econ (economyst please help)

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?

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  1. 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.

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  2. 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%.

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