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 1 would produce ____ units to maximize profit.

Question

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In a Cournot competition, each firm decides its quantity based on the quantity produced by the other firm. The inverse demand function is P = 60 - 2Q, where Q = q1 + q2. Given that the marginal cost (MC) is constant at $12 for both firms and assuming symmetry (each firm produces the same quantity for maximization), we can find the reaction function for each firm. To maximize profit, we set marginal revenue (MR) equal to marginal cost (MC). The total revenue (TR) for a firm is P*Q, and MR is the derivative of TR with respect to its own quantity. Solving the optimization problem (MR=MC) for one firm, taking into account the reaction of the other firm, leads to each firm producing 8 units in equilibrium.

Two Firms Are Producing Identical Goods in a Market Characterized