4) 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,Pz) = 10 - 2p1 + p2 and the demand for firm 2 is q2 (P2, P1) = 10 - 2p2 + P1. Also, assume that firm I has a constant marginal cost of C, = 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. 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