The Law of One Price is an economics principle stating that identical products will sell for the same price in different markets, given a competitive landscape and the absence of transaction and transportation costs. The rule applies only to tradable goods (houses and many other local services are immobile and are therefore not tradable between countries). At first glance, the law of one price may look like the purchasing power parity theory. In reality, the two are distinct as the law of one price provides the underlying basis for the purchasing power parity theory.

When expressed in the same currency, the equalization of prices exists because of the opportunity for arbitrage, the riskless process of taking advantage of different prices for the same good. In other words, buying it for cheap, and then selling it for more. For example, suppose that a certain pair of tennis shoes sells for £100 (GBP) in London. The same pair of tennis shoes should sell for $150 (USD) in New York if the exchange rate between the United Kingdom and United States is 1.50 USD/GBP. If the price of the tennis shoes in London was only £80 GBP, then consumers in New York would have an incentive to buy the tennis shoes in London, since the price of the shoes when converted back to USD would be cheaper overseas. This process of arbitrage carried out on a large scale equalizes prices by allowing US consumers taking advantage of the lower British prices to bid up the value of the GBP until the goods, in this case, the pair of tennis shoes have a single price again across different markets.

The assumption for the law of one price theory is that trade is open, costless, and free of barriers (such as tariffs). Only then, can identical goods sell at the same relative price regardless of where the goods are sold. The law of one price also applies to financial instruments and securities.

Source: Krugman, P. & Obstfeld, M. (2009). Price levels and the exchange rate in the long run. International Theory & Policy Economics (pp.383-384). Boston, MA: Pearson Education.