Answered: Assume the following equations describe…

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

ChapterB: Differential Calculus Techniques In Management

Section: Chapter Questions

Problem 5E

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Question

Assume the following equations describe the conditions for an unregulated monoply:

Q_d= q = 160,000 - 2,500P

TC = 400,000 +22q + 0.0001q²

where Qd is the quantity demanded for both the market and the firm, P is the commodity's price in dollars, TC is total cost in dollars, and q is the quantity of output produced by the firm. Based upon the above equations, answer the following questions:

a. What is the firm's equation for total revenue expressed as a function of quantity?

b. What is the firm's equation for marginal revenue expressed as a function of quantity? What is the firm's equation for marginal cost expressed as a function of quantity?

c. What is the firm's profit-maximizing quantity of output?

d. What price will the firm charge for the commodity?

Assume the total cost function and the market demand remain unchanged. The equations are:

Qd = q = 160,000 - 2,500P

TC = 400,000 +22q + 0.0001q²

The monopolist now engages in first-degree price discrimination.

e. What quantity of output will maximize the monopolist's profit given first-degree price discrimination?

f. What will the monopolist's total profit equal given first-degree price discrimination?

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