Question

You are given the following information. The current dollar/euro exchange rate is 1.25 dollars per euro. A U.S. basket that costs $100 would cost 64 euro in the euro area. For the next year, the Fed is predicted to keep U.S. inflation at 3% and the ECB is predicted to keep euro area inflation at 1%. The speed of convergence to absolute PPP is 15% per year.

a. What is the current U.S. real exchange rate, with the euro area?
b. How much is the dollar overvalued/undervalued?
c. What do you predict the U.S. real exchange rate with the euro will be a year from now?
d. What is the expected rate of real depreciation for the United States (versus the euro)?
e. What is the expected U.S. minus euro area inflation differential for the coming year?
f. What is the expected rate of nominal depreciation for the United States (versus the euro)?

Answer 1

a) 1.562

b) ( overvalued by 56.2% )

c) 1.477

d ) -5.3% ( appreciation of dollar vs euro )

e) 2%

f) -5.1% ( appreciation of dollar vs euro )

Step-by-step explanation:

Given that : $1.25 = 1 euro

Inflation rate next year in U.S = 3%

Inflation rate next year in euro area = 1%

U.S basket that cost $100 cost 64 euro in the euro area

a) Determine the current U.S real exchange rate with the euro area

= $100 / $64 = 1.562

b) The dollar is overvalued because the given exchange rate is lower than the real exchange rate

= ( 1.562 - 1 ) * 100% = 56.2% ( overvalued by 56.2% )

c) prediction of the U.S real exchange rate with euro in a year's time

given that the speed of convergence to absolute PPP = 15% pear year ( i.e. exchange rate will be adjusted by 15% each year )

assume prices do not change in each economy

Today's real exchange rate = 1.562 ∴ an adjustment of 0.562 is needed( decrease )

and 15% of the adjustment = ( 15/100 ) * 0.562 = 0.084

hence the real exchange rate in a year's time = 1.562 - 0.084 = 1.477

d) Determine the expected rate of real depreciation for the U.S vs Euro

= - 0.084 / 1.562 = -0.053 = -5.3% ( appreciation of dollar vs euro )

e) Determine The expected inflation differential

= 3% - 1% = 2%

f) determine the rate of nominal depreciation for the U.S vs Euro

inflation rate differential = 2%

real exchange rate = 1.47 therefore change required = ( 15% * 0.47 ) = 0.075

hence the rate of nominal depreciation = - 0.075 / 1.47 = -0.051 = -5.1% ( appreciation of dollar vs euro )