. Consider a market with n firms, where all firms produce identical commodities. The market demand curve is p = a bq where a > 0 and b > 0, and where q = q1 + q2 + + qn, with qi being the quantity produced by Firm i, i = 1, . . . n. Firm i's profits are i(q1, q2, . . . , qn) = pqi cqi , where c is the per-unit cost of production. (Note that c is the same for all firms.)

(a) Find the best-response function for firm i.

(b) What is a Nash equilibrium in this game?

(c) Find a symmetric Nash equilibrium (this is an equilibrium where all firms produce the same quantity).

(d) What is the market price in equilibrium? What are profits for each firm?

(e) What happens to the price and to profits as n goes to infinity? Compare this outcome to the case of perfect competition.