2. [18 points] (Cournot competition) Consider a variant of the Cournot's duopoly game. Two firms compete through output and the inverse demand function is 90 - Q if Q 90 where Q is the total output. Two firms have different production costs. Firm 1 is a smaller firm with a increasing marginal cost and also has limited capacity of production. Specifically, Firm 1 has cost function C1(q1) = 297 and capacity F (Firm 1 can produce at most F units). Firm 2 has a constant marginal cost with cost function C2(q2) = 30q2 and no capacity constraint. Both firms try to maximize their profits (you can use the profits as payoffs for firms). (a) [10 points] Write down the payoff function and best response function of each firm.(b) [4 points] If the capacity F = 30, find the Nash equilibrium of the game. (c) [4 points] If the capacity F = 20, find the Nash equilibrium of the game