Problem 3 (Profit maximization under different product market structure)

Suppose the market demand is Q=100-P. You are asked to find out how this market operates under perfect competition, monopoly and oligopoly, with the same market demand and cost structure for each firm.

a)Suppose the industry is perfectly competitive. The long-run cost function of each firm is c(Q)=2Q. Calculate the market price, total quantity supplied of the market, and each firm's profit (in the long run).

b)Suppose there is a single firm serving the whole market, i.e. it is a monopolist. The cost function of the firm is c(Q)=2Q.Calculate the total quantity supplied of the market, the market price, and the firm's profit. How do they compare with a)?

c)Suppose the market is under duopoly. There are two identical firms playing Cournot competition, and the cost function of each firm is c(Q)=2Q.Calculate the total quantity supplied of the market, the market price, and each firm's profit. How do they compare with b)?

d)Suppose there are 3 identical firms playing Cournot competition, and their cost function of each firm is c(Q)=2Q. Calculate the total quantity supplied of the market, the market price, and each firm's profit. How do they compare with c)?