Consider the United States and the countries ittrades with the most (measured in trade vol-ume): Canada, Mexico, China, and Japan. Forsimplicity, assume these are the only fourcountries with which the United States trades.Trade shares and exchange rates for these fourcountries are as follows:Country Share of $ per FX $ per FX(currency) Trade in 2009 in 2010Canada (dollar) 36% 0.9225 0.9643Mexico (peso) 28% 0.0756 0.0788China (yuan) 20% 0.1464 0.1473Japan (yen) 16% 0.0105 0.0112a. Compute the percentage change from 2009to 2010 in the four U.S. bilateral exchangerates (defined as U.S. dollars per units offoreign exchange, or FX) in the table pro-vided.b. Use the trade shares as weights to computethe percentage change in the nominal effec-tive exchange rate for the United Statesbetween 2009 and 2010 (in U.S. dollars perforeign currency basket).c. Based on your answer to (b), what hap-pened to the value of the U.S. dollaragainst this basket between 2009 and2010? How does this compare with thechange in the value of the U.S. dollar rela-tive to the Mexican peso? Explain youranswer
Question
Consider the United States and the countries ittrades with the most (measured in trade vol-ume): Canada, Mexico, China, and Japan. Forsimplicity, assume these are the only fourcountries with which the United States trades.Trade shares and exchange rates for these fourcountries are as follows:Country Share of per FX(currency) Trade in 2009 in 2010Canada (dollar) 36% 0.9225 0.9643Mexico (peso) 28% 0.0756 0.0788China (yuan) 20% 0.1464 0.1473Japan (yen) 16% 0.0105 0.0112a. Compute the percentage change from 2009to 2010 in the four U.S. bilateral exchangerates (defined as U.S. dollars per units offoreign exchange, or FX) in the table pro-vided.b. Use the trade shares as weights to computethe percentage change in the nominal effec-tive exchange rate for the United Statesbetween 2009 and 2010 (in U.S. dollars perforeign currency basket).c. Based on your answer to (b), what hap-pened to the value of the U.S. dollaragainst this basket between 2009 and2010? How does this compare with thechange in the value of the U.S. dollar rela-tive to the Mexican peso? Explain youranswer
Solution 1
a. To compute the percentage change in the four U.S. bilateral exchange rates from 2009 to 2010, we use the formula:
Percentage Change = [(Value in 2010 - Value in 2009) / Value in 2009] * 100%
For Canada: Percentage Change = [(0.9643 - 0.9225) / 0.9225] * 100% = 4.53%
For Mexico: Percentage Change = [(0.0788 - 0.0756) / 0.0756] * 100% = 4.23%
For China: Percentage Change = [(0.1473 - 0.1464) / 0.1464] * 100% = 0.61%
For Japan: Percentage Change = [(0.0112 - 0.0105) / 0.0105] * 100% = 6.67%
b. To compute the percentage change in the nominal effective exchange rate for the United States between 2009 and 2010, we use the trade shares as weights. This is calculated as:
Percentage Change in NEER = Σ (Trade Share * Percentage Change in Bilateral Exchange Rate)
Percentage Change in NEER = (0.36 * 4.53%) + (0.28 * 4.23%) + (0.20 * 0.61%) + (0.16 * 6.67%) = 1.63% + 1.18% + 0.12% + 1.07% = 4.00%
c. Based on the answer to (b), the value of the U.S. dollar against the basket of currencies increased by 4.00% between 2009 and 2010. This means that the U.S. dollar appreciated in value. When compared to the Mexican peso, the U.S. dollar appreciated by a smaller amount (4.23%). This means that the U.S. dollar strengthened more against the Mexican peso than it did against the overall basket of currencies.
Solution 2
a. To compute the percentage change in the four U.S. bilateral exchange rates from 2009 to 2010, we use the formula:
Percentage Change = [(Value in 2010 - Value in 2009) / Value in 2009] * 100%
For Canada: Percentage Change = [(0.9643 - 0.9225) / 0.9225] * 100% = 4.53%
For Mexico: Percentage Change = [(0.0788 - 0.0756) / 0.0756] * 100% = 4.23%
For China: Percentage Change = [(0.1473 - 0.1464) / 0.1464] * 100% = 0.61%
For Japan: Percentage Change = [(0.0112 - 0.0105) / 0.0105] * 100% = 6.67%
b. To compute the percentage change in the nominal effective exchange rate for the United States between 2009 and 2010, we use the trade shares as weights. This is calculated as:
Nominal Effective Exchange Rate Change = Sum of (Trade Share * Exchange Rate Change)
= (0.36 * 4.53%) + (0.28 * 4.23%) + (0.20 * 0.61%) + (0.16 * 6.67%) = 1.63% + 1.18% + 0.12% + 1.07% = 4.00%
c. Based on the answer to (b), the value of the U.S. dollar against the basket of currencies increased by 4.00% between 2009 and 2010. This means that the U.S. dollar appreciated in value.
When compared to the Mexican peso alone, the U.S. dollar appreciated by 4.23%, which is slightly higher than the appreciation against the basket of currencies. This means that the U.S. dollar strengthened more against the Mexican peso than it did on average against the basket of currencies.
Similar Questions
Country Share of $ per FX $ per FX(currency) Trade in 2009 in 2010Canada (dollar) 36% 0.9225 0.9643Mexico (peso) 28% 0.0756 0.0788China (yuan) 20% 0.1464 0.1473Japan (yen) 16% 0.0105 0.0112a. Compute the percentage change from 2009to 2010 in the four U.S. bilateral exchangerates (defined as U.S. dollars per units offoreign exchange, or FX) in the table pro-vided.b. Use the trade shares as weights to computethe percentage change in the nominal effec-tive exchange rate for the United Statesbetween 2009 and 2010 (in U.S. dollars perforeign currency basket).
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