You are given the following information. Thecurrent dollar-pound exchange rate is $2 perpound. A U.S. basket that costs $100 wouldcost $120 in the United Kingdom. For thenext year, the Fed is predicted to keep U.S. in-flation at 2% and the Bank of England is pre-dicted to keep U.K. inflation at 3%. Thespeed of convergence to absolute PPP is 15%per year.a. What is the expected U.S. minus U.K. infla-tion differential for the coming year?b. What is the current U.S. real exchange rateqUS/UK with the United Kingdom?c. How much is the dollar overvalued/under-valued?d. What do you predict the U.S. real exchangerate with the United Kingdom will be in oneyear’s time?e. What is the expected rate of real deprecia-tion for the United States (versus the UnitedKingdom)?f. What is the expected rate of nominal depre-ciation for the United States (versus theUnited Kingdom)?g. What do you predict will be the dollar priceof one pound a year from now?
Question
You are given the following information. Thecurrent dollar-pound exchange rate is 100 wouldcost $120 in the United Kingdom. For thenext year, the Fed is predicted to keep U.S. in-flation at 2% and the Bank of England is pre-dicted to keep U.K. inflation at 3%. Thespeed of convergence to absolute PPP is 15%per year.a. What is the expected U.S. minus U.K. infla-tion differential for the coming year?b. What is the current U.S. real exchange rateqUS/UK with the United Kingdom?c. How much is the dollar overvalued/under-valued?d. What do you predict the U.S. real exchangerate with the United Kingdom will be in oneyear’s time?e. What is the expected rate of real deprecia-tion for the United States (versus the UnitedKingdom)?f. What is the expected rate of nominal depre-ciation for the United States (versus theUnited Kingdom)?g. What do you predict will be the dollar priceof one pound a year from now?
Solution
a. The expected U.S. minus U.K. inflation differential for the coming year can be calculated by subtracting the predicted U.K. inflation rate from the predicted U.S. inflation rate. So, 2% - 3% = -1%.
b. The current U.S. real exchange rate qUS/UK with the United Kingdom can be calculated by dividing the cost of the U.S. basket in the U.K. by the cost of the U.S. basket in the U.S. and then dividing that by the nominal exchange rate. So, (100) / 2 = 0.6.
c. To determine how much the dollar is overvalued or undervalued, we compare the real exchange rate to the nominal exchange rate. If the real exchange rate is less than the nominal exchange rate, the dollar is overvalued. In this case, 0.6 < 2, so the dollar is overvalued.
d. The U.S. real exchange rate with the United Kingdom in one year’s time can be predicted using the speed of convergence to absolute PPP. The formula is: Real exchange rate in one year = Current real exchange rate + Speed of convergence * (1 - Current real exchange rate). So, 0.6 + 0.15 * (1 - 0.6) = 0.66.
e. The expected rate of real depreciation for the United States (versus the United Kingdom) can be calculated by subtracting the predicted real exchange rate in one year from the current real exchange rate and then dividing by the current real exchange rate. So, (0.66 - 0.6) / 0.6 = 10%.
f. The expected rate of nominal depreciation for the United States (versus the United Kingdom) can be calculated by adding the U.S. minus U.K. inflation differential to the expected rate of real depreciation. So, -1% + 10% = 9%.
g. The dollar price of one pound a year from now can be predicted by multiplying the current dollar-pound exchange rate by one plus the expected rate of nominal depreciation. So, 2 * (1 + 0.09) = $2.18.
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