Question

Suppose that you are the managing director of a pharmaceutical company that sells a unique patented drug to hospitals and drug stores. You are free to charge different perunit prices at these two markets. Let p be the price per unit of drug and q be the quantity demanded. The hospitals demand curve is described by p = 12 – q and the drug stores demand curve is given by p = 8− q. The marginal cost of producing the drug is constant and equal to c = 2 per unit

A. What is the price that you will charge to hospitals (H)? To drug stores (D)?

B. If you were to charge a uniform price to all the buyers, what would it be?

C. If the Antitrust Division cares about the sum of your company’s profits plus the total consumer surplus of all the buyers, do you think it should ban price discrimination? (Computation required for full credit. Hint: compute the consumer surplus separately for drug stores and hospitals, even if they buy at the same price, and then add them up.)

Answer 1

a) Price charge to hospital

P = 12-q or MR = 12 - 2q

MC = 2

MR=MC

12-2q = 2 or 10 = 2q

q = 5

P = 12 - 5 = $7 ( price charged to hospital )

price harge to drug strore

P = 8-q or MR = 8 -2q

MC = 2

8-2q= 2

6 = 2q or q = 3

P = 8 - 3 = $5 ( price to drug store)

b) Uniform price to all buyers. hence we would find aggregate demand first.

P = 12-q + 8-q = 20 - 2q

MR = 20 - 4q

MC= 2

20-4q = 2

18= 4q or q = 4.5

P = 20 - 2*4.5

P = 20 - 9 = $11

c) Consumer surplus of hospital = 1/2 * ( 12-7) * 5 = 12.5

consumer surplus of drug store = 1/2 * ( 8 - 5) * 3 = 4.5

consumer surplus at uniform price = 1/2* ( 20-11) * 4.5 = 20.25

yes, Anti trust division can ban price discrimination since the consumer surplus is large in the uniform pricing .