# ECON 434

I. The FX Market

1. Suppose quotes for the dollareuro exchange rate, E$=AC, are as follows: in New York,

$1.50 per euro; and in Tokyo, $1.55 per euro. Describe how investors use arbitrage to take

advantage of the dierence in exchange rates. Explain how this process will aect the dollar

price of the euro in New York and Tokyo.

1. Consider a Dutch investor with 1,000 euros to place in a bank deposit in either the

Netherlands or Great Britain. The (one-year) interest rate on bank deposits is 2% in Britain

and 4.04% in the Netherlands. The (one-year) forward europound exchange rate is 1.575 euros

per pound and the spot rate is 1.5 euros per pound. Answer the following questions, using the

exact equations for UIP and CIP as necessary.

a. What is the euro-denominated return on Dutch deposits for this investor?

b. What is the (riskless) euro-denominated return on British deposits for this investor using

forward cover?

c. Is there an arbitrage opportunity here? Explain why or why not. Is this an equilibrium

in the forward exchange rate market?

d. If the spot rate is 1.5 euros per pound, and interest rates are as stated previously, what

is the equilibrium forward rate, according to CIP?

e. Suppose the forward rate takes the value given by your answer to (d). Calculate the

forward premium on the British pound for the Dutch investor (where exchange rates are in

euros per pound). Is it positive or negative? Why do investors require this premium/discount

in equilibrium?

f. If UIP holds, what is the expected depreciation of the euro against the pound over one

year?

g. Based on your answer to (f), what is the expected europound exchange rate one year

ahead?

II. The Monetary Approach to ERs

3. You are given the following information. The current dollar-pound exchange rate is $2

per British 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. ination at 2% and the Bank of England is

predicted to keep U.K. ination at 3%. The speed of convergence to absolute PPP is 15% per

year.

a. What is the expected U.S. minus U.K. ination dierential for the coming year?

b. What is the current U.S. real exchange rate, qUK=US, with the United Kingdom?

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 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?

4. Consider two countries, Japan and Korea. In 1996, Japan experienced relatively slow

output growth (1%), whereas Korea had relatively robust output growth (6%). Suppose the

Bank of Japan allowed the money supply to grow by 2% each year, whereas the Bank of Korea

chose to maintain relatively high money growth of 12% per year. For the following questions,

use the simple monetary model (where L is constant). You will nd it easiest to treat Korea as

the home country and Japan as the foreign country.

a. What is the ination rate in Korea? In Japan?

b. What is the expected rate of depreciation in the Korean won relative to the Japanese

yen?

c. Suppose the Bank of Korea increases the money growth rate from 12% to 15%. If nothing

in Japan changes, what is the new ination rate in Korea?

d. Using time series diagrams, illustrate how this increase in the money growth rate aects

the money supply, MK; Korea’s interest rate; prices, PK; real money supply; and EWON=U

over time. (Plot each variable on the vertical axis and time on the horizontal axis.)

e. Suppose the Bank of Korea wants to maintain an exchange rate peg with the Japanese

yen. What money growth rate would the Bank of Korea have to choose to keep the value of the

won xed relative to the yen?

f. Suppose the Bank of Korea sought to implement policy that would cause the Korean won

to appreciate relative to the Japanese yen. What ranges of the money growth rate (assuming

positive values) would allow the Bank of Korea to achieve this objective?

5. This question uses the general monetary model, in which L is no longer assumed constant

and money demand is inversely related to the nominal interest rate. Consider the same scenario

described in the beginning of the previous question. In addition, the bank deposits in Japan

pay 3% interest; iU = 3%.

a. Compute the interest rate paid on Korean deposits.

b. Using the denition of the real interest rate (nominal interest rate adjusted for ination),

show that the real interest rate in Korea is equal to the real interest rate in Japan. (Note that

the ination rates you calculated in the previous question will apply here.)

c. Suppose the Bank of Korea increases the money growth rate from 12% to 15% and the

ination rate rises proportionately (one for one) with this increase. If the nominal interest rate

in Japan remains unchanged, what happens to the interest rate paid on Korean deposits?

d. Using time series diagrams, illustrate how this increase in the money growth rate aects

the money supply, MK; Korea’s interest rate; prices, PK; real money supply; and EWON=U

over time. (Plot each variable on the vertical axis and time on the horizontal axis.)

