Question

You are in the market for a new car and you have your eyes on a Mercedes Benz (MB). The (identical) car is available in Europe and the US and we assume away all transactions costs and transportation costs. Suppose that the MB costs $120,000 in the US and the current spot rate is 1.3 $/euro.

Please answer the following questions:

a. What is the euro price of the MB in Europe consistent with the law of one price (LOOP)?

b. If the MB was selling for 95,000 euro, explain how you could make a profit since this pair of prices is not consistent with the LOOP. Be sure to state profit in terms euros and $ US of buying one MB low and selling one MB high.

c. Now explain how arbitrage would work in terms of influencing the US dollar price and the euro price to be consistent with the law of one price. Please explain in detail - referring to your answer in part b).

Answer 1

Part a

Given that,

            Dollar price = 120000

            Current spot rate = 1.3 $/euro

Solving for euro price in the below equation,

            Dollar price / euro price = current spot rate

            Euro price = dollar price / current spot rate = 120000 / 1.3 = 92307.69 euro

Part b

Current selling price in euro = 95000 euro which is higher than the euro price we just calculated in part a.

Hence, we will buy 1 MB in US market at euro price equivalent to 92307.69 euro and then sell 1MB in Europe market at 95000 euro, hence deriving a profit of

P = 95000 - 92307.69 = 2692.31 euro

Part c

The law of one price theory follows from the concept of purchasing power parity. Purchasing power parity states that the value of two currencies is equal when identical goods are priced the same in both countries.

In this case, it is clear that at current spot rate, 1 MB is overpriced in Europe market. Hence the exchange rate needs to be adjusted to,

Adjusted exchange rate $ / Euro = Dollar price / Current Euro price

                                                = 120000 / 95000 = 1.26 $ / Euro to restore LOOP