Question

You are given the following information. The current dollar-pound exchange rate is $2 per pound. A representative basket of goods and services costs $100 in the US and $120 (dollars, not pounds) 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 20% per year. That is, if the real exchange rate today is 1.4 and the speed of convergence to absolute PPP is 15% per year, the real exchange rate in one year will be 1.4-0.30*0.4=1.28).

1. What is the expected U.S. minus U.K. inflation differential for the coming year?

2. What is the current U.S. real exchange rate qUS/UK with the United Kingdom? (recall that qUS/UK is defined as the ratio of prices in the UK to the US, both expressed in a common currency).

3. By what percentage is the dollar overvalued or undervalued relative to its absolute PPP level

4. What do you predict the U.S. real exchange rate with the United Kingdom will be in one year’s time?

5. What is the expected rate of real depreciation for the United States (versus the United Kingdom)?

6. What is the expected rate of nominal depreciation for the United States (versus the United Kingdom)?

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

Answer 1

Answer:1

The inflation differential is equal to -1% ( =2% - 3%).

Answer:2

qUK/US= (E$/£PUK)/PUS= $120/$100 = 1.2.

Answer:3

The British pound is undervalued by 20% and the U.S. dollar is overvalued by 20% (=1.2 - 1 /1).

Answer:4

We can use the information on convergence to compute the implied change in the U.S. real exchange rate. We know the speed of convergence to absolute PPP is 15%; that is, each year the exchange rate will adjust by 15% of what is needed to achieve the real exchange rate equal to 1 (assuming prices in each country remain unchanged). Today, the real exchange rate is equal to 1.2, implying a 0.2 decrease is needed to satisfy absolute PPP. Over the next year, 15% of this adjustment will occur, so the real exchange rate will decrease by 0.03. Therefore, after one year, the U.S. real exchange rate,qUK/US,will equal 1.17.

Answer:5

From (d), the real exchange rate will decrease by 0.03. Therefore, the rate of real depreciation is equal to - 2.5% ( = -0.03 / 1.20). This implies a real appreciation in the United States relative to the United Kingdom.

Answer:6

The expected rate of nominal depreciation can be calculated based on the inflation differential plus the expected real depreciation from (e). In this case, the inflation differential is - 1% and the expected real appreciation is - 2.5%, so the expected nominal depreciation is - 3.5%. That is, we expect a 3.5% appreciation in the U.S. dollar relative to the British pound.

Answer:7

The current nominal exchange rate is $2 per pound and we expect a 3.5% appreciation in the dollar (from [f]). Therefore, the expected exchange rate in one year is equal to $1.93 ( =$2 * (1 - 0.035).