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Purchasing power parity theory is the idea that exchange rates between different currencies will naturally settle on a position that means the same goods cost the same price in each country. The theory argues that where this is not the case, the cause is transaction costs and barriers to trade. Purchasing power parity theory is certainly not borne out in reality, though its supporters would argue that this simply shows the extent of barriers to a free market.
To understand how purchasing power parity theory would work in practice, imagine that a DVD movie costs $20 US Dollars (USD) in the United States. If the exchange rate between the US Dollar and the Mexican peso was 1:10, then the theory would suggest the same DVD movie could cost 200 pesos in Mexico. Put another way, the theory suggests that is the movie actually costs 160 pesos in Mexico, then the exchange rate will move to 1:8.
The logic behind the purchasing power parity theory is based on the concept of the law of one price. In the absence of local tax variations or transportation costs, the same good should cost the same amount in different countries. This is because, in free market theory, people will exploit price differentials. For example if, once the exchange rate was taken into account, the DVDs worked out cheaper in Mexico, US traders would buy them in Mexico and sell them at a profit in the US. In turn this would increase demand in Mexico until the price rose up to meet that charged in the US.
Purchasing power parity theory simply takes the law of one price to an aggregate level. In other words it looks at the combined effects of the way the law affects each individual item. For example, the American traders will need to exchange US Dollars for pesos in order to buy the DVDs. Across all goods and services, the theory is that this will have an effect on the exchange rate. The combination of the demand and supply for goods in different countries, and the demand and supply for currency, should eventually lead to the purchasing power parity.
In practice, purchasing power parity is extremely rare. Indeed, there are often vast price differences between different areas of the same country, let alone between countries with two different exchange rates. The theory states that this is caused by differences in sales taxation between the different countries, by the cost of transporting goods between countries, and by trade barriers such as import restrictions or duties. Some economists argue the differences are also caused by varying patterns of demand, such as Americans as a whole being less interested in buying Spanish-language DVD movies then Mexicans.