Work It Out, Chapter 14, Question 1

(Transcript of audio with descriptions. Transcript includes narrator headings and description headings of the visual content)

(Speaker)
This problem will ask you to consider the following information: The current dollar–pound exchange rate is 1.5 dollars per British pound. A U.S. basket that costs 100 dollars would cost 120 dollars in the United Kingdom. For the next year, the Federal Reserve is predicted to keep U.S. inflation at 2 percent and the Bank of England is predicted to keep U.K. inflation at 3 percent. The speed of convergence to absolute PPP is 15 percent per year. We begin by setting the problem. Be careful and use the correct symbols. The current dollar–pound exchange rate is 1.5 dollars per British pound.

(Description)
The following relation is written: E subscript the dollars sign over the pound sign equals 1.5 dollars.

(Speaker)
A U.S. basket that costs $100 would cost $120 in the United Kingdom.

(Description)
The following text is written below the previous relation: 100 dollar US basket would cost 120 dollars in United Kingdom.

(Speaker)
For the next year, the Federal Reserve is predicted to keep U.S. inflation at 2 percent and the Bank of England is predicted to keep U.K. inflation at 3 percent.

(Description)
The following relations are written below the previous text: pi subscript the dollars sign (US) equals 2 percent. pi subscript the pound sign (Great Britain) equals 3 percent.

(Speaker)
The speed of convergence to absolute PPP is 15 percent per year.

(Description)
The following relation is written below the previous ones: Speed of convergence to absolute PPP equals 15 percent per year.

(Speaker)
Question (a) will ask for the expected U.S. minus U.K. inflation differential for the coming year. We start by identifying the correct formula for the inflation differential and writing it down.

(Description)
The following formula is written: pi subscript the dollar sign minus pi subscript the pound sign equals the question mark.

(Speaker)
Then, using the information we already identified when we set up the problem, we plug in the correct values. The answer is negative 1 percent.

(Description)
The following relation is written: Expected inflation differential equals 2 percent minus 3 percent equals negative 1 percent.

Work It Out, Chapter 14, Question 2

(Transcript of audio with descriptions. Transcript includes narrator headings and description headings of the visual content)

(Speaker)
Question (b) will ask for the current U.S. real exchange rate q US to UK, with the United Kingdom. We start with the formula for the real exchange rate.

(Description)
The following formula is written: q subscript US over UK equals E subscript the dollar sign over the pound sign multiplied bu P subscript UK divided by P subscript US.

(Speaker)
However, since we do not have the price of the British basket in terms of pounds, we transform the dollar price to the pound price. Thus, we will multiply the dollar price by the dollar per pound exchange rate. Then, using the information we already identified when we set up the problem, we plug in the correct values. The answer is 1.2.

(Description)
The following relation is written: q subscript US over UK equals 120 over 100 equals 1.2.

Work It Out, Chapter 14, Question 3

(Transcript of audio with descriptions. Transcript includes narrator headings and description headings of the visual content)

(Speaker)
Question (c) will ask how much is the dollar overvalued or undervalued.

(Description)
The following relation is written: Pound overevaluation equals 1.2 minus 1 equals 0.2 or 20 percent.

(Speaker)
If the real exchange rate q US to UK is below 1 by x percent we say that the pound is overvalued by x percent. In this example we can see that the real exchange rate q US to UK is 20 percent above purchasing power parity. If the real exchange rate q US to UK is above 1 by 20 percent, we say the dollar is undervalued by 20 percent. If the dollar is undervalued by 20 percent, the pound is overvalued by 20 percent.

Work It Out, Chapter 14, Question 4

(Transcript of audio with descriptions. Transcript includes narrator headings and description headings of the visual content)

(Speaker)
Question (d) will ask you to predict the U.S. real exchange rate with the United Kingdom in one year’s time. We start by identifying the correct formula and writing it down.

(Description)
The following formula is written: q subscript US over UK, t plus 1, equals q subscript US over UK, t plus minus change in q subscript US over UK.

(Speaker)
The formula for the change in q US to UK takes into consideration that the overvaluation will decrease due to the convergence process.

(Description)
The following relation is written: Change in q subscript US over UK equals Overvaluation times speed of convergence.

(Speaker)
Then we plug in the correct values.

(Description)
The following relation is written: Change in q subscript US over UK equals 0.2 times 0.15 equals 0.03.

(Speaker)
The change in the real exchange rate is 15 percent of the 20 percent difference between the real exchange rate and 1 (due to convergence the gap is closed by 15 percent each year). Finally, we plug all the values in the formula. The real exchange rate in a year will be 1.17.

(Description)
The following relation is written: q subscript US over UK, t plus 1, equals 1.2 minus 0.03 equals 1.17.

Work It Out, Chapter 14, Question 5

(Transcript of audio with descriptions. Transcript includes narrator headings and description headings of the visual content)

(Speaker)
Question (e) will ask for the expected rate of real depreciation for the United States (versus the United Kingdom). We start by identifying the correct expected rate of real depreciation formula and writing it down.

(Description)
The following formula is written: Expected rate of real depreciation equals Real exchange rate decrease divided by Real exchange rage.

(Speaker)
Then we plug in the correct values. The answer is –0.025 or –2.5 percent, which is a 2.5 percent real appreciation.

(Description)
The following relation is written: Expected rate of real depreciation equals negative 0.03 over 1.2 equals negative 0.025 equals negative 2.5 percent.

Work It Out, Chapter 14, Question 6

(Transcript of audio with descriptions. Transcript includes narrator headings and description headings of the visual content)

(Speaker)
Question (f) will ask you compute the expected rate of nominal depreciation for the United States (versus the United Kingdom). The expected rate of nominal depreciation takes into consideration the change in the exchange rate due to convergence and due to the inflation differential.

(Description)
The following formula is written: Expected rate of nominal depreciation equals inflation differential plus Expected real depreciation.

(Speaker)
The values for each component were already computed in (a) and (e). The answer is negative 3.5 percent. The dollar will appreciate by 3.5 percent.

(Description)
The following relation is written: Expected rate of nominal depreciation equals negative 1 percent minus negative 2.5 percent equals negative 3.5 percent.

Work It Out, Chapter 14, Question 7

(Transcript of audio with descriptions. Transcript includes narrator headings and description headings of the visual content)

(Speaker)
Question (g) will ask you to predict the dollar price of one pound a year from now. The nominal exchange rate one year from now equals the spot exchange rate minus the nominal depreciation.

(Description)
The following relation is written: E subscript the dollar sign over the pound sign, t plus 1, equals E subscript the dollars sign over the pound sign, t, plus nominal depreciation.

(Speaker)
To compute the nominal depreciation we need to know by how much the dollar will depreciate.

(Description)
The following relation is written: Nominal depreciation equals Expected rate of nominal depreciation times E subscript the dollars sign over the pound sign, t.

(Speaker)
The spot exchange rate is given and the nominal depreciation was computed above. 3.5 percent of the nominal rate of 1.5 is 0.05. The spot exchange rate will decrease by 0.05.

(Description)
The following relation is written: Nominal depreciation equals negative 0.035 times 1.5 equals negative 0.05.

(Speaker)
The spot exchange minus the expected decrease gives us the expected price of one pound a year from now. The answer is 1.45.

(Description)
The following relation is written: E subscript the dollar sign over the pound sign, t plus 1, equals 1.5 minus 0.05 equals 1.45.

(Speaker)
Since we will need fewer dollars than this year, we say the dollar appreciates.