Consider a market in which two firms are engage in quantity competition a la Cournot, but with differentiated products. As in the standard model each firm i = 1,2 has a cost function TCi (qi) F+c* qi. However, now each firm may recieve a different price for it's output. In particular, firm 1 recieves the price P = a - b * q dq2 and firm 2 recieves the price = P2a-bq2 - d *q1. = (a) Use the fact that MR = P + and 92. dP dq1 *q1 to find an expression for MR in terms of a, b, d, q (b) Use your answer from part (a) to find firm 1's reaction function. (c) Find a simplified expression for each firm's equilibrium output, q. (d) Find each firm's equilibrium price, P*. Use your expression for P* to find a simplified expression for P* c, the firms markup over marginal cost. - (e) Find a simplified expression for firm i's equilibrium profits, . (f) Now consider your expressions for q, P** and . How do these expression change if we start without differentiation (i.e. d = b) and then move to a situation in which there is differentiation (i.e. d