(4) Consider a duopoly selling in a market with inverse demand function p = 12 q. Firm 1's cost function is 01(q1) = q1 and rm 2's cost function is 02(q2) = 2:32. (a) Assume rms choose output simultaneously (Cournot model). Compute the equilibrium quantities and the market price in a Nash equilibrium. (b) Now assume that rm 1 is a leader and chooses its output ql rst. Then, rm 2 chooses its output qg after observing ql (Stackelberg model). Find a. subgame-perfect Nash equilibrium of this game. Carefully specify the strategies for rm 1 and rm 2. What quantities are produced in equilibrium and what is the market price in equilibrium