Also, how do total industry profits change as n approaches infinity.

Problem 5: Differentiated Products with n Firms Suppose there are n > 2 firms whose goods are substitutes. Each firm chooses its price p. Let P = pi + p2+ + Pn be the sum of all prices, and P_, = P - p; be the sum of all prices except firm i. Each firm i's demand is then given by qi = 2 - Pi+ 27 . In other words, if the average price of other firms (which is P_;/(n -1)) goes up, then firm i's demand goes up. Also, the number of consumers who would buy from firm i if all prices were zero is 120, which decreases as n increases. Firms have a constant marginal cost, which we'll assume is zero for simplicity. Problem 5.1 Suppose all firms set the competitive price, which is zero since marginal costs are zero. How many units would be sold to each firm i? Problem 5.2 At the competitive price (pi = 0 for all firms), how does the total quantity sold change as n - co? How does the total quantity sold (which is nq; ) change as n - co? Problem 5.3 Solve for firm i's best response function BR;(P-;). Problem 5.4 Solve for the 'symmetric' Nash equilibrium of this game. 'Symmetric' means each firm chooses the same price p" Problem 5.5 What is each firm's quantity sold in equilibrium (q; )? Problem 5.6 What is each firm's profit in equilibrium (n; )