A manufacturer of CD players currently sells them domestically for price v1, and

Question

A manufacturer of CD players currently sells them domestically for price v1, and allows foreign customers to purchase them by mail for price v2 where v1, v2 are the domestic and foreign reservation prices The problem is that frequent travelers are tempted to purchase the CD players domestically, then sell them overseas. Assume risk-neutrality.

a. How high would transportation costs/tari?s have to be to render this practice unprofitable for travelers?
b. Now suppose that transportation costs and tari?s are zero, but each CD player breaks down in the ?rst year with probability p. Assume for simplicity that consumer valuation of a good that breaks down during the ?rst year is zero. The manufacturer attempts to stop arbitrage by voiding all warranties overseas, unless the CD player was purchased directly through the mail. Give the necessary condition relating v1, v2, and p for the manufacturer to be successful.

Explanation / Answer

a. Which practice? The third degree price discrimination engaged in by the manufacturer or the arbitrage engaged in by travelers? In order to make it unprofitable for the manufacturer to third degree price discriminate, the transportation costs/tariffs must be high enough that the manufacturer will not benefit from selling in foreign markets. A reservation price is the highest price a consumer would be willing to pay for a good. So, foreign consumers are not willing to pay any more than v2 for goods. This means that with a tariff, the manufacturer will always charge v2 and get to keep v2' where: v2' + t = v2 The manufacturer will only sell to the foreign market if v2' > v1. Substituting this value, v2 - t > v1 -t > v1 - v2 t > v2 - v1 This is intuitive, a tariff that is larger than the difference between v2 and v1 will make it unprofitable for the manufacturer to sell internationally. Frequent travelers do not pay tariffs and transportation costs are sunk costs. That is, they are already traveling for some other reason. So, frequent travelers will engage in arbitrage as long as v2 > v1, no matter how large tariffs are. If travelers had to pay tariffs, they would stop engaging in arbitrage under the same condition as manufacturers, t > v2 - v1. If arbitrage was made illegal, they would face a similar condition, p*f > v2 - v1, where f is the fine associated with arbitrage and p is the probability of being caught. b. The consumer surplus received by a foreign consumer if he or she purchases by mail is: CSm = v2 - v2 = 0 because v2 is the reservation price of foreign consumers. The consumer surplus received by a foreign consumer if he or she purchases from a traveler is: CSt = (v2 - a)*(1-p) - v2*p, where a is the arbitrage price. v1

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