Question: A company produces an antiretroviral drug to treat HIV infection. Let the price per dose be measured in U.S. dollars and the quantity demanded be measured in thousands of doses per year.

The inverse demand function in Africa is given by

P _A = 100 - Q _A

while in the U.S. it is P _B = 300 – 4Q _B

Once the research and development costs for the drug are sunk, the marginal cost of producing each dose is constant at $4, so the total cost function becomes

TC = 4(Q _A + Q _B ).

Suppose the company is able to segment the markets and charge different prices in Africa and the U.S. by practicing third-degree price discrimination.

1. What are the profit-maximizing quantities to sell in the U.S. and Africa? What are the corresponding prices? Please show and explain. How much profit does the company earn?
2. Verify that the inverse elasticity rule holds at the two quantity/price combinations that you found in part (A).

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