Suppose there are two firms that compete in prices, say firms 1 and 2, but that the firms produce differentiated products. Suppose that the demand for firm 1 is q1(p1.p2)-10-2p1 +p2 and the demand for firm 2 is q2(p2.p1)-10-2p2 +p1. Also, assume that firm 1 has a constant marginal cost of c1=2 and firm 2 has a constant marginal cost of c2 =3. a) What are the reaction functions for both firms? b) Solve for the Bertrand equilibrium in prices. c) Now, suppose firms 1 and 2 agree to merge. However, under the merger, only firm 1 will operate and firms 1 and 2 will split the resulting profits equally. Will both firms agree to such a plan or do they prefer the Bertrand outcome?