Consider the Cournot duopoly game with demand p = 100 - (q1 + q2) and variable costs ci (qi) = 0 for i = 1 and 2. There is a fixed cost of production k = 225 (i.e. which is incurred whenever the firm produces positive output, and not incurred if the firm produces nothing) that is the same for both firms.

(a) Assume first that both firms choose their quantities simultaneously. Write down the firm's best response function (assume that the firm produces nothing if it cannot make strictly positive profits). Solve for all pure strategy Nash equilibria.

(b) Now suppose that firm 1 is a "Stackelberg leader" in the sense that it moves first and chooses q1. Then after observing q1 firm 2 chooses q2. Solve the game by backward induction and write down your solution in terms of the players' strategies.