Economics 5315 - Baylor University



Economics 5315

Managerial Economics

Fall 1997

Final Exam

1. Dr. Leona Williams, a well-known plastic surgeon, has a reputation for being one of the best surgeons for reconstructive nose surgery. Dr. Williams enjoys a rather substantial degree of market power in this market. Dr. Williams has estimated demand for her work to be Q = 480 - 0.2 P, where Q is the number of nose operations performed monthly, and P is the price of a nose operation.

a. Write the demand function in terms of P instead of Q.

b. What is the marginal revenue function?

The average variable cost function for reconstructive nose surgery is estimated to be

AVC = 2 Q2 - 15 Q + 400, where AVC is average variable cost (measured in dollars). The doctor’s total fixed costs each month are $8,000.

c. If the doctor wishes to maximize her profit, how many nose operations should she perform each month?

d. What price should Dr. Williams charge to maximize profits?

e. How much profit will she earn each month?

2. Suppose a firm serves two distinct markets. The forecasted demand functions in the two markets are:

Market 1: Q1 = 50 - 0.25 P1

Market 2: Q2 = 100 - 1.0 P2

The firm’s marginal cost function has been estimated to be MC = 20 + 0.4 Q.

a. What is the profit-maximizing total level of output? Explain what you did.

b. How should this output be allocated between the two markets? Explain the theory.

c. What are the profit-maximizing prices in the two markets?

d. Which market has the more elastic demand curve? Explain.

3. A firm produces refined chemicals. In one of its divisions a joint product is produced. That is, as it refines the raw chemical inputs, the processes will yield equal amounts of two products X and Y. The demand function for the two products has been forecasted as

Product X: QX = 200 - PX

Product Y: QY = 75 - 0.5 PY

where outputs are measured in thousands of pounds and prices are measured in cents per pound (for information purposes only; does not require any extra calculations).

a. What are the marginal revenue curves associated with the two demand functions?

b. What is the relevant marginal revenue function upon which the firm will base its pricing and output decisions?

c. Suppose the marginal cost function has been estimated to be MC = 10 + 4 Q. What are the profit maximizing levels of production for X and Y and what prices should be charged?

Question 3 (continued):

d. Suppose instead that the marginal cost is estimated to be MC = -10 + 2 Q. What are the output levels and prices for X and Y that maximize profits?

4. [Did you answer 3 d above?] Two firms, the Alliance Company (A) and the Bangor Corporation (B), produce vision systems. The demand curve for vision systems is P = 200,000 - 6 Q, where Q = QA + QB. P is the price of the vision systems (in dollars) and Q is the number of vision systems produced per month. Alliance’s total cost (in dollars) is TCA = 8,000 QA. Bangor’s total cost (in dollars) is TCB = 12,000 QB.

a. If each of these two firms sets its own output level to maximize its profits, assuming that the other form holds constant its output level, what is the output of each firm?

b. What is the equilibrium price for the vision systems?

c. What is each firm’s profit?

d. Suppose that Alliance buys Bangor and is now the only producer of vision systems in the market. Does this change the equilibrium output level and price? If so, what are the new levels? How much will be produced in each plant, A and B? What will total profit be? Explain you answer.

5. A vertically integrated firm produces both rubber and automobile tires. Assume the demand for tires is PT = 100 - 0.001 QT, where Q is the number of tires demanded and PT is the price in dollars. The marginal cost of fabricating the rubber into a tire is $10 (excluding the production cost of rubber). The marginal cost of producing the rubber necessary for each tire is MCR = 20 + 0.001Q.

a. Suppose there is no external market for the rubber. A senior manager of the tire division argues that the rubber division’s main purpose for existence is to serve the firm’s tire division. Accordingly, rubber should be offered free of charge to the tire division; that is PR = 0. An executive in the rubber division counters with the argument that the rubber division should treat the tire division as it would any outside buyer and mark up the transfer price above marginal cost. You have been assigned by top management to settle the dispute. What are your recommendations? (In your answer determine Q, QR, P, and PR. How will the firm’s profits compare using your optimal strategy compared with how they would fare with either of the two alternatives suggested? Present a systematic argument with appropriate documentation.)

b. Suppose an external market exists and rubber’s current market price is PR = $50. What production decisions should the firm make in this case? How does your answer change if the firm can purchase rubber on the open market at a price of $30?

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