Ferdinand Sludge has just written a disgusting new book, The Piggery. His publisher, Graw McSwill, estimates that the demand for this book in the United States is Q1 = 50,000 - 2,000P1, where P1 is the price in the U.S. measured in U.S. dollars. The demand for Sludge's opus in England is Q2 = 10, 000 - 500P2, where P2 is its price in England measured in U. S. dollars. His publisher has a cost function C(Q) = $50, 000 + $2Q, where Q is the total number of copies of The Piggery (Q1 + Q2) that it produces.
a. If McSwill must charge the same (uniform) price in both countries the find profit maximizing (Q) quantity and price and the associated profit.
b. Find the own price elasticity of substitution in each market at the uniform price.
c. If McSwill charges a different (third degree price discrimination)price in each country and wants to maximize profits, how many copies should it sell in the United States and at what price? Also, how many copies should it sell in England and at what price? How much is the total profit