In a homogeneous-good Cournot model where each of the n firms has a constant marginal cost m and the market demand curve is p = a – bQ, show that the Nash-Cournot equilibrium output of a typical firm is q = a – m / (n + 1) b. Show that industry output, Q (= nq), equals the monopoly level if n = 1 and approaches the competitive level as n gets very large.