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Homework answers / question archive / The inverse demand curve a monopoly faces is
The inverse demand curve a monopoly faces is . The firm's cost curve is .
1. What is the profit-maximizing quantity and price? (Round to two decimal places.)
2. What is the firm's economic profit? (Round to two decimal places.)
3. How does your answer change if ? The increase in fixed cost
A. has no effect on the equilibrium quantity, but the equilibrium price increases and profit decreases.
B. causes the firm to increase both the price and quantity, and profit increases.
C. has no effect on the equilibrium price and quantity, but profit will decrease.
D. has no effect on the equilibrium quantity, but the equilibrium price increases and profit increases.
1. What is the profit-maximizing quantity and price?
P = 120 - Q
C (Q) = 50 + 5Q, therefore, MC = 5
Revenue = PQ
= (120 - Q) Q = 120Q - Q^2
MR = 120 - 2Q
The profit maximization implies that MR = MC, so,
120 - 2Q = 5
Q = 57.5
Substituting Q for P,
P = 120 - Q
P = 120 - 57.5
P = $62.5
2. What is the firm's economic profit?
Economic Profit = Revenue - Cost
= (120 - Q) Q - 50 + 5Q
= (120 - 57.5) 57.5 - 50 + 5 (57.5)
= $3593.75 - $337.5
Economic Profit = $3256.25
3. How does your answer change if C(Q) = 150 + 5Q
A change in the total cost has no effect on the equilibrium price and quantity. The marginal cost is constant at $5 and is similar before. The profit maximization rule is still the same at MR = MC. However, the economic profit in this situation has changed due to changes in the fixed costs.
Economic Profit = Revenue - Cost
= (120 - Q) Q - 150 + 5Q
= (120 - 57.5) 57.5 - 150 + 5 (57.5)
= $3593.75 - $437.5
= $3156.25
The answer to this question is letter C, which has no effect on the equilibrium price and quantity, but profit will decrease.
