A monopolist faces the inverse demand curve P = 60

Question

A monopolist faces the inverse demand curve P = 60 - Q.It has variable costs of Q² so that its marginal costs are 2Q,and it has fixed costs of 30.The monopoly's maximum profit is A) 220. B) 370. C) 420. D) 510.

Quizplus · Accepted Answer

To find the profit-maximizing level of output, we need to find the quantity of output where marginal revenue equals marginal cost.
The marginal revenue curve for a monopolist is the same as the demand curve, since the monopolist is the only supplier in the market. Therefore, the marginal revenue curve is P=60-Q.

Setting marginal revenue equal to marginal cost, we have: 60 - Q = 2Q
Solving for Q, we get Q = 20.

Plugging Q = 20 into the demand curve, we get P = 40.

Therefore, the profit-maximizing quantity is Q = 20, and the profit-maximizing price is P = 40.

Total revenue is TR = P*Q = 40*20 = 800.

Total variable cost is TVC = integral of MC dQ = integral of 2Q dQ = Q^2 = 400.

Total cost is TC = TVC + FC = 400 + 30 = 430.

Profit is π = TR - TC = 800 - 430 = 370.

Therefore, the monopoly's maximum profit is 370, which corresponds to answer choice C.