Question

An industry is currently monopolised by an incumbent, firm 1. A challenger, firm 2, is considering entry, which entails a fixed cost setup cost f=300 in addition to its production cost. If the challenger enters, the two firms compete as in the Cournot duopoly. If the challenger stays out, its profits are zero and the incumbent obtains monopoly profits. The market demand is given by P(Q)=90−Q, where Q denotes the aggregate output supplied to the market. a) Suppose that, for each firms, the cost of producing q units of output is cq, where c=30 is a constant marginal cost. The interpretation is that both firms have a access to the same production technology. Calculate the Cournot outputs and the firms' resulting profits if the challenger decides to enter the market.

Answer 1

To calculate the Cournot outputs and profits if challenger firm 2 enters the market, establish reaction functions for both firms, solve for equilibrium quantities, and then calculate profits using total revenue minus total and fixed costs.

Step-by-step explanation:

When firm 2 considers entering the market, it faces a setup cost of 300, with a constant marginal cost c=30. Competing in a Cournot duopoly means that each firm decides its production quantity assuming the other's quantity remains fixed. The market demand is P(Q)=90−Q, where Q is the total output.To calculate the Cournot equilibrium, we first establish the reaction function for each firm, which shows how one firm's output decision depends on the other firm's output. For firm 1, the profit maximization condition is dπ/dq1 = P(Q) + dP/dQ*(-q1) - c = 0. After solving for firm 1's optimal output, we follow the same steps for firm 2. Substituting firm 2's optimal output decision given firm 1's output into firm 1's reaction function gives us the quantities for both firms in equilibrium.Profits are then calculated using the formula π = PQ - cQ - f, where f is the fixed cost and c the constant marginal cost.