Question

Suppose the price indexes in Mexico and the U.S., which both began the year at 100, are at 160 and 120, respectively, by the end of the year. If the exchange rate began the year at $0.25/M$ and ended the year at $0.20/M$,

• What is the change in the real value of the U.S. dollar during the year?

• What is the PPP rate at the end of the year as a direct quote in the U.S.?

• What is the real exhchange rate at the end of the year as a direct quote in the U.S.?

Answer 1

CPI at start of the year in both countries = 100

CPI in mexico = 160

CPI in US = 120

Exchange rate at starting of the year US$ /M$ = 0.25

Exchange rate at end of the year US$ /M$ = 0.20

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1) What is the change in the real value of the U.S. dollar during the year?

More recent dollars in terms of past dollars = Dollar Amount × Beginning-period CPI ÷ Ending-period CPI.

More recent dollars in terms of past dollars = 100 × 100÷120 = $ 80

In other words, we know that $100 in the begining of the year would buy as many goods and services as 80 at the end of the year

Change in real value of dollar is 20

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• What is the PPP rate at the end of the year as a direct quote in the U.S.?

PPP = Cost of good in US/ Cost of goods in mexico = 120/160 = 0.75

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• What is the real exhchange rate at the end of the year as a direct quote in the U.S.?

Real exchnage rate = nominal exchange rate * prices in US/ prices in mexico =

0.2*120/160 = 0.15