One unit of US GDP will get you two units of European GDP. The real exchange rate is intimately linked to the law of one price. The easiest way to see this is to suppose that we measure US real GDP and European GDP in the same units: that is, suppose we use the same bundle of goods in each case. We know that the law of one price should hold for tradable goods—that is, goods for which arbitrage is possible and practical. If every good that went into GDP were tradable, then the law of one price would hold for every good, and the real exchange rate would equal 1. If the real exchange rate was not 1, you could make arbitrage profits by buying and selling “units of GDP.” As before, suppose the US price level is $1,600, the European price level is EUR 400, and the nominal exchange rate (dollars per euro) is 0.5. Imagine that US GDP and European GDP measure the same bundle of (tradable) goods. Then you could take $800 and buy EUR 400. With these euros, you could buy a basket of goods in Europe. You could sell this basket in the United States for $1,600. The law of one price is violated. We would expect the following:
Prices in the United States would increase. Prices in Europe would decrease. The nominal exchange rate would depreciate (the dollar would become less valuable).
Because arbitrage is not possible for all goods and services, we do not expect—nor do we observe—the real exchange rate to be exactly one. But this benchmark is still useful in understanding movements in the real exchange rate. The Real Exchange Rate in Action The real exchange rate matters because it is the price that is relevant for import and export decisions. Suppose you are trying to decide between buying a mobile phone manufactured in the United States and one manufactured in Finland. If the dollar appreciates against the euro, then the US phone retailer needs fewer dollars to purchase euros, so Finnish phones will be cheaper in US stores. If prices decrease in Finland, the imported phone again becomes relatively cheaper. If prices increase in the United States, the US phone will be more expensive. In other words, increasing prices in the United States, decreasing prices in Finland, and appreciation of the dollar all make you more likely to buy the imported phone rather than the domestically produced phone. More generally, anything that causes the real exchange rate to increase will make imports look more attractive compared to goods produced in the domestic economy. Examined from the point of view of Europe, the same increase in the real exchange rate makes US goods look more expensive relative to goods produced in Europe, so Europeans will be likely to import fewer goods from the United States. An increase in the real exchange rate therefore leads to an increase in US imports and a decrease in US exports—that is, it leads to a decrease in net exports.