12.1.3 Real exchange rate

However, many economic issues, especially those concerning international trade, do not depend on the nominal exchange rate in the strict sense. The question in which country a good is cheaper, has three components: the domestic price, the price abroad and the exchange rate. For questions of international trade and investment, the domestic price $P$ must be compared with the price abroad converted into domestic currency $S\cdot P^{\ast }$.

The real exchange rate is the ratio of the amount of domestic currency that must be changed into foreign currency to acquire a representative basket of foreign goods, to the value of a representative basket of domestic goods in domestic currency.

$$Q=\frac{S\cdot P_{\mathit{Ausland}}}{P_{\mathit{Inland}}}$$

There are two things to consider:

1. It is important to use the correct nominal exchange rate $S$, the price quotation, i.e. how much domestic currency do I have to pay for a unit of foreign currency.
2. We compare the price levels, i.e. the prices of representative baskets of goods determined by the statistical offices, and not the prices of individual goods. When using the real exchange rate in macroeconomic models, we are looking at entire economies and at exports or imports as a whole, not at individual industries. Therefore, a weighted average of all prices within the economies is used. Otherwise, one would have to determine the real exchange rate for each industry or commodity, and this would be neither practically feasible nor appropriate for macro models.

The use of price indices of representative baskets of goods has, of course, also disadvantages and must be considered with the corresponding reservations. On the one hand, the baskets of goods do not match between economies, so that relevant differences can develop over time. On the other hand, the weights of the representative baskets of goods usually correspond approximately to the sales in the respective domestic market. This usually differs significantly from the sales of exported or imported goods. Thus, the price index of the representative basket of goods is only a distorted measure for calculating the real exchange rate for international trade. The more the average price trend for exported and imported goods differs from the average domestic price trend, the greater the distortion. The third problem with the use of representative baskets of goods is the initial level. While the rates of change can be compared relatively well (taking into account the first two caveats), it is not possible to make a reliable price index comparison of a single year because there is no natural reference point for an index. Often, the long-term, trend-adjusted mean value is used.