When discussing international trade and foreign exchange, two types of exchange rates are used. The *nominal exchange rate* simply states how much of one currency (i.e. money) can be traded for a unit of another currency. The *real exchange rate*, on the other hand, describes how many of a good or service in one country can be traded for one of that good or service in another country. For example, a real exchange rate might state how many European bottles of wine can be exchanged for one US bottle of wine.

This is, of course, a bit of an oversimplified view of reality -- after all, there are differences in quality and other factors between the U.S. wine and the European wine. The real exchange rate abstracts away these issues, and it can be thought of as comparing the cost of equivalent goods across countries.

### The Intuition Behind Real Exchange Rates

Real exchange rates can be thought of as answering the following question: If you took an item produced domestically, sold it at the domestic market price, exchanged the money you got for the item for foreign currency, and then used that foreign currency to purchase units of the equivalent item produced in the foreign country, how many units of the foreign good would you be able to buy?

The units on real exchange rates, therefore, are units of foreign good over units of domestic (home country) good, since real exchange rates show how many foreign goods you can get per unit of domestic good. (Technically, the home and foreign country distinction are irrelevant, and real exchange rates can be calculated between any two countries, as shown below.)

The following example illustrates this principle: if a bottle of US wine can be sold for $20, and the nominal exchange rate is 0.8 Euro per US dollar, then the bottle of US wine is worth 20 x 0.8 = 16 Euro. If a bottle of European wine costs 15 Euro, then 16/15 = 1.07 bottles of European wine can be purchased with the 16 Euro. Putting all of the pieces together, the bottle of US wine can be exchanged for 1.07 bottles of the European wine, and the real exchange rate is thus 1.07 bottles of European wine per bottle of US wine.

The reciprocal relationship holds for real exchange rates in the same way that it holds for nominal exchange rates. In this example, if the real exchange rate is 1.07 bottles of European wine per bottle of US wine, then the real exchange rate is also 1/1.07 = 0.93 bottles of US wine per bottle of European wine.

### Calculating the Real Exchange Rate

Mathematically, the real exchange rate is equal to the nominal exchange rate times the domestic price of the item divided by the foreign price of the item. When working through the units, it becomes clear that this calculation results in units of foreign good per unit of domestic good.

### The Real Exchange Rate with Aggregate Prices

In practice, real exchange rates are usually calculated for all goods and services in an economy rather than for a single good or service. This can be accomplished simply by using a measure of aggregate prices (such as the consumer price index or GDP deflator) for the domestic and the foreign country in place of the prices for a particular good or service.

Using this principle, the real exchange rate is equal to the nominal exchange rate times the domestic aggregate price level divided by the foreign aggregate price level.

### Real Exchange Rates and Purchasing Power Parity

Intuition might suggest that real exchange rates should be equal to 1 since it's not immediately obvious why a given amount of monetary resources wouldn't be able to buy the same amount of stuff in different countries. This principle, where the real exchange rate is, in fact, equal to 1, is referred to as purchasing-power parity, and there are various reasons why purchasing-power parity need not hold in practice.