A monopolist has constant marginal costs of $1 per unit.The demand for her output is 1,000/p if p is less than or equal to 50.The demand is 0 if p 50.What is her profit maximizing level of output?
A)5
B)10
C)15
D)20
E)25

Question

A monopolist has constant marginal costs of $1 per unit.The demand for her output is 1,000/p if p is less than or equal to 50.The demand is 0 if p > 50.What is her profit maximizing level of output?
A)5
B)10
C)15
D)20
E)25

Quizplus · Accepted Answer

To maximize profits, the monopolist should produce where marginal revenue (MR) equals marginal cost (MC).

- When p is less than or equal to 50, the demand function is 1000/p. Therefore, the revenue function is R = pq = 1000q/p. 
- The marginal revenue function is the derivative of the revenue function with respect to q: MR = dR/dq = 1000/p. 
- Since the marginal cost is constant at $1 per unit, the monopolist should produce where MR = MC = 1: 
1000/p = 1 
p = 1000

Since p cannot be greater than 50, the monopolist should produce at the highest possible price, which is $50. Therefore, the profit maximizing level of output is: 
q = 1000/50 = 20.

A Monopolist Has Constant Marginal Costs of $1 Per Unit