Cournot duopolists face a market demand curve given by P = 90 - Q where Q is total market demand. Each firm can produce output at a constant marginal cost of 30 per unit. If the duopolists behave as a shared monopoly, the equilibrium price and total quantity of output will be
A)Q = 30, P = 60.
B)Q = 60, P = 30.
C)Q = 40, P = 50.
D)Q = 45, P = 45.

Question

Quizplus · Accepted Answer

In a shared monopoly, the firms act together to maximize total profit. The total cost for producing Q units is 30Q (since marginal cost is constant at 30 per unit for each firm). To find the profit-maximizing quantity, set marginal revenue (MR) equal to marginal cost (MC). The market demand curve is P = 90 - Q, so the total revenue (TR) is P*Q = (90 - Q)Q. Differentiating TR with respect to Q gives MR = 90 - 2Q. Setting MR equal to MC (30) gives 90 - 2Q = 30, solving for Q gives Q = 30. Substituting Q = 30 into the demand equation gives P = 90 - 30 = 60.

Cournot Duopolists Face a Market Demand Curve Given by P