5. COURNOT WITH N ASYMMETRIC FIRMS Consider an industry with n output-setting firms, each with constant marginal cost c; and fixed cost F;. Market demand is given by p = a - bQ, where Q = _=1 qi- (1) Show that firm i's best-response mapping is given by q, (Q_;) = 26 - 2Q_;, where Q-i = Litj 9j. (2) Show that, in equilibrium, total output is given by Q = (na - 21=1 Ci) b(n +1) Hint: add up all n first-order conditions for profit maximization. (3) Show that equilibrium price is given by p = a+ Ziel Ci n+1 (4) Show that in equilibrium, firm i's output level is given by a - nci+ Zizicj qi = b(n + 1) (5) Show that, in equilibrium, firm i's profit is given by: ( a - ncit Zizi ci)? _ Fi n +1 (6) Show that, in equilibrium, consumer surplus is given by CS = = 1 (na - Lici \\ 2 2b n+ 1