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).
Question
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).
Solution
a. To compute the percentage change from 2009 to 2010 in the four U.S. bilateral exchange rates, we subtract the 2009 rate from the 2010 rate, divide by the 2009 rate, and then multiply by 100 to get the percentage.
For Canada: ((0.9643 - 0.9225) / 0.9225) * 100 = 4.53%
For Mexico: ((0.0788 - 0.0756) / 0.0756) * 100 = 4.23%
For China: ((0.1473 - 0.1464) / 0.1464) * 100 = 0.61%
For Japan: ((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 multiply the percentage change in each country's exchange rate by its trade share, and then sum these products.
(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%
So, the percentage change in the nominal effective exchange rate for the United States between 2009 and 2010 is 4.00%.
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