The value of real GDP of other countries in comparison to a unit of the buys of the real GDP of America is real rate of exchange. Hence it is the value which is reached on comparing the value of commodities and services of America against that of other countries. The formula which can be applied to find the real exchange rate is RER= (E X P)/P*
This equation can be better understood with an example. Taking the Indian rupee as the currency to compare with the American dollar, the equation stands as follows. E is the value do the rupee per dollar, P is the price level of America, P* is the price level at India. The value which is attained after calculation will be real rate of exchange. Therefore if the calculations need to be further analyzed an example can be used like if a commodity is taken up in this context, for example if it is assumed that the exchange rate or E is 100 rupees per dollar, the price of software in America is $150 so the P is $150 and the P* is set out at 5000. After calculation one chip is equal to here iPods.
The short run
On a short term basis the change in nominal exchange rate brings about alterations in the value of real rate of exchange. Taking India and America as examples again there is no guarantees that a change in prices or price level occurs at each instance that exchange rate alter. Thus changes in real rate of exchange only impact on a short term basis, and are limited to change in import demands and quantity of exports which are supplied.
The long run
Situations undergo rapid change when times shift from the short to long run. Here the nominal exchange rate and the real rate of exchange are fixed simultaneously and a shift in the nominal value does not affect real rate of exchange. Demand and supply for products deter mine real rate of exchange. There is no alternative for this and only when there is a real fluctuation in the rate of demand and supply will the exchange rate change. Similarly based on this equation the relative price levels that help stipulate an exchange rate is determined.
As per the quantity theory of money as explained in chapter 8 there is a change in exchange rate on appreciation of money. The quantity theory uniformly applies to all countries therefore an increase in price levels in Ukraine lead to a rise in exchange rate in Ukraine, while an increase of price in China leads to rise of exchange rate in the nation-state. If the exchange rate is given then fluctuations of the quantity of money alter not just price levels but exchange rates too. To understand this better one can go back to the example of India and America.
Suppose the value of the Indian rupee was raised from 100 to 200 would it change the equation of 3 iPods to software? The answer is no, because the real exchange value remains unaltered. Now provided that the two countries had the capacity to create goods which were identical, like for example if both India and America created software then the real rate of exchange would over a period of time become equal to 1. Even though these examples have been stated assuming that each country produces just one product, in reality there is an overlap.
However it does not change the fact that the real GDP of one country stands different from that of another country. Hence if the GDP is not similar in two countries than the real rate of exchange is also constantly under change and not equal to 1. This means that rate changes over time. This again reinstates that the goods and services which are produced by different countries and the demand which they create are instrumental in determining real rate of exchange. Also the changes in this rate are undertaken as a result of fluctuation of the demands.