You are the manager of a monopoly that faces a demand curve described by P = 85 − 5Q.Your costs are C = 20 + 5Q.The profit-maximizing price is:
A) 45.
B) 55.
C) 60.
D) 50.

Question

Quizplus · Accepted Answer

To maximize profits, the monopolist sets marginal revenue equal to marginal cost. Marginal revenue is the derivative of total revenue with respect to quantity, and marginal cost is the derivative of total cost with respect to quantity.Total revenue is equal to price times quantity, or TR = P*Q. Substituting the demand curve into this equation, we get TR = (85 - 5Q)*Q = 85Q - 5Q^2.Marginal revenue is the derivative of total revenue with respect to quantity, or MR = dTR/dQ = 85 - 10Q.Total cost is equal to fixed costs plus variable costs, or TC = FC + VC. Substituting the cost function into this equation, we get TC = 20 + 5Q.Marginal cost is the derivative of total cost with respect to quantity, or MC = dTC/dQ = 5.Setting marginal revenue equal to marginal cost, we get 85 - 10Q = 5. Solving for Q, we get Q = 8.Substituting Q = 8 into the demand curve, we get P = 85 - 5(8) = 55.Therefore, the profit-maximizing price is $55.

You Are the Manager of a Monopoly That Faces a Demand