Econ question:

Problem 1. A pharmaceutical company faces the following demand function for one of its products in the American market: QA = 2,000,000 20,0001), where QA is the number of prescriptions sold in the American market annually and PA is the price per prescription. The rm's annual total cost function is: TCA = 40,000,000 + SQA The company is considering also entering the Brazilian market where the demand for the pharmaceutical is: 3 = 200,000 2,500PB The cost function for the Brazilian market is: TCB = 1,000,000 + 5Q3 A. Calculate the rm's optimal price in the US. Show your work. B. What is the optimal price to charge in the Brazilian market? Show your work. C. Explain why the problem of parallel imports, a form of arbitrage, may result from the pricing structure you have calculated in the previous questions. [A quantitative answer is not required] D. If it cost the company $1,500,000 annually to eliminate the problem of parallel imports, should it do so? Explain! (Eliminating parallel imports means that the company can pay $1,500,000, set one price in Brazil and a different price in the US, and no one will be able to take advantage of this arbitrage opportunity so that the two markets can be thought of as two completely separated markets). [Hint: Answer this question by comparing the prots for two scenarios: i) total prots of the company if it could separate the two markets (here, much of the work has been done in A. and B.); ii) prots that the company would make if it treated the US and Brazil as a joint market. Here, you will have to compute aggregate demand QA+QB, adding the demand functions given above]