Question

A monopoly firm has two types of customers, but cannot identify customer type before a purchase is made One customer type has inverse demand P1(Q1) = 140 2Q while the other customer type has inverse demand P2(Q2)= 180 - 402 The cost of production is C(Q) 20Q (there are no fixed costs) Which of the following pricing schemes will provide the firm with the highest profit? Charge $100 per unit for any quantity, or $80 per unit if buying 20 or more units a. b. Charge $100 per unit for any quantity, or $80 per unit if buying 30 or more units Charge $100 per unit for any quantity or $80 per unit if buying 35 or more units C. d. Charge $80 per unit for any quantity, or $60 per unit if buying 35 or more units

show the explanation please

Answer 1

The monopolist would maximize profits by setting MR=MC for each customer group

MC=20

MR=twice the slope of the demand curve

Group 1: -

140-2Q

MR = 140-4Q

Setting MR=MC

140-4Q=20

140-20 = 4Q

Q=120/4 = 30

P=140-2(30) = 80

Group 2:-

180-4Q

MR=180-8Q

Setting MR=MC

180-8Q=20

180-20=8Q

Q=160/8 = 20

P=180-4(20) = 100

So,option (B) is correct as the firm will maximize profits by setting P=100 for any quantity but when the Q is greater than 30,the firm will maximize profits by setting P=80