Consider a Cournot oligopoly with two firms, denoted as i = 1,2. Each firm ; has the same total cost function TC(q) = c.q . i i Firms have different inverse demands. The inverse demand for firm i is P = a-bQ, where Q=9 +9 i Assume that 2a -c>a>a for parts (a), (b), and (c). 2 (Hint: The case in which 2a-c>a >a is the case in which everything works as normal, so you might want to just ignore this until you get to part (d).) 1 2 2 (a) We know that MR = P + i I dP i 9. . Use this fact to express firm 1's marginal revenue as an explicit and simplified function of q dq; (b) Use your answer to part (a) to derive firm 1's reaction function. 192 1 and (c) Use your answer to part (b), and the symmetry of the model to arrive at a reaction function for firm 2. Use these two reaction functions to derive the Cournot equilibrium outputs for each firm. (d) What are the equilibrium outputs if a>2a-c? Explain. (Explanation should be under 30 words.)