The law of one price
The theory of PPP is based on the Law of One Price (LOP).The law of one price states that identical commodities or goods must have the same price in all markets.If this were not the case, profit-seeking entrepreneurs could exploit the situation by buying in the market with the lower price and selling in the market with the higher price.The increased demand in the market with the lower price would tend to raise the price in that market, while the increased supply in the higher priced market would tend to lower its price.This activity would continue until the prices in both markets equalized, thereby eliminating the potential for profit.Exploiting price differentials in this way is known as arbitrage.
Suppose, for example, that the price of gold in Zurich is USD 370 an ounce and in London it is USD 355 an ounce.Arbitragers will buy gold in London and simultaneously sell it in Zurich for a profit of USD 15 per ounce.As more and more gold is bought in London, its price will rise while the price in Zurich will fall as more and more gold is offered for sale.In a very short time the prices will become equal or at least close enough so that, when the costs associated with buying and selling are taken into consideration, the opportunity for arbitrage profits disappears.
Even without arbitrage, the law of one price should hold for internationally traded goods because outside buyers would be only in the market with the lowest price.In practice, of course, it costs money and takes time to ship goods from one place to another and there are often restrictions of various forms on international trade.In this sense prices might differ somewhat.For example, a banana should cost more in Holland than in Honduras where it is produced because of the cost of shipping the banana from Honduras to Holland.
When only one currency is involved, the law of one price is easy to see.When more than one currency is involved, the law of one price states that when financial and commodity markets are perfect (no controls, delays, transaction or shipping costs, etc.), identical commodities of goods must have the same price in all markets when quoted in a common currency.For example, let PGBP and PUSD be the price of natural gas in the United Kingdom and the United States respectively and S0(GBP/USD)be the number of pounds it takes to buy one dollar at time 0.Then, by the law of one price:
Or conversely:
Thus, if the price of natural gas in the United States is USD 5.00 a cubic meter and it takes GBP 2 to buy USD 1, by Equation 5.1 the price of natural gas in the United Kingdom should be:
In other words, the price of natural gas should be the same in the United Kingdom and in the United States when quoted in the same currency.If the price is GBP10 in the United Kingdom, by Equation (5.2)the price in the United States should be:
The price is the same in the United Kingdom and the United States whether it is quoted in dollars or pounds.