Game Theory question about a duopoly:

F. Duopoly w/Continuous Strategies. Suppose Firm 1 and 2 each have the following demand curves: Q1 = 200 - 4P, + P2 and Q2 = 200 + P, - 4P2. Firm I has a unit cost of 10 and Firm 2 has a cost of 10 per unit of output so that profits for each firm are given by: " = (P, - 10) (200 - 4P, + P2) = 240P, - 4P.? + P. P. 10P2 - 2000 and T2 = (P2 - 10) (200 + P1 - 4P2) = 240P2 - 4P2 2 + PiP2 - 10P, - 2000. F.1) Below is each firm's best response curve. Solve for the Nash equilibrium using the two equations. What is the equilibrium price that each firm charges? Show your work. (4 points) P1 = 30 + - P2 1 8 P2 = 30 + - P1 F.2) Suppose there is a increase in Firm I's unit costs so that it is now 20 per unit, so that the best-response curves of the two firms are given below. (Note that only Firm 1's best-response curve changes). Find the new equilibrium prices for each firm. (4 points) P1 = 35 + - P P2 - 30 + - P1