Question

Consider the following market: Two firms compete in quantities, i.e., they are Cournot competitors. The firms produce at constant marginal costs equal to 20. The inverse demand curve in the market is given by P(q) = 260 − q.

a. Find the equilibrium quantities under Cournot competition as well as the quantity that a monopolist would produce. Calculate the equilibrium profits in Cournot duopoly and the monopoly profits.

Suppose that the firms compete in this market for an infinite number of periods. The discount factor (per period) is δ, δ ∈ (0, 1).

b. The firms would like to collude in order to restrict the total quantity produced to the monopoly quantity. Write down strategies that the firms could use to achieve this outcome.

c. For which values of δ is collusion sustainable using the strategies of subquestion (2)? [Hint: Think carefully about what the optimal deviation is.]

Answer 1