(20 pts.) Consider the following sequential game between City, C, and Firm, F. The demand for Firms product is () = 200 0.5, where q equals Firms output quantity and p is the market price. Firms marginal cost is 40 and fixed cost is 500. In the beginning of the game, City announces its per unit tax amount, t [0, 400]. After Citys tax announcement, Firm decides its output q

[0, 200]. City and Firms objectives are to maximize own profits.

1. a) Draw a corresponding fully labeled game tree of this sequential game. (5 pts.)

2. b) Derive the optimal output of Firm as a function of the tax, t, set by City. (3 pts.)

3. c) Derive the optimal tax amount t, . (3 pts.)

4. d) What is the subgame perfect equilibrium, outcome, and payoffs to players? (4 pts.)

5. 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.)