The LOP states that identical goods, once their national prices are expressed in a common currency, should sell for the same price across different international locations. The LOP is viewed as a long-run proposition about arbitrage in international goods market that suggests that once arbitrage opportunities arise they do not persist forever; adjustment can take place either via prices or via the exchange rate, which moves in such a way as to restore the LOP over time. While in its purest form, the LOP compares identical products or services sold in two different geographical locations, the most relevant case in practice is the comparison of similar goods, with different origin of production and different pricing currency, for which prices should be very close, after accounting for transaction costs, due to competition in international goods market.
Ignoring transaction costs for the moment, the LOP stated above in its absolute version may be written formally as
where Pi, t denotes the price of good i in terms of the domestic currency at time t, is the price of good i in terms of the foreign currency at time t, and St is the nominal exchange rate expressed as the domestic price of the foreign currency at time t. In its relative version, the LOP ...