Problem 1. Multi market price discrimination.
Sony faces two distant markets for its toy – “PlayStation 3”: USA and Australia. The demand in USA is p=3500-q/2. The demand in Australia is p=4500-q. Sony’s MC(q)=500.
a) Suppose resale is prohibited. No one can buy the toy in the USA and then sell it in Australia and vice versa. What is the profit maximizing pair of prices?
b) Now suppose there is resale and the transportation cost is $600. That is one can buy the good in one country, ship it to the other country (for $600) and resell it there. How does your answer about the optimal prices change?
c) Now suppose there is perfect resale market, the transportation cost is 0. Assume that every customer will rather buy from Sony if Sony and the secondary market charge the same price, but if the prices are different – the customers buy at lower price. How does your answer about the optimal price change now?
Hint. To figure out the total demand don’t forget to invert the demand curves so that you are adding quantities. Further if you intend to use MR=MC equation you should express the total demand again as a function of quantity.
Notice that if Sony decides to charge two different prices in two different countries – this does not work as before, there will be no sales at a higher price.
Problem 2. Two-part tariff.
Suppose the monopoly has a constant marginal cost of 0 and can sell its good to two different groups of customers. One group of “poor” has demand function P = 1.5 – Q; the other – equally large group of “rich” has demand: P = 2 – Q. The seller cannot tell whether a particular consumer is rich or poor, but she knows that there is equal number of both types.
a. What is the optimal pair of two-part tariffs: the pairs Fr – the entry fee and pr – the price per unit that monopoly intends for the rich guy and Fp – the entry fee and pp – the price per unit that monopoly intends for the poor guy?
b. Does the monopoly serve both groups of customers? Compare the monopoly’s profit from the optimal pair of two part tariffs with the profit that she could make if she ignored the poor consumers altogether.
Compare this profit also to the profit that she could make if she offer a single two part tariff to everybody.
c. Now suppose there is 3 times more poor people that rich. How does your answer to a) change?