# The Exchange Rate: Dollars for Yen or Yen for Dollars, Which Way is It?

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Forex exchange-rate index is designed to measure how, over time, movements in the dollar will affect U.S. imports and exports. And to do this well, Forex index must also take account of any differences between the rate of inflation in the United States and the rates of inflation in other countries. Suppose that the rate of inflation were 10 percent a year in the United States but only 3 percent a year in Germany. The buying power of the dollar in the United States is falling 7 percent a year faster than the buying power of the German mark.

Now suppose that Forex exchange rate of the dollar declined by 7 percent from one year to the next against the mark. Then German buyers would be getting 7 percent more dollars for their marks; but the decline in the exchange rate would be exactly undone by the greater increase in prices in the United States than in Germany. The number of Mercedes that it took to trade for one Boeing 757 would be the same in the two years. (At least, this would be true on average for many goods.) This means that, when a change in Forex exchange rate simply compensates for differences in inflation rates, the relative prices of U.S. imports (from Germany) and U.S. exports (to Germany) do not change.

Readers let us notify: international Forex trade economists do it differently. One of the most confusing concepts in economics is the way in which Forex rate of exchange between two currencies should be expressed. As we indicate in the article, we choose to express the rate as the number of units of foreign currency that can be purchased with one dollar (e.g., let’s say the yen is trading at 130 yen to the dollar). This approach is commonly used in the media and it squares with the intuitive idea of appreciation or devaluation of the dollar. When Forex exchange as we have defined it goes up (e.g., from 100 yen to 120 yen), the dollar buys more foreign currency – the dollar has appreciated. When Forex exchange rate goes down (e.g., from 100 yen to 90 yen), the dollar buys less foreign currency – the dollar has depreciated.

Unfortunately, this approach is the inverse of the concept that international trade economists focus on when they describe Forex foreign-exchange markets. They define Forex exchange rate in terms of the price of foreign exchange, so the yen to dollar exchange rate is the cost of purchasing one yen with dollars. If Forex exchange rate in our terms is equal to 100 yen to the dollar, the inverse would be \$0,01 (one cent) per yen. If the dollar appreciates, from 100 yen to 120 yen to the dollar (dollar purchases more yen), then Forex exchange rate, expressed as the cost of yen, declines in dollar terms, in this example dropping from \$0,01 to \$0,0083.

The appreciating dollar means that yen purchased in foreign exchange Forex markets are now cheaper to buy with dollars, exactly the concept that trade economists wish to show. But it also means that their definition of the Forex dollar-exchange rate falls when the dollar appreciates! This is very confusing and so we define Forex exchange rate as yen per dollar, rather than dollars per yen.

For those who go on to further studies in international economics, however you, you will find that the trade economists’ definition usually appears in international Forex articles and journals.

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