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 per unit 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.

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

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

3. 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

1. From mid pricing rule for maximizing profits, we can find the optimal price. P' = 12, which is the choke price for hospitals demand.

Phosp= ( P' + MC)/2 = (12 + 2)/2 = 7

Similarly, for drug stores, P' = 8

Pdrug = (8 + 2)/2 = 5

So, these are the ideal prices to be set by the pharma company

2. In order to charge a uniform price to all the buyers, first we add their demand functions and follow the same process.

p = 20 - 2q

Pcommon = (10 + 2)/2 = 6

So, this could be the common price for the buyer

3. Consumer surplus is nothing but the difference between the maximum price a customer is willing to pay and the price he actually pays. So, from the demand curve we can drive those values

Surplus of Hospital = ½(P' - Phosp )(qat p=Phosp)

=½(12 - 7)5 = 12.5

Similarly, surplus of drug stores = ½(3)(3)= 4.5

Total = 17

Total Surplus when they are charged the same price = 49/2 = 24.5

Since the consumer surplus is more when charging same price and assuming a fair market, the overall economic surplus will be greater in this case. Hence the pharmaceutical firm can ban price discrimination.

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