1. Assuming the following demand for European luxury automobiles:
Where P = price of European luxury cars
P_{A} = price of American luxury cars
P_{J} = price of Japanese luxury cars
Y = annual income of car buyers
a. Comment on the degree of substitutability between European and American and between European and Japanese luxury cars. Explain some possible reasons for the results in the equation.
b. Comment on the coefficient for income.
c. Comment on the coefficient for the European car price.
2. The maker of a leading brand of low-calorie microwavable food estimated the following demand equation for its product using data from 26 supermarkets around the country for the month of April:
Assume the following values for the independent variables:
Q = Quantity sold per month
P (in cents) = Price of the product = 500
P_{X} (in cents) = Price of leading competitor’s product = 600
Y (in dollars) = per capita income = 5,500
A (in dollars) = monthly advertising expenditure = 10,000
M = number of microwaves sold in the market = 5,000
a. Compute the elasticities for each variable
b. How concerned should the company be about the impact of a recession on its sales? Explain.
c. Do you think the company should cuts its price to increase its market share? Explain.
d. How confident are you about the results from this estimation? Explain.
3. A manufacturer faces the following (inverted) demand for its product:
P = 41.5 – 1.1 Q
And has the following Total Cost function:
TC = 150 + 10Q – 0.5 Q^{2} + 0.02 Q^{3}
- What is the profit maximizing level of output? Show all work.
- What are the level of profits? Show all work.
- Draw this situation in a diagram.
4. Data on electric power consumption in a Midwestern town (in billions of kilowatt hours), income (in millions of dollars), and electricity prices (in cents per kilowatt hour) for the period 1987-2001 are shown below:
Year |
Consumption |
Income |
Price |
1987 |
407.9 |
944.0 |
2.09 |
1988 |
447.8 |
992.7 |
2.10 |
1989 |
479.1 |
1,077.6 |
2.19 |
1990 |
511.4 |
1,185.9 |
2.29 |
1991 |
554.2 |
1,326.4 |
2.38 |
1992 |
555.0 |
1,434.2 |
2.83 |
1993 |
586.1 |
1,594.2 |
3.21 |
1994 |
613.1 |
1,718.0 |
3.45 |
1995 |
652.3 |
1,918.3 |
3.78 |
1996 |
679.2 |
2,163.9 |
4.03 |
1997 |
696.0 |
2,417.8 |
4.43 |
1998 |
734.4 |
2,613.7 |
5.12 |
1999 |
730.5 |
2,957.8 |
5.80 |
2000 |
732.7 |
3,069.3 |
6.44 |
2001 |
750.9 |
3,304.8 |
6.83 |
a) Using regression analysis, estimate consumption as a linear function of income, price, and the previous year’s consumption (assume consumption in 1986 was 367.7 Billion kilowatt hours). Write the equation, the t-stats, the R^{2}, the Standard Error of the Estimate, and the F-statistic. Provide interpretation of the estimation (i.e., are the signs what you’d expect; what level of significance do the coefficients have, etc…). Provide a copy of your output from your regression analysis.
b) Assume that income in 2002 is $3,661.3 million and the price of electricity is 7.16 cent per kilowatt hour. Predict the consumption of electricity. How confident are you that the prediction is accurate?
5. A manufacturer of computer workstations has estimated the following demand for its product:
R^{2} = 0.68
SEE = 786
F = 21.25
The number in parenthesis below each parameter estimate is the standard error of the estimate of that parameter. Assume that the number of observations used to generate these results was large (i.e., df >30).
The variables and their assumed values are:
Q = quantity (units)
P = Price of basic model = $7,000
A = Advertising expenditures (in thousands of dollars) = 52
P_{PC} = Average price of a personal computer = $4,000
P_{M} = Average price of a minicomputer = $15,000
P_{C} = Average price of a leading competitor’s workstation = $8,000
a. Compute the elasticities for each of the variables. Discuss the relative importance that each variable has on demand. What implications can you draw for the firm’s marketing and pricing decisions?
b. Conduct a significant test for each of the variables. Discuss the results of the t-tests in light of your suggestions in part a.