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Converting Currencies With Exchange Rates

Converting Currencies with Exchange Rates

To compare the GDP of countries with different currencies, it is necessary to convert to a “common denominator” using an exchange rate, which is the value of one currency in terms of another currency. Exchange rates are expressed either as the units of country A’s currency that need to be traded for a single unit of country B’s currency (for example, Japanese yen per British pound), or as the inverse (for example, British pounds per Japanese yen). Two types of exchange rates can be used for this purpose, market exchange rates and purchasing power parity (PPP) equivalent exchange rates. Market exchange rates vary on a day-to-day basis depending on supply and demand in foreign exchange markets. PPP-equivalent exchange rates provide a longer run measure of the exchange rate. For this reason, PPP-equivalent exchange rates are typically used for cross country comparisons of GDP. Exchange rates will be discussed in more detail in Exchange Rates and International Capital Flows. The following example explains how to convert GDP to a common currency.

Converting GDP to a Common Currency

Using the exchange rate to convert GDP from one currency to another is straightforward. Say that the task is to compare Brazil’s GDP in 2013 of 4.8 trillion reals with the U.S. GDP of $16.6 trillion for the same year. Step 1. Determine the exchange rate for the specified year. In 2013, the exchange rate was 2.230 reals =$1. (These numbers are realistic, but rounded off to simplify the calculations.)

Step 2. Convert Brazil’s GDP into U.S. dollars:

$$\begin{array}{rcl}\text{Brazil’s GDP in \ U.S.}& \text{=}& \cfrac{\text{Brazil’s GDP in reals}}{\text{Exchange rate (reals/\ U.S.)}}\\ & \text{=}& \cfrac{\text{4.8 trillion reals}}{\text{2.230 reals per \ U.S.}}\\ & \text{=}& \text{\2.2 trillion}\end{array}$$

Step 3. Compare this value to the GDP in the United States in the same year. The U.S. GDP was \$16.6 trillion in 2013, which is nearly eight times that of GDP in Brazil in 2012.

Step 4. View this table which shows the size of and variety of GDPs of different countries in 2013, all expressed in U.S. dollars. Each is calculated using the process explained above.

Comparing GDPs Across Countries, 2013 (Source: http://www.imf.org/external/pubs/ft/weo/2013/01/weodata/index.aspx)

CountryGDP in Billions of Domestic CurrencyDomestic Currency/U.S. Dollars (PPP Equivalent)GDP (in billions of U.S. dollars)
Brazil4,844.80reals2.1572,246.00
China58,667.30yuan6.1969,469.10
Egypt1,753.30pounds6.460271.40
Germany2,737.60euros0.7533,636.00
India113,550.70rupees60.5021,876.80
Japan478,075.30yen97.5964,898.50
Mexico16,104.40pesos12.7721,260.90
South Korea1,428,294.70won1,094.9251,304.467
United Kingdom1,612.80pounds0.6392,523.20
United States16,768.10dollars1.00016,768.10

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