Question

A pharmaceutical firm faces the following monthly demands in the U.S. and Mexican markets for its only patented drug: Q(U.S.) = 300,000 - 5,000P(U.S.) Q(Mex) = 240,000 - 8,000P(Mex) where quantities Q represent the number of prescriptions per month and the prices P are denominated in U.S. dollars (i.e., the Mexican demand has already been adjusted for the dollar/peso exchange rate). The marginal cost of the drug is constant at $2 per prescription in both markets. The firms monthly overhead costs for this drug are $1 million in the U.S. and $500,000 in Mexico.

a) Suppose that arbitrage between the markets is impossible, so the firm is able to charge different prices in each market. If the firm practices third degree (i.e., verifiable characteristics) price discrimination, what price will it charge in the U.S.? What price will it charge in Mexico? How much will it produce and sell in the U.S.? How much will it produce and sell in Mexico? What are the firm's total profits from the sale of the drug in this case?

b) Now suppose the firm cannot prevent arbitrage between the countries, so it is forced to charge the same price in the U.S. and Mexico. What price will it charge for the drug? How much will it produce and sell overall? What are the firm's total profits from the sale of the drug in this case?

c) Now suppose Congress is considering a law that would make arbitrage legal between the U.S. and Mexico (i.e., the law would allow for the importation and sale of drugs from Mexico to the U.S.). How much would the pharmaceutical firm spend per month on lobbying efforts to defeat this law, given your answers to parts (a) and (b).

Answer 1

A) for US

Q=300,000-5000p

P=60-0.0002Q

MR=60- 0.0004Q

MC=2

MR=MC

60-0.0004Q=2

Q(US)=58/0.0004= 145,000

P(US)=60-0.0002*145,000=31

For Mexico,

Q=240,000-8000p

P=30-0.000125Q

MR=30-0.000250Q

30-0.00025Q=2

Q(Mexico)=28/0.00025=112,000

P(Mexico)=30-0.000125*112,000=16

Profit=(31-2)*145,000-1,000,000+(16-2)*145,000-500,000

Profit=4,205,000-1,000,000+1,568,000-500,000=4,273,000

B)profit=(300k-5kp)p +(240k -8kp)p- 2(300k-5kp+240k-8k)-1 million-500k

DERIVATIVE of profit with respect to p and put equals to zero

∆profit/∆p=300k-10kp+240k-16p+10k+16k=0

566k-26kp=0

P=566,000/26,000=21.77

Qus+Q(Mexico)=300,000-5000*21.77+240,000-8000*21.77=256,990

Profit=(21,77-2)*256,990-1 million- 500,000=3,580,692.3

C)the firm will spend lobbying fee equal to the difference between profit.

Lobbying fee=4,.273 million-3.58 million=0.693 million or 693,000