Answered: 4. You are the manager of a monopoly,…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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4. You are the manager of a monopoly, and your demand and cost functions are given by P = 300 − 3Q and C(Q) = 1,500 + 2Q2, respectively. (LO3, LO4) a. What price–quantity combination maximizes your firm’s profits? b. Calculate the maximum profits. c. Is demand elastic, inelastic, or unit elastic at the profit-maximizing price–quantity combination? d. What price–quantity combination maximizes revenue? e. Calculate the maximum revenues. f. Is demand elastic, inelastic, or unit elastic at the revenue-maximizing price–quantity combination? 6. The accompanying diagram shows the demand, marginal revenue, and marginal cost of a monopolist. (LO1, LO3, LO5) a. Determine the profit-maximizing output and price. b. What price and output would prevail if this firm’s product were sold by price-taking firms in a perfectly competitive market? c. Calculate the deadweight loss of this monopoly. 8. The elasticity of demand for a firm’s product is –2.5 and its advertising elasticity of demand is 0.2. (LO8) a. Determine the firm’s optimal advertising-to-sales ratio. b. If the firm’s revenues are $40,000, what is its profit-maximizing level of advertising? 9. A monopolist’s inverse demand function is P = 150 − 3Q. The company produces out- put at two facilities; the marginal cost of producing at facility 1 is MC1(Q1) = 6Q1, and the marginal cost of producing at facility 2 is MC2(Q2) = 2Q2. (LO1, LO8) a. Provide the equation for the monopolist’s marginal revenue function. (Hint: Recall thatQ1 +Q2 =Q.) b. Determine the profit-maximizing level of output for each facility. c. Determine the profit-maximizing price.

4. You are the manager of a monopoly, and your demand and cost functions are given by
P = 300 – 3Q and C(Q) = 1,500 + 2Q², respectively. (LO3, LO4)
a. What price-quantity combination maximizes your firm's profits?
b. Calculate the maximum profits.
c. Is demand elastic, inelastic, or unit elastic at the profit-maximizing price-quantity
combination?
d. What price-quantity combination maximizes revenue?
e. Calculate the maximum revenues.
f. Is demand elastic, inelastic, or unit elastic at the revenue-maximizing price-quantity
combination?
5. You are the manager of a firm that produces a product according to the cost function
C(q) = 160 + 58q; – 6q² + q?. Determine the short-run supply function if: (LO1, LO7)
a. You operate a perfectly competitive business.
b. You operate a monopoly.
c. You operate a monopolistically competitive business.
6. The accompanying diagram shows the demand, marginal revenue, and marginal cost of
a monopolist. (LO1, LO3, LO5)
a. Determine the profit-maximizing output and price.
b. What price and output would prevail if this firm's product were sold by price-taking
firms in a perfectly competitive market?
c. Calculate the deadweight loss of this monopoly.
$120
MC
110
100
90
80
70
60
50
40
30
20
10
MR
>Quantity
1
2
3
7.
8.
9 10 11 12 13 14 15
7. You are the manager of a monopolistically competitive firm, and your demand and cost
functions are given by Q = 36 – 4P and C(Q) = 4 + 4Q+ Q². (LO1, LO3, LO5)
a. Find the inverse demand function for your firm's product.
b. Determine the profit-maximizing price and level of production.
c. Calculate your firm's maximum profits.
d. What long-run adjustments should you expect? Explain.
8. The elasticity of demand for a firm's product is -2.5 and its advertising elasticity of
demand is 0.2. (LO8)
a. Determine the firm's optimal advertising-to-sales ratio.
b. If the firm's revenues are $40,000, what is its profit-maximizing level of advertising?
9. A monopolist's inverse demand function is P = 150 – 3Q. The company produces out-
put at two facilities; the marginal cost of producing at facility 1 is MCQ1) = 6Q1, and
the marginal cost of producing at facility 2 is MC2(Q2) = 2Q2. (LO1, LO8)
a. Provide the equation for the monopolist's marginal revenue function. (Hint: Recall
that Q1 + Q2 = Q.)
b. Determine the profit-maximizing level of output for each facility.
c. Determine the profit-maximizing price.

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