2004 (in millions)

Year Quarter Sales

1995 1 133

2 135

3 140

4 181

1996 1 141

2 170

3 172

4 186

1997 1 143

2 148

3 150

4 194

1998 1 154

2 156

3 158

4 196

1999 1 153

2 161

3 193

4 204

2000 1 158

2 169

3 171

4 209

2001 1 172

2 207

3 209

4 214

2002 1 183

2 212

3 184

4 219

2003 1 181

2 190

3 222

4 227

2004 1 199

2 228

3 230

4 229

a. Firms in the industry are concerned about sales. They would like to know if there is an

upward trend in sales of children’s toys. Use the data above to estimate the quarterly trend in

sales using a linear trend model of the form: Qt = a + bt. Does your statistical analysis

indicate a trend? If so, is it an upward or downward trend and how great is it? (use the 5

percent level of significance to test for statistical significance)? (12 pts)

b. A follow manager points out that there might be a seasonal variation in the data and

suggested that you tested for statistically significant seasonal pattern. How would you adjust

your statistical model to account for seasonal variation in children’s toys sales. Describe your

model completely. Then estimate the adjusted model using the data provided. Does the data

indicate a statistically significant seasonal pattern in sales (use the 5 percent level of

significance)? If so, explain the nature of the variation. (15 pts)

c. Comparing your estimates of the trend in sales in parts a and b, which estimate is

likely to be more accurate? Why? (10 pts)

d. Using the estimated forecast equation from part b, forecast the industry’s sales for the next

quarter (winter 2005). ( 5 pts)

4. Use the information in the table to answer the questions below. (8 pts) (see attachemnt)

The amount of total output produced from various combinations of labor and capital.

a. If the capital stock is fixed at one unit, how much does the third unit of labor add to total output?

b. If the capital stock is fixed at one unit, diminishing returns begin with the

c. If the capital stock is fixed at four units and there are three units of labor, what is the average product of

labor?

d. If labor is fixed at three units, how much does the second unit of capital add to total output?

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