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Managerial Economics and Business Strategy - Regression Questions

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Problem # 10
You are the manager of a firm that sells a leading brand of alkaline batteries. The accompanying Excel file contains data on the demand for your product. Specifically, the file contains data on the natural logarithm of your quantity sold, price, and the average income of consumers in various regions around the world. Use this information to perform a log-linear regression, and then determine the likely impact of a 3 percent decline in global income on the overall demand for your product.

Problem # 15
As a newly appointed "Energy Czar," your goal is to reduce the total demand for residential heating fuel in your state. You must choose one of three legislative proposals designed to accomplish this goal: (a) a tax that would effectively increase the price of residential heating fuel by $2; (b) a subsidy that would effectively reduce the price of natural gas by $1; or (c) a tax that would effectively increase the price of electricity (produced by hydroelectric facilities) by $5. To assist you in your decision, an economist in your office has estimated the demand for residential heating fuel using a linear demand specification. The regression results are presented below. Based on this information, which proposal would you favor? Explain.

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Problem # 15
As a newly appointed "Energy Czar," your goal is to reduce the total demand for residential heating fuel in your state. You must choose one of three legislative proposals designed to accomplish this goal: (a) a tax that would effectively increase the price of residential heating fuel by $2; (b) a subsidy that would effectively reduce the price of natural gas by $1; or (c) a tax that would effectively increase the price of electricity (produced by hydroelectric facilities) by $5. To assist you in your decision, an economist in your office has estimated the demand for residential heating fuel using a linear demand specification. The regression results are presented below. Based on this information, which proposal would you favor? Explain.

SUMMARY OUTPUT

Regression statistics
Multiple R 0.76
R-Square 0.57
Adjusted R-Square 0.49
Standard Error 47.13
Observations 25

Analysis of Variance
Degrees of freedom Sum of Squares Mean Square F Significance F
Regression 4 60936.56 15234.14 6.86 0.03
Residual 20 44431.27 2221.56
Total 24 105367.84

Coefficients Standard Error t-Statistic P-Value Lower 95% Upper 95%
Intercept 136.96 43.46 3.15 0.01 50.6 223.32
Price of residential heating fuel -91.69 29.09 -3.15 0.01 -149.49 -33.89
Price of natural ...

Solution Summary

The solutions answers 2 questions on regression from Managerial Economics and Business Strategy, Fourth Edition by Michael R. Baye.

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Managerial Economics and Globalization

Imagine that you work for the maker of a leading brand of low-calorie, frozen microwavable food that estimates the following demand equation for its product using data from 26 supermarkets around the country for the month of April.

For a refresher on independent and dependent variables, please go to Sophia's Website and review the Independent and Dependent Variables tutorial, located at http://www.sophia.org/tutorials/independent-and-dependent-variables--3.

Option 1
Note: The following is a regression equation. Standard errors are in parentheses for the demand for widgets.
QD = - 5200 - 42P + 20PX + 5.2I + 0.20A + 0.25M
(2.002) (17.5) (6.2) (2.5) (0.09) (0.21)
R2 = 0.55 n = 26 F = 4.88

Your supervisor has asked you to compute the elasticities for each independent variable. Assume the following values for the independent variables:

Q = Quantity demanded of 3-pack units
P (in cents) = Price of the product = 500 cents per 3-pack unit
PX (in cents) = Price of leading competitor's product = 600 cents per 3-pack unit
I (in dollars) = Per capita income of the standard metropolitan statistical area
(SMSA) in which the supermarkets are located = $5,500
A (in dollars) = Monthly advertising expenditures = $10,000
M = Number of microwave ovens sold in the SMSA in which the
supermarkets are located = 5,000

Option 2
Note: The following is a regression equation. Standard errors are in parentheses for the demand for widgets.

QD = -2,000 - 100P + 15A + 25PX + 10I
(5,234) (2.29) (525) (1.75) (1.5)
R2 = 0.85 n = 120 F = 35.25

Your supervisor has asked you to compute the elasticities for each independent variable. Assume the following values for the independent variables:

Q = Quantity demanded of 3-pack units
P (in cents) = Price of the product = 200 cents per 3-pack unit
PX (in cents) = Price of leading competitor's product = 300 cents per 3-pack unit
I (in dollars) = Per capita income of the standard metropolitan statistical area
(SMSA) in which the supermarkets are located = $5,000
A (in dollars) = Monthly advertising expenditures = $640

Answer these questions in 4-6 pages::

1. Compute the elasticities for each independent variable. Note: Write down all of your calculations.
2. Determine the implications for each of the computed elasticities for the business in terms of short-term and long-term pricing strategies. Provide a rationale in which you cite your results.
3. Recommend whether you believe that this firm should or should not cut its price to increase its market share. Provide support for your recommendation.
4. Assume that all the factors affecting demand in this model remain the same, but that the price has changed. Further assume that the price changes are 100, 200, 300, 400, 500, 600 cents.
a. Plot the demand curve for the firm.
b. Plot the corresponding supply curve on the same graph using the following MC / supply function Q = -7909.89 + 79.1P with the same prices.
c. Determine the equilibrium price and quantity.
d. Outline the significant factors that could cause changes in supply and demand for the low-calorie, frozen microwavable food. Determine the primary manner in which both the short-term and the long-term changes in market conditions could impact the demand for, and the supply, of the product.
5. Indicate the crucial factors that could cause rightward shifts and leftward shifts of the demand and supply curves for the low-calorie, frozen microwavable food.

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