Question

Suppose there are 2 types of customers. Type A have the following demand P=200-2Q and type B have the following demand P=240 -8Q. The total cost is MC=80. The market is monopolized and the producer is considering a pricing strategy involving 3rd degree price discrimination. What prices should the monopoly charge each type of consumer and what should be the optimal output to be sold to each type of consumer?

Answer 1

FOR TYPE A CONSUMER

P=200-2Q

TR = PQ = Q(200-2Q)

MR = dTR/dQ = 200 - 4Q

According to profit maximizing condition : In order to maximize profit a firm should produce that quantity at which MR = MC

here MC = 80 and MR = 200 - 4Q

=> 200 - 4Q = 80

=> Q = 30

Hence P = 200 - 2Q = 200 - 2*30 = 140

Hence For Type A consumer, Monopoly should charge Price = 140 and  optimal output to be sold to type A consumer = 30

FOR TYPE B CONSUMER

P=240-8Q

TR = PQ = Q(240 - 8Q)

MR = dTR/dQ = 240 - 16Q

According to profit maximizing condition : In order to maximize profit a firm should produce that quantity at which MR = MC

here MC = 80 and MR = 240 - 16Q

=> 240 - 16Q = 80

=> Q = 10

Hence P = 240 - 8Q = 240 - 8*10 = 160

Hence For Type B consumer, Monopoly should charge Price = 160 and  optimal output to be sold to type B consumer = 10