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(55 points) There are two rms, each of which can produce any quantity of a good at 0 cost. Firm 1 is the incumbent operating in the market. Firm 2 is considering entering the market. Entry is costly for rm 2 and the cost is some known 0 2 0. Market demand is given by p = A q, where A is the level of advertising and q = q1 + qz is the aggregate amount of the good produced (the sum of the amounts both rms produce). If the rms produce more than A, that is, if q > A, then the price is p = 0. The game proceeds as follows. First, rm 1 decides on the level of advertising A 2 0 and pays 2A3 / 54. Firm 2 observes A and decides whether to enter the market. If rm 2 enters, it pays the entry cost 0 2 O and the two rms engage in Cournot competition (rm 1 chooses ql and rm 2 chooses Q2, simultaneously). If rm 2 does not enter, then rm 1 produces as a monopolist in the market. (a) (10 points) Draw the game in extensive form. (b) (10 points) What is each rm's set of strategies? (c) (10 points) Suppose that c = 0. Solve for a subgameperfect equilibrium. Hint: this is very similar to the advertising application we saw in class. ((1) (15 points) Suppose that c > O. Solve for a subgameperfect equilibrium. Hint: Firm 1 wants to choose A to be as high as possible while keeping it low enough to convince rm 2 to stay out of the market. Therefore, in a subgameperfect equilibrium rm 2 must be indifferent between entering and not entering (you can use this observation without proving it). (e) (10 points) Suppose that c > 0. Find another Nash equilibrium that is not subgame perfect