6. Both advanced economies and developing countries have experienced a decrease in ina-

tion since the 1980s. This question considers how the choice of policy regime has inuenced this

global disination. Use the monetary model to answer this question.

a. The Swiss Central Bank currently targets its money growth rate to achieve policy objec-

tives. Suppose Switzerland has output growth of 3% and money growth of 8% each year. What

is Switzerland’s ination rate in this case? Describe how the Swiss Central Bank could achieve

an ination rate of 2% in the long run through the use of a nominal anchor.

b. Like the Federal Reserve, the Reserve Bank of New Zealand uses an interest rate target.

Suppose the Reserve Bank of New Zealand maintains a 6% interest rate target and the world

real interest rate is 1.5%. What is the New Zealand ination rate in the long run? In 1997, New

Zealand adopted a policy agreement that required the bank to maintain an ination rate no

higher than 2.5%. What interest rate targets would achieve this objective?

c. The central bank of Lithuania maintains an exchange rate band relative to the euro. This

is a prerequisite for joining the Eurozone. Lithuania must keep its exchange rate within 15%

of the central parity of 34,528 litas per euro. Calculate the exchange rate values corresponding

to the upper and lower edges of this band. Suppose PPP holds. If Eurozone ination is currently

2% per year and ination in Lithuania is 5%, calculate the rate of depreciation of the litas.

Will Lithuania be able to maintain the band requirement? For how long? Does your answer

depend on where in the band the exchange rate currently sits? A primary objective of the

European Central Bank is price stability (low ination) in the current and future Eurozone. Is

an exchange rate band a necessary or su‑cient condition for the attainment of this objective?

III. The Asset Approach to ERs

7. Use the money market and foreign exchange (FX) diagrams to answer the following

questions. This question considers the relationship between the euro (AC) and the U.S. dollar

($). The exchange rate is in U.S. dollars per euro, E$=AC. Suppose that with nancial innovation

in the United States, real money demand in the United States decreases. On all graphs, label

the initial equilibrium point A.

a. Assume this change in U.S. real money demand is temporary. Using the FX and money

market diagrams, illustrate how this change aects the money and FX markets. Label your

short-run equilibrium point B and your long-run equilibrium point C.

b. Assume this change in U.S. real money demand is permanent. Using a new diagram,

illustrate how this change aects the money and FX markets. Label your short-run equilibrium

point B and your long-run equilibrium point C.

c. Illustrate how each of the following variables changes over time in response to a permanent

reduction in real money demand: nominal money supply MUS, price level PUS, real money

supply MUS/PUS, U.S. interest rate i$, and the exchange rate E$=AC.

8. This question considers how the FX market will respond to changes in monetary policy.

For these questions, dene the exchange rate as Korean won per Japanese yen, EWON=U. Use

the FX and money market diagrams to answer the following questions. On all graphs, label the

initial equilibrium point A.

a. Suppose the Bank of Korea permanently decreases its money supply. Illustrate the short-

run (label the equilibrium point B) and long-run eects (label the equilibrium point C) of this

policy.

b. Now suppose the Bank of Korea announces it plans to permanently decrease its money

supply but doesn’t actually implement this policy. How will this aect the FX market in the

short run if investors believe the Bank of Korea’s announcement?

c. Finally, suppose the Bank of Korea permanently decreases its money supply but this

change is not anticipated. When the Bank of Korea implements this policy, how will this aect

the FX market in the short run?

d. Using your previous answers, evaluate the following statements:

i. If a country wants to increase the value of its currency, it can do so (temporarily)

without raising domestic interest rates.

ii. The central bank can reduce both the domestic price level and the value of its currency

in the long run.

iii. The most effective way to increase the value of a currency is through surprising

investors.