I got this long question i am not sure how to do.
The current dollar-pound exchange rate is $2 per pound. A U.S. basket that costs $100 would cost $120 in the United Kingdom. For the next year, the Fed 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 convergence to absolute PPP is 15% per year.
(a) What is the expected U.S. minus U.K. inflation differential for the coming year?
-is this one simply just 2%-3%= -1%?
(b) What is the current U.S. real exchange rate q UK/US with the United Kingdom?
-is it $120/$100 =1.2?
(c) How much is the dollar overvalued/undervalued?
(d) What do you predict the U.S. real exchange rate with the United Kingdom will be in one year's time?
(e) What is the expected rate of real exchange depreciation for the United States (versus the United Kingdom)?
(f)What is the expected rate of nominal depreciation for the United States (versus the United Kingdom)?
(g) What do you predict will be the dollar price of one pound a year from now?
I am mucho confused by your given: A "basket" costs $120 in the UK. Given the current exchange rate of $/L=2, does that mean the basket in the UK costs L60. Your question hinges on this interpretation. (Note that I'm using L for British Pounds).
a) I agree
b) Assuming that the basket cost L60, then the real exchange rate is $100=L60 -- so $/L = 100/60 = 1.67.
c) Dollar is over-valued by 2/1.667 = %20
Im confused about what you mean by "convergence to absolute PPP is 15% per year" I presume this means that the dollar will be over-valued by 15% less than currently. That is, 2/x=(.2*.85) -- solve for x. I get 1.71.
That is $/L = 2/1.71 = 1.17 or 17% overvalued. (But I could be wrong).
e), f) and g) -- I can see I will need to think about and research this some more.
I hope this helps, lottsa luck.
This is the covergence to absolute PPP part from my text:
The evidence suggests that PPP works better in the long run but not in the short run. In reality, research shows that price differences, the deviations from PPP, can be large and persistent in the short run. Estimates suggest that these deviations may die out at a rate of about 15% per year. This kind of measure is often referred to as a speed of convergence. It implies that after one year, 85% (0.85) of an initial price difference persisits; compounding, after two years 72% of the gap persists and after four years 52%.
(a) The expected U.S. minus U.K. inflation differential for the coming year can be calculated as follows:
Expected U.S. inflation - Expected U.K. inflation = 2% - 3% = -1%.
(b) The current U.S. real exchange rate q UK/US with the United Kingdom can be calculated as follows:
Current U.S. real exchange rate = (U.S. dollar price in the U.K.)/(U.S. dollar price in the U.S.) = $120/$100 = 1.2.
(c) To determine whether the dollar is overvalued or undervalued, we need to compare the current U.S. real exchange rate with the long-run equilibrium real exchange rate. The long-run equilibrium real exchange rate can be calculated using the formula:
Long-run equilibrium real exchange rate = (1 + expected difference in inflation rates) / (1 + speed of convergence to absolute PPP).
Since the speed of convergence to absolute PPP is given as 15% per year, the long-run equilibrium real exchange rate would be:
(1 + (-1%)) / (1 + 15%) = 0.99 / 1.15 ≈ 0.8609.
Comparing this with the current U.S. real exchange rate (1.2), we can see that the dollar is overvalued.
(d) To predict the U.S. real exchange rate with the United Kingdom in one year's time, we can use the formula for the speed of convergence to absolute PPP. Assuming the speed of convergence to absolute PPP remains at 15% per year, the U.S. real exchange rate in one year's time would be:
Current U.S. real exchange rate * (1 + speed of convergence to absolute PPP) = 1.2 * (1 + 15%) = 1.2 * 1.15 = 1.38.
(e) The expected rate of real exchange depreciation for the United States (versus the United Kingdom) can be calculated using the following formula:
Expected rate of real exchange depreciation = (Expected U.S. inflation - Expected U.K. inflation) / (1 + Expected U.K. inflation) = -1% / (1 + 3%) = -1% / 1.03 ≈ -0.9709%.
(f) The expected rate of nominal depreciation for the United States (versus the United Kingdom) is the sum of the expected rate of real exchange depreciation and the expected U.S. inflation rate. Using the values given, we can calculate:
Expected rate of nominal depreciation = Expected rate of real exchange depreciation + Expected U.S. inflation = -0.9709% + 2% = 1.0291%.
(g) To predict the dollar price of one pound a year from now, we need to multiply the current dollar-pound exchange rate by the expected rate of nominal depreciation for the United States. Using the values given, we can calculate:
Predicted dollar price of one pound = Current exchange rate * (1 - Expected rate of nominal depreciation) = $2 * (1 - 1.0291%) = $2 * 0.989709 ≈ $1.9794.
Please note that these calculations are based on the information provided in the question and assumptions regarding the speed of convergence to absolute PPP.
To answer these questions, we need to understand the concepts of inflation, exchange rates, and purchasing power parity (PPP).
(a) The expected U.S. minus U.K. inflation differential can be calculated by subtracting the U.K. inflation rate from the U.S. inflation rate. In this case, it would be 2% - 3% = -1%.
(b) The current U.S. real exchange rate (q UK/US) with the United Kingdom can be calculated by dividing the price of the U.K. basket by the price of the U.S. basket. In this case, it would be $120/$100 = 1.2.
(c) To determine if the dollar is overvalued or undervalued, we need to compare the current exchange rate with the equilibrium exchange rate based on PPP. If the current exchange rate is higher than the equilibrium exchange rate, the dollar is overvalued. If it is lower, the dollar is undervalued. Since we only have the U.S. real exchange rate, we need to use the speed of convergence to absolute PPP to estimate the equilibrium exchange rate. The speed of convergence to absolute PPP is 15% per year, so we can multiply the current U.S. real exchange rate by 1.15 to get the estimated equilibrium exchange rate. If the estimated equilibrium exchange rate is higher than the current exchange rate, the dollar is overvalued. If it is lower, the dollar is undervalued.
(d) To predict the U.S. real exchange rate with the United Kingdom in one year's time, we can multiply the current U.S. real exchange rate by 1 plus the expected rate of real exchange depreciation for the United States (versus the United Kingdom). This rate can be calculated using the expected U.S. minus U.K. inflation differential. For example, if the expected rate of real exchange depreciation is -1%, we would multiply the current U.S. real exchange rate by 0.99.
(e) The expected rate of real exchange depreciation for the United States (versus the United Kingdom) is equal to the expected U.S. minus U.K. inflation differential. In this case, it is -1%.
(f) The expected rate of nominal depreciation for the United States (versus the United Kingdom) can be calculated by adding the expected rate of real exchange depreciation to the expected U.S. inflation rate. For example, if the expected rate of real exchange depreciation is -1% and the expected U.S. inflation rate is 2%, the expected rate of nominal depreciation would be 2% - 1% = 1%.
(g) To predict the dollar price of one pound a year from now, we can multiply the current dollar-pound exchange rate by 1 plus the expected rate of nominal depreciation for the United States (versus the United Kingdom). For example, if the current dollar-pound exchange rate is $2 per pound and the expected rate of nominal depreciation is 1%, we would multiply $2 by 1.01 to get the predicted dollar price of one pound.