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2. (20 pts.) Consider the following sequential game between City, C, and Firm, F. The demand for Firm's product is q(p) = 200 - 0.5p, where q equals Firm's output quantity and p is the market price. Firm's marginal cost is 40 and fixed cost is 500. In the beginning of the game, City announces its per unit tax amount, te [0, 400]. After City's tax announcement, Firm decides its output q e [0, 200]. City and Firm's objectives are to maximize own profits. a) Draw a corresponding fully labeled game tree of this sequential game. (5 pts.) b) Derive the optimal output of Firm as a function of the tax, t. set by City. (3 pts.) c) Derive the optimal tax amount t, t*. (3 pts.) d) What is the subgame perfect equilibrium, outcome, and payoffs to players? (4 pts.) e) Now, suppose that Firm now wants to maximize its after-tax revenue. How does it change your answers in part b and c? Is the resulting outcome sustainable? (5 pts.)