Country x conducts 60% of its trade with country y and 40% of its trade with country z. The initial value of the trade weighted exchange rate index of country x is 100. What will be its new trade...

Country x conducts 60% of its trade with country y and 40% of its trade with country z. The initial value of the trade weighted exchange rate index of country x is 100. What will be its new trade weighted exchange rate index value if it's currency falls in value by 20% against the currency of y and rises by 10% against the currency of z?           The answer is apparently 25 according to the answer sheet(mock exam) but I don't understand why? Can someone please help explain this to me?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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Country X conducts 60% of its trade with country Y and 40% of its trade with country Z. The initial value of the trade weighted exchange rate index of country X is 100.

The value of X's currency falls by 20% against the currency of Y and it rises by 10% against the currency of Z.

When the value of X's currency falls by 20% against the currency of Y, and X conducts 60% of its trade with Y, this changes the component of the exchange rate index contributed by Y to 0.6*(1-0.2) = 0.6*0.8 = 0.48. The value of X's currency rises against the currency of Z by 10% and it conducts 40% of its trade with Z. This changes the value of the component of the exchange rate index contributed by Z to 0.4*(1+0.1) = 0.44 .

Adding the two components gives 0.48 + 0.42 = 0.92

The exchange rate index was initially at 100. It is now changed to 100*0.92 = 92.

The answer is not 25. The new trade weighted exchange rate index value is 92.

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