1. (6 points) Suppose an oil company has 3 divisions. The "production" company pumps crude oil out of the ground. The "refinery" company refines the crude oil into gasoline. The "retail" company sells gasoline to consumers. The demand for gasoline can be expressed as: P = 400 - Q The cost functions for the three division are: Production: TCp = 200 + 0.25Q2 Refining: TCf = 400 + 0.5Q2 Retail: TCr = 100 + 40Q + 0.25Q2 A. What quantity should the firm produce, what price of gasoline should they charge, and how much profit will they make? B. What transfer prices should the firm set, if each division is to make their own decision? (Hints: There will be two of them. It is probably easiest if you have the retail division pay both directly to the others.) C. Find the profits for each division under the transfer pricing that you found in B. Compare to A and comment. D. Suppose that they Refining division successfully lobbies to have its transfer price raised by 20. What problems might this cause? Now return to the scenario in part C, and further suppose that production occurs in a country with a profits tax of 10%, refining occurs in a country with a profits tax of 50%, and retail happens in a country with a profits tax of 30%. E. Find the after tax profits for each division and the company as a whole. F. Choose new transfer prices that would allow you to have a larger after-tax profit. (Assume they continue with the optimal quantity.) Find the after tax profits for each division and the company as a whole