1. A local supermarket lowers the price of its Atlantic

1. A local supermarket lowers the price of its Atlantic Salmon fillets from $12/lb. to $9.00/lb.

Sales increase by 20 percent. The store manager notices that T-bone steak sales decrease by

15 percent.

a. Calculate the arc price elasticity of salmon fillets. Explain what it means.

b. Calculate the arc cross-price elasticity of T-bone steak. Based on your calculation is T-

bone steak a substitute or a complement? Why?

c. Was the price decision good or bad for the supermarket? Explain.

d. If you were to estimate a demand equation for salmon fillets, which variables would you

choose as explanatory variables?

2. One of the leading TV producers has estimated the following demand equation after

analyzing 36 regional markets:

Q = + 25,000 – 50P + 25A + 20 cP

– 40 CA

+ 120 I

(12000) (22.2) (12) (8.5) (52) (55)

R 2 = 0.82 F = 32.26

The variables and their assumed values are

Q = Quantity

P = Price of the basic Model = 600 (dollars)

A = Advertising Expenditures = 100 (thousand dollars)

CP

= Average price of the competitor’s product = 700 (dollars)

CA

= competitor’s advertising expenditures = 80 (thousand dollars)

I = per capita income = 50 (thousand dollars)

a. Compute the elasticities for each variable. On this basis, discuss the relative impact that

each variable has on the demand. What implications do these results have for the firm’s

marketing, pricing, and production policies?

b. What would be the effect of a 6 unit increase in the competitor’s advertising

expenditures?

c. What would be the change in your advertising expenditures to offset your competitor’s

strategy?

d. Conduct a t-test for the statistical significance of each variable. Discuss the results of the

t-tests in light of the policy implications mentioned.

e. What proportion of the variation in sales is explained by the independent variables in the

equation? How confident are you about this answer? Explain conducting an F-test.

3. Given the Production Function of a perfectly competitive firm, Q = 120L + 9L 2 – 0.5L 3 ,

where Q = Output and L = labor input

a. At what value of L will Diminishing Returns take effect?

b. Calculate the range of values for labor over which stages I, II, and III occur?

c. Suppose that the wage rate is $60 and the price of output is $2 per unit. How many

workers should the firm hire?

d. If demand forecasts predict an output level between 3500 and 3800 in the next decade,

what would be your long-run strategy to optimize the resources of your company?

4. Suppose that you estimate the following cost function for your company, which is a firm

operating in a monopolistically competitive market:

23

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You also estimate the following demand curve for the output you are producing.

3608PQ

a. Derive the equations for average cost and marginal cost curves.

b. Over what range of output does economies of scale exist? Diseconomies of scale?

c. How many units of output will you produce and what price will you charge for each unit?

d. Is the company making a profit or loss at the suggested output level? How much?

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