The BCY Corporation provides accounting services to a wide variety of customers,
ID: 1120105 • Letter: T
Question
The BCY Corporation provides accounting services to a wide variety of customers, most of whom have had a business association with BCY for more than five years. BCY's demand and marginal revenue curves are: P = 10,000 - 10Q MR = 10,000 - 20Q. BCY's marginal cost of service is: MC = 5Q.
a. If BCY charges a uniform price for a unit of accounting service, Q, what price must it charge per unit, and how many units must it produce per time period in order to maximize profit? Calculate the consumer surplus.
b. If BCY could enforce first-degree price discrimination, what would be the lowest price that it would charge and how many units would it produce per time period?
c. With perfect price discrimination and ignoring any fixed cost, what is total profit? How much additional consumer surplus is captured by switching from a uniform price to first-degree price discrimination?
Explanation / Answer
(a) Profit is maximized by equating Marginal revenue (MR) with MC.
10,000 - 20Q = 5Q
25Q = 10,000
Q = 400
P = 10,000 - (10 x 400) = 10,000 - 4,000 = 6,000
From demand function, when Q = 0, P = 10,000 (Reservation price)
Consumer surplus (CS) = Area between demand curve & price = (1/2) x (10,000 - 6,000) x 400 = 200 x 4,000
= 800,000
(b) With perfect price discrimination the firm charges a price equal to MC and profit equals entre CS.
10,000 - 10Q = 5Q
15Q = 10,000
Q = 667
P = MC = 5 x 667 = 3,335
(c) Profit = CS = (1/2) x (10,000 - 3,335) x 667 = (1/2) x 6,665 x 667 = 2,222,777.5
Additional CS = 2,222,777.5 - 800,000 = 1,422,777.5
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