Question

3. (20 points) Consider the monopoly pricing problem involes a distributor and a manufac- turor (both are monopoly). The demand function is P-10-20 And the marginal cost of producing is MC-1, while the marginal cost of distribution is assmed to be zero a). (10 points) If two firms are separate, determine the optimal monopoly pricing of each firm. b). (10 points) If two firms merge into a single monopoly, determine the optimal pricing and compare the profit level with the total profit level in part (a).

Answer 1

P = 10 - 2Q implies MR = 10 - 4Q MC_1 = 1 - - - - - - magnificent of production MC_2 = 0 - - - - - - - marginal cost of distribution At equation, MR = MC_1 = MC_2 implies 10 - 4Q_1 = 1 implies Q_1 = 9/4 implies p_1 = 10 - 2(9/4) p_1 = 11/2 therefore pi_1 = (9/4)(11/2) - 1(9/4) = 9/2 times 9/4 pi_1 = 81/8 tildeequal 10 10 - 4 cos = 0 Q_2 = 10/4 = 5/2 implies p_2^alpha = 10 - 2(5/2) p_2^alpha = 5 pi_2 = 5 times 5/2 = 0 pi/2 = 25/2 tildeequal 12.5 \r\n Now, Total MC = MC_1 + MC_2 = 1 therefore MR = Total MC implies 10 - 42 = implies Q_1^alpha = Q_2^alpha = 2/4 implies p_1^alpha = p_2^alpha = 11/2 therefore pi^alpha = p_1^alpha Q_1^alpha + p_2^alpha Q_2^alpha - 1 Q_1^alpha - 0 Q_2^alpha = (2/4)(11/2) + (2/4)(11/2) - 1(2/4) - 0. Pi = 25 < pi_1^alpha + pi_2^alpha = 10 + 12, 5 = 22, 5 Hence single monopoly generates higher profits.