1. (Limit Pricing) Consider the following two-period model with two rms: incumbent (I) and entrant (E). These two rms produce differentiated products and compete in prices. The incumbent rm Operates in both periods. The entrant does not Operate in period 1, but considers entering in period 2. Both rms have a constant marginal cost c : 30. The entry cost (for the entrant only) is F = 395. There is no other xed cost. The market demand is as follows. If there is only one rm (the incumbent) in the market, the demand is given by q; = 90 3)]. If there are two rms, the market demand is given by 1 9'1 = 45 Pr + gm: 1 (IF; = 45+pIpE To summarize, in period 1, the incumbent is a monopolist. In period 2, if the entrant stays out, the incumbent remains a monopolist, but if the entrant enters the market, then the two rms compete in prices. (a) Consider rst the case where the incubment does not adopt any entry-deterring strategies so the entrant will enter in period 2. Denote the prices charged by the incument in period 1 and 2 by p1 and 392, respectively. Solve prices p1, p2 and pg, and compute the two rms' total prot g and an (2 7T1 + 7T2), where rrl and 7T2 are incumbent's prot in period 1 and 2, respectively. (b) Now suppose the incumbent wants to deter entry. Suppose that the incumbent can com- mit to charging p1 : p2 = 49 in both periods. Would the entrant enter in period 2? What is the incurnbent's total prot by charging p1 = p2 = 49? Does the incumbent benet from this limit pricing strategy, in comparison to part (a)? (c) Finally, suppose that in period 1 the incumbent announces that it will charge price 301 = p2 = 49 in both periods, but the incumbent cannot commit to charging p2 = 49 in period 2 when period 2 arrives. If you are the entrant, will you believe that the incumbent will charge p2 : 49 in period 2? In particular, if you ignore the incumbent's announcement and enter anyway in period 2, what is the optimal price p2 should the incumbent charge if the incumbent is rational and prot-maximizing? Will you enter in the second period