4. Two firms compete by choosing price. Their demand functions are Q, = 20 - P. + P2 and Q2 = 20 + 1 TA P 2 where P, and P, are the prices charged by each firm, respectively, and Q, and Q, are the resulting demands. Marginal costs are zero. a. Suppose the two firms set their prices at the same time. Find the resulting Nash equilibrium. What price will each firm charge, how much will it sell, and what will its profit be? (Hint: Maximize the profit of each firm with respect to its price.) b. Suppose Firm 1 sets its price first (leader) and then Firm 2 (follower) sets its price. What price will each firm charge, how much will it sell, and what will its profit be