A monopolist faces the (inverse) demand for its product: p = a - bQ. The monopolist has a marginal cost given by c and a fixed cost given by F
a. Assume that F is sufficiently small such that the monopolist produces a strictly positive level of output. What is the profit-maximizing price and quantity?
b. Compute the maximum profit for the monopolist.
c. For what values of F will the monopolist earn negative profit?
a. The monopolist will choose p = MR (or derive from first order condition of profit function).
a - 2bQ = c
Solving for Q
Q* = (a - c)/2b
The price follows from plugging the optimal output into the demand:
p* = a - b(a - c)/2b = a - (a - c)/2 = (a + c)/2
b. The profit comes from plugging the price and quantity into the profit equation:
Pi* =[(a + c)/2 - c](a - c)/2b - F = (a - c)2/4b - F
c. Find F* such that Pi* = 0:
F* = (a - c)2/4b
For F > F*, profits will be negative.
You might also like to view...
Starting from long-run equilibrium, a large increase in government purchases will result in a(n) ________ gap in the short-run and ________ inflation and ________ output in the long-run.
A. expansionary; higher; potential B. recessionary; higher; potential C. recessionary; lower; lower D. expansionary; higher; higher
Cyrus McCormick and Eli Whitney were important in the technology of
A. steel. B. automobiles. C. agriculture. D. oil.
Using the above table, when Jefferson's Cleaners hires three workers
A) the average product of labor is greater than the marginal product. B) the marginal product of labor is greater than the average product. C) it has already experienced diminishing marginal returns. D) Both answers A and C are correct.
Which of the following statements is true?
a. Total utility is the extra satisfaction from the consumption of a good or service. b. Marginal utility is the amount of satisfaction received from all the units of a good or service consumed. c. The law of diminishing marginal utility states that as more of a good or service is consumed total utility decreases. d. Consumer equilibrium is a combination of goods and services consumed which maximizes total utility from a given budget.