Consider a market with inverse demand P = 9Q, where Q is the sum of output produced by all firms in the market. Firms have identical cost functions c(q) = 4 + q.
1. Suppose there is a single firm in this market (monopoly). Derive the equilibrium industry price, quantity, profit, and the Lerner index. What will the consumer surplus be?
2. Derive the Nash equilibrium industry price, quantity, profit, and the Lerner index if the market is served by Cournot duopolists. What will the consumer surplus be?