Consider two firms that produce identical products and compete in prices (i.e. their strategies are their prices). The demand function is given by q = 1 - p where q is the quantity demanded and p is the lower price of the two. The marginal cost of firm 1 is 0,and the marginal cost of firm 2 is c2 < 1. The prices charged by firm 1 and firm 2 are denoted by p1 and p2, respectively. If pl = p2, then the demand is shared equally between the two firms. a) Suppose c2 = 0. Show that pl = p2 = 0 is a Nash equilibrium, by demonstrating that neither firm deviates from the equilibrium strategy. b) Suppose 0 < c2 < 1. Show that there is no Nash equilibrium such that p1 = p2.Hint: you need to look at three different cases, namely pl = p2 < c2, p1 = p2 = c2, and p1 = p2 > c2.

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