Consider a market that consists of n ≥ 2 identical firms. Each firm produces output at a constant average and marginal cost of 2. The market demand curve in this industry p = 20 – 2Q, where Q is market demand and p is price. Firms will choose output simultaneously.
(a) Find the symmetric Nash equilibrium.
(b) Show that as n becomes large the market output in this industry will approach the level of output under perfect competition.