Two firms are producing identical goods in a market characterized by the inverse demand curve P = 60 - 2Q, where Q is the sum of Firm 1 and Firm 2's output, q₁ + q₂. Each firm's marginal cost is constant at $12, and fixed costs are zero. Answer the following questions, assuming that the firms are Cournot competitors. In this case, Firm 2 would produce ____ units to maximize profit.

Question

Quizplus · Accepted Answer

In a Cournot competition, each firm decides its quantity to maximize profit given the quantity produced by the other firm. The inverse demand function is P = 60 - 2Q, where Q = q1 + q2. Given the marginal cost (MC) of $12 for each firm, we can derive the reaction functions for each firm to find the equilibrium quantities. The reaction function for a firm in a Cournot duopoly is derived by maximizing the firm's profit given the output of the other firm, taking into account the inverse demand curve and the firm's cost structure. Without going through the full derivation, the equilibrium quantities for each firm in a symmetric Cournot duopoly with identical costs and the given inverse demand curve typically result in each firm producing less than what would be produced in a monopoly but more than what would be produced in perfect competition. The correct quantity for Firm 2, given the symmetry of the situation and the provided information, is 8 units, as this is a common result for such problems when solved algebraically.

Two Firms Are Producing Identical Goods in a Market Characterized