Question

You are given the following information.The current dollar-pound exchangerate is $1.5 per pound. A U.S. basket that costs $100 would cost 80 poundsin theU.K. For thenext year, theFederal Reserve is predicted to keep U.S. inflation at 2%, and the Bank of England is predicted to keep U.K. inflation at 3%. The speed of convergenceto absolutePPP is 15% per year. a)What is the expected US minus UK inflation differential for coming year?

b)What is the current US real exchange rate qus/uk with the UK?

c) How much is the dollar overvalued/ undervalued?

d)What do you predict the US real exchange rate with UK will be in one year's time?

e)What is the expected rate of real depreciation for US(versus the UK)?

f)What is the expected rate of nominal depreciation for the US(versus the UK)?

g) What do you predict will be the dollar price of one pound a year from now?

Answer 1

The expected US minus UK inflation differential is -1%. The current real exchange rate of the US with the UK is 0.8333, indicating the dollar is overvalued by 20%. Predictions for the future include a real exchange rate of 0.8833 in one year and an expected nominal depreciation of the dollar by roughly 0.85%.

Step-by-step explanation:

Exchange Rate and Purchasing Power Parity (PPP) Analysis

To answer a series of questions regarding exchange rates, inflation, and purchasing power parity between the United States and the United Kingdom, consider the following calculations and predictions based on the given data:

1. US-UK Inflation Differential: The expected US minus UK inflation differential for the coming year is the difference between the US inflation rate (2%) and the UK inflation rate (3%), which is -1%.
2. Current US Real Exchange Rate (qus/uk): The real exchange rate can be calculated by adjusting the nominal rate by the price level difference between the two countries. It is ($100 / 80 pounds) / (1.5 dollars per pound) = 0.8333.
3. Dollar Overvaluation/Undervaluation: The dollar's over- or undervaluation against the pound can be analyzed by comparing the real exchange rate to the nominal exchange rate. Currently, the nominal rate is 1.5 dollars per pound, and the real exchange rate is 0.8333. This indicates that the dollar is overvalued (overvalued by 20%).
4. Predicted US Real Exchange Rate in One Year: Considering the speed of convergence to absolute PPP (15% per year), we adjust the current real exchange rate (0.8333) towards the nominal exchange rate (1.5) by 15%. This results in a predicted real exchange rate of approximately 0.8833.
5. Expected Rate of Real Depreciation for US: The expected rate of real depreciation for the US (versus the UK) can be expressed as the percentage change in the real exchange rate, which would be roughly 6%.
6. Expected Rate of Nominal Depreciation for the US: The expected nominal depreciation for the US against the UK is the inflation differential adjusted for the speed of PPP convergence, resulting in a nominal depreciation of approximately 0.85%.
7. Predicted Dollar Price of One Pound in One Year: Using the predicted rate of nominal depreciation, the dollar price of one pound a year from now would be higher. The exact figure would depend on the market dynamics and the actual realized inflation rates but could be around $1.5135 per pound.

Answer 2

a) the expected US minus UK inflation differential for coming year is - 1% = 2% - 3%

b) the current US real exchange rate us/uk with the UK 1.25 = 100/80

c) the dollar overvalued 20% = (1.5/1.25-1)

d) the US real exchange rate with UK will be in one year's time is 1.24

e) the expected rate of real depreciation for US (versus the UK) is 1.1

f) the expected rate of nominal depreciation for the US(versus the UK) is 1.24

g) I predict the dollar price of one pound a year from now will be 1.1

Step-by-step explanation:

a) The inflation rate differential is the difference between the inflation rate in one country and the inflation rate in another.

b) The real exchange rate can be defined by Purchase Power Parity (PPP)

FX = P 2 / P 1

​where: FX = Exchange rate of currency 1 to currency 2

P 1 = Cost of good X in currency 1

P 2 = Cost of good X in currency 2

c) current quoted rate compared to real exchange rate based on PPP is higher, then USD is overvalued

d) Real exchange rate is defined based on PPP in next 1 year. In next 1 year, U.S. basket is $102 = 100 x(1+ inflation rate 2%) while this basket in UK is 82.4 pound = 80 x (1+ inflation rate 3%)

thus expected rate us/uk = 102/82.4 = 1.24

e) The speed of convergence to absolute PPP is 15% per year, then US real exchange rate us/uk with the UK 1.1 = current US real exchange rate us/uk with the UK 1.25 - 15%

f) Nominal depreciation is same as real depreciation in item d

d) I used the calculation with convergence to absolute PPP as item e

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