Suppose three identical firms are engaged in Cournot competition in quantities. They all have marginal costs equal to 40.
Market demand is given by:
P(X) = 200 - X = 200 - (x1 + x2 + x3),
where P denotes price, X total quantity demanded, and xi individual demand for firms i = 1,2, and 3.
a) Explain in what type of markets Cournot type competition can occur. Write down the demand curve and marginal revenue curve for firm 1.
b) What is the first order condition for profit maximization for firm 1? Compute the optimum quantity x1* for firm 1 as a function of quantities x2 and x3.
c) Since the firms are identical, symmetrical solutions exist also for the two other firms. Use this to compute the optimum quantity produced (and sold) for each firm.
d) Compute total demand, X, and market price, P. Compute each firm's profit, πi, and the sum total of all profits.