Foreign Exchange

Prices and Exchange Rates

• The law of one price:
• Identical products sold in different countries must sell for one price if their price is expressed in one currency
• Assumptions:
• Competitive markets
• No transportation costs; no trade barriers
• Purchasing Power Parity (PPP):
• If the law of one price holds for all goods / services, the PPP exchange rate is found by comparing prices of identical products in different countries

• The law of one price says that identical goods should sell for the same price in two separate markets when there are no transportation costs and no differential taxes applied in the two markets.

• Consider the following information about movie video tapes sold in the US and Mexican markets.
• Price of videos in US market : $20
• Price of videos in Mexican market: p150
• Spot exchange rate (Ep/$): 10 p/$
• The dollar price of videos sold in Mexico can be calculated by dividing the video price in pesos by the spot exchange rate as shown,

• To see why the peso price is divided by the exchange rate (rather than multiplied) notice the conversion of units shown in the brackets. If the law of one price held, then the dollar price in Mexico should match the price in the US. Since the dollar price of the video is less than the dollar price in the US, the law of one price does not hold in this circumstance.

The Law of One Price

• We can mathematically state the law of one price as follows, for the case of any good g sold in two locations:

• expresses the rate at which goods can be exchanged: it tells us how many units of the U.S. good are needed to purchase one unit of the same good in Europe.

• expresses the rate at which currencies can be exchanged ($/€).

The Law of One Price

• We can rearrange the equation for price equality

• to show that the exchange rate must equal the ratio of the goods’ prices expressed in the two currencies: