The real exchange rate (RER) compares the relative price of two countries’ consumption baskets. You may be interested in getting more information than the relative price of two currencies, or the nominal exchange rate. For example, you may want to know what one dollar can buy in the Euro-zone countries or what one euro can buy in the United States. In this case, you’re interested in the (RER).

Therefore, to calculate the RER, you need to know two things: the nominal exchange rate and the price of the two countries’ consumption baskets.

A country’s consumption basket tells you what the average consumer buys, and its price indicates how much consumers pay for it. For example, in the U.S., the Consumer Price Index (CPI) is calculated based on a consumption basket consisting of about 80,000 goods and services.

Each country’s consumption basket is expressed in its domestic currency. If you know the nominal exchange rate and the prices of two countries’ consumption baskets, you can express the price of one country’s consumption basket in the other country’s currency. This information enables you to calculate the RER. In other words, you can compare the prices of two countries’ consumption baskets in the same currency.

Suppose you know the dollar–euro nominal exchange rate, the euro price of the European consumption basket, and the dollar price of the U.S. consumption basket. You can’t divide the price of the European consumption basket by that of the U.S. consumption basket because the prices of these consumption baskets are denominated in different currencies. Therefore, follow this concept:

RER = (Nominal exchange rate x Price of the foreign basket) / (Price of the domestic basket)

The next equation reflects this concept:

Here, RER, PE, and PUS indicate the real exchange rate, the price of the Euro-zone’s consumption basket, and the price of the U.S. consumption basket, respectively.

Consider a numerical example for the RER. Assume that the dollar–euro exchange rate is \$1.42 per euro, PE (the price of the Euro-zone’s consumption basket) is €100, and PUS (the price of the U.S. consumption basket) is \$142. In this case, the real exchange rate is 1:

In the previous equation, first note that, in the numerator, you multiply the dollar–euro exchange rate with a euro amount. Doing so changes the European basket so that it’s expressed in dollars. Second, note that you have the dollar price of the American basket in the denominator. Because now the price of both consumption baskets is expressed in dollars, you can compare them.

Suppose that the dollar–euro exchange rate increases to \$1.52, but the prices of the Euro-zone and U.S. consumption baskets remain the same. In this case, the real exchange rate increases to 1.07:

This increase in the real exchange rate implies that the dollar price of the Euro-zone’s consumption basket increases, or the dollar’s purchasing power over the Euro-zone’s consumption basket falls. Alternatively, you can increase the price of the Euro-zone’s consumption basket or decrease the price of the U.S. basket to achieve an increase in the real exchange rate.

Suppose that the nominal exchange rate decreases to \$1.35, with the prices of the Euro-zone and U.S. consumption baskets remaining the same. In this example, the real exchange rate decreases to 0.95:

A decline in the real exchange rate indicates that the dollar price of the Euro-zone’s consumption basket decreases, or the dollar’s purchasing power over the Euro-zone’s consumption basket increases. Again, you can also decrease the price of the Euro-zone’s consumption basket or increase the price of the U.S. basket to achieve a decline in the real exchange rate.