Suppose three identical firms are engaged in Cournot competition in quantities. They all have marginal costs = 40. Market demand is given by: P(X) = 180 - X = 180 - (x1 + x2 + x3), where P denotes price, X total quantity demanded, and xi individual demand for firms i = 1, 2, and 3. a) 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 function of quantities x2 and x3.
c) Since the firms are identical, symmetrical solutions exist also for 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 Ki, and the sum total of all profits.
e) Suppose firm1 and firm2 merge. Call the new firm A. It has output Xa and profit Ka. Suppose there's a Cournot competition after the merger, and assuming for now, the marginal cost for firm A is still 40 (same as firm3), compute quantities, market price, and profits for both the merged firm and firm3
f) Is the total quantity produced (and sold) larger or smaller than before?