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Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/ license.
Theories that invoke purchasing power parity assume that in some circumstances (for example, as a long-run tendency) it would cost exactly the same number of, for example, US dollars to buy euros and then to use the proceeds to buy a market basket of goods as it would cost to use those dollars directly in purchasing the market basket of goods.
The concept of purchasing power parity allows one to estimate what the exchange rate between two currencies would have to be in order for the exchange to be at par with the purchasing power of the two countries' currencies. Using that PPP rate for hypothetical currency conversions, a given amount of one currency thus has the same purchasing power whether used directly to purchase a market basket of goods or used to convert at the PPP rate to the other currency and then purchase the market basket using that currency. Observed deviations of the exchange rate from purchasing power parity are measured by deviations of the real exchange rate from its PPP value of 1.
PPP exchange rates help to minimize misleading international comparisons that can arise with the use of market exchange rates. For example, suppose that two countries produce the same physical amounts of goods as each other in each of two different years. Since market exchange rates fluctuate substantially, when the GDP of one country measured in its own currency is converted to the other country's currency using market exchange rates, one country might be inferred to have higher real GDP than the other country in one year but lower in the other; both of these inferences would fail to reflect the reality of their relative levels of production. But if one country's GDP is converted into the other country's currency using PPP exchange rates instead of observed market exchange rates, the false inference will not occur.
The idea originated with the School of Salamanca in the 16th century and was developed in its modern form by Gustav Cassel in 1918. The concept is based on the law of one price, where in the absence of transaction costs and official trade barriers, identical goods will have the same price in different markets when the prices are expressed in the same currency.
Another interpretation is that the difference in the rate of change in prices at home and abroad—the difference in the inflation rates—is equal to the percentage depreciation or appreciation of the exchange rate.
Deviations from parity imply differences in purchasing power of a "basket of goods" across countries, which means that for the purposes of many international comparisons, countries' GDPs or other national income statistics need to be "PPP-adjusted" and converted into common units. The best-known purchasing power adjustment is the Geary–Khamis dollar (the "international dollar"). The real exchange rate is then equal to the nominal exchange rate, adjusted for differences in price levels. If purchasing power parity held exactly, then the real exchange rate would always equal one. However, in practice the real exchange rates exhibit both short run and long run deviations from this value, for example due to reasons illuminated in the Balassa–Samuelson theorem.
There can be marked differences between purchasing power adjusted incomes and those converted via market exchange rates. For example, the World Bank's World Development Indicators 2005 estimated that in 2003, one Geary-Khamis dollar was equivalent to about 1.8 Chinese yuan by purchasing power parity—considerably different from the nominal exchange rate. This discrepancy has large implications; for instance, when converted via the nominal exchange rates GDP per capita in India is about US$1,704 while on a PPP basis it is about US$3,608. At the other extreme, Denmark's nominal GDP per capita is around US$62,100, but its PPP figure is US$37,304.
The purchasing power parity exchange rate serves two main functions. PPP exchange rates can be useful for making comparisons between countries because they stay fairly constant from day to day or week to week and only change modestly, if at all, from year to year. Second, over a period of years, exchange rates do tend to move in the general direction of the PPP exchange rate and there is some value to knowing in which direction the exchange rate is more likely to shift over the long run.