Even though the law of one price does not literally hold for all goods and services, it reminds us that the value of $1 in the United States is linked to its value in the rest of the world. As a result, we expect that price level changes are likely to lead to changes in the exchange rate. We see this more clearly if we write our previous equation in terms of growth rates. Using the formula for growth rates, we find the following: growth rate of price of dollar in euros = growth rate of price of European bundle of goods− growth rate of price of US bundle of goods.
Toolkit:
The formulas for using growth rates can be found in the toolkit.
If the bundle of goods in each country corresponds roughly to the goods in the Consumer Price Index (CPI), then the growth rate of these prices corresponds to the inflation rate. The growth rate of the exchange rate is just another term for the percentage appreciation of the currency. Thus we get the following:
percentage appreciation of the dollar ≈ European inflation rate − US inflation rate.
So, if the inflation rate in the United States is higher than it is in Europe, we expect the euro price of the dollar to decrease. We expect depreciation of the dollar if US inflation exceeds European inflation. Inflation reduces the real value of money domestically; it will also tend to reduce the value of money in terms of what it can purchase in the rest of the world. This makes sense. If our currency is becoming less valuable at home, then we should also expect it to become less valuable in the rest of the world.
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