Question

1. Suppose that demand is given by P=100-Q, marginal revenue is MR=100-2Q, and marginal cost (and average cost) is constant at 20. a. What single price will maximize a monopolist's profit? b. What will be the prices and quantity under two-part pricing? It involves a lump sum fee (e.g., membership fee) equal to the consumer surplus at competitive prices and user fees (i.e., unit price) equal to the competitive price. c. Now the monopolist has another group of consumers whose demand is P-80-Q. Suppose that the membership fee (M) must be the same for all consumers. Calculate the optimal membership fee when the unit price (P) is 20. Calculate profits from the groups (you can use profit=(P-MC) Q+M, where M is the membership fee charged by the monopolist). d. While the two-part pricing can increase the monopolist's profit, there is an even better way to increase its profit. In the previous part, the monopolist makes zero revenue from unit sales since unit price equals the marginal cost; Calculate the optimal membership fee when unit price (P) is 30. Calculate profits from the groups.

Answer 1

Solution-

a)Profit maximizing condition for a monopolistic firm will be where the marginal cost incurred by the firm is equal to marginal revenue earned by the firm

(a Given, PE 100-9 MR = 100-20, me=20. So, Profit Maximizing condition will be MR = mc. 100-28 = 20. 20 = 80. i 8 = 8% = 40 Profit Maximizing output E So, Putting of in vrice function we get, p* = 100 - 8 = 100 - 40 260. So I Profit maxiniezing Price = $60]

b) At competitive scenario, price will be set equal to marginal cost.

:P= 100-0, Mc=20. corner Points of Demand come ha 0=0, P=0 P= 100 &= 100 - Price T Loo Bk CS 20/A el ison Q-80 100 MC=20 quantity By competitive pricing strategy, Po Mc 100-Q = 20. Q = 100-20 = sol So, membership feeo = CS = 1 x A cx Consumer = 1 x 80 x 80 suuplus C. = 3200 W So, Price & (P) = 100-80-20 and quantity = 80 un Two part pricing Strategy

c) membership fee will be equal to consumer surplus at price equal to $20.

doo KB A = 20 Á ~ 80 c p= 20 Quantity PY Q+= 80 100 pt = 100-o* 20= 400-o* 18* = 100-20 = 80 l Membership fee = consumer Surplus. Areale AB C) = 1 X ALX AB C.S= x 80 x 100-20) ICS = £ x 80 x 80 - 3200 So, Priofit = (P-MC) & + M P=mc con 200 + 3200 So, (20-20) & +3200 So Profit - $3200]

d)

Prices 200A cs To p* 30 or 70 c P=30. Q = 70. 100 quantity :Pa 100-o* 30 = 100- * Q+ 100-30 = 70. So, mumbership fee consumer Surplus Areas AB C = 1 x B C X AB = 1/2 x 70 x (100-30) a = 1 x70 x 7o. [M= 2450) So, Profit = (PP_MC) Q + M = (30-20) 70 + 2450 Profita E 1070 + 2450 & Too +2450 = $31501