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3. In this question you are asked to compute the rationalizable strategies in a linear Bertrand-duopoly with discrete prices and fixed "startup" costs. We consider a world where the prices must be an odd multiple of 10 cents, i.e., P = {0.1, 0.3, 0.5, .... 0.1 + 0.2n, ...} is the set of feasible prices. For each price p, the demand is: Q(p) = max{1 - p. 0}. We have two firms / = {1, 2}, each with 0 marginal cost, but each with a fixed "start- up" cost k. That is, if the firm produces a positive amount, it must bear the cost k. If it produces 0, it does not have to pay k. Simultaneously, each firm sets a price p; E P. Observing prices p, and p2, consumers buy from the firm with the lowest price. When prices are equal, they divide the demand equally between the two firms. Each firm i wishes to maximize its profit. p:Q(pi) - k if pi 0) mi(PI, P2) = { P:@(p:)/2 -k pi = p; and Q(pi) >0 0 otherwise (a) If k = 0.1 : 1. (5 points) Show that p; = 0.1 is strictly dominated. 2. (5 points) Show that there are prices greater than the monopoly price (p = 0.5) that are not strictly dominated. 3. (15 points) Iteratively eliminate all strictly dominated strategies to find the set of rationalizable strategies. Explain your reasoning.4. There are three "dates", t = 1, 2,3, and two players: Government and Worker. . At t = 1, Worker expends effort to build K e [0, co) units of capital. . At t = 2, Government sets tax rates Tx ( 0, 1] and 7. ( [0, 1] on capital-holdings and on labor income. . At t = 3, Worker chooses effort ez ( [0, co) to produce output Kez. The payoffs of Government and Worker are: UG = TKK +T.Keg and Uw = (1 -Te)Ke2 + (1 - TK)K - K2/2 - e,/2. (a) (20 points) Solve the game by backwards induction