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 swelling differential is equivalent to - 1% ( =2% - 3%).

Answer:2

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

Answer:3

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

Answer:4

We can utilize the data on combination to figure the inferred change in the U.S. genuine swapping scale. We know the speed of intermingling to total PPP is 15%; that is, every year the swapping scale will alter by 15% of what is expected to accomplish the genuine conversion scale equivalent to 1 (accepting costs in every nation stay unaltered). Today, the genuine swapping scale is equivalent to 1.2, suggesting a 0.2 abatement is expected to fulfill total PPP. Throughout the following year, 15% of this change will happen, so the genuine swapping scale will diminish by 0.03. In this way, following one year, the U.S. genuine trade rate,qUK/US,will equivalent 1.17.

Answer:5

From (d), the genuine conversion standard will diminish by 0.03. In this way, the pace of genuine deterioration is equivalent to - 2.5% ( = - 0.03/1.20). This infers a genuine gratefulness in the United States comparative with the United Kingdom.

Answer:6

The normal pace of ostensible deterioration can be determined dependent on the swelling differential in addition to the normal genuine devaluation from (e). For this situation, the expansion differential is - 1% and the normal genuine gratefulness is - 2.5%, so the normal ostensible deterioration is - 3.5%. That is, we anticipate a 3.5% gratefulness in the U.S. dollar comparative with the British pound.

Answer:7

The present ostensible swapping scale is $2 per pound and we anticipate a 3.5% gratefulness in the dollar (from [f]). Accordingly, the normal swapping scale in one year is equivalent to $1.93 ( =$2 * (1 - 0.035)