Question

2. Esta Estelle is a monopolistic provider of a service in a small town (she helps people organize their closets). The demand for her services is given by Q = 600 - 4P where is the number of customers she serves and P is the price she charges (in dollars). Finally, suppose that Estelle's marginal cost and average cost of production are given by LRAC = LRMC = 30. (a) If Estelle chooses to use a liner pricing strategy, what price will maximize her profits and how many customers will she serve at that price? (b) Calculate profit, consumer surplus and deadweight loss at the profit maximizing price. (c) How much potential profit is Estelle throwing away by using this pricing strategy? Explain.

Answer 1

(a)

Q = 600 - 4P

4P = 600 - Q

P = 150 - 0.25Q

With linear (single) pricing, profit is maximized when MR = MC.

TR = P x Q = 150Q - 0.25Q²

MR = dTR/dQ = 150 - 0.5Q

150 - 0.5Q = 30

0.5Q = 120

Q = 240

P = 150 - (0.25 x 240) = 150 - 60 = 90

(b)

From demand function, when Q = 0, P = 150 (vertical intercept)

Consumer surplus (CS) = Area between demand curve and price = (1/2) x (150 - 90) x 240 = 120 x 60 = 7,200

Profit = Q x (P - AC) = 240 x (90 - 30) = 240 x 60 = 14,400

When P = MC,

150 - 0.25Q = 30

0.25Q = 120

Q = 480

P = MC = 30

Deadweight loss = (1/2) x Change in P x Change in Q = (1/2) x (90 - 30) x (480 - 240) = (1/2) x 60 x 240 = 7,200

(c)

With perfect price discrimination, P = MC and Profit = CS.

When P = MC = 30, Q = 480.

Profit = (1/2) x (150 - 30) x 480 = 240 x 120 = 28,800

Profit thrown away = 28,800 - 14,400 = 14,400