Question

a) Assume that yesterday (April 22, 2020) the interest rate on dollar deposits in the U.S. was 0.02 (2%) per year and the interest rate on euro deposits was 0.02 (2%) per year. Investors yesterday expected that the exchange rate in one year (April 22, 2021) will be 2.02 dollars for one euro.

What was the current exchange rate in terms of dollars per euro yesterday (April 22, 2020)?

Illustrate your answer, using a graph with the rates of return (in dollars terms) on the horizontal axis, and the exchange rate on the vertical axis.

b) Now, assume that today (April 23, 2020) the Federal Reserve lowers the interest rate on dollar deposits to 0.01 (1%), and the European Central Bank lowers the interest rate on euro deposits to zero (0%). There is no change in the expected exchange rate a year from now - that is, on April 23, 2020 investors expect that the exchange rate on April 23, 2021 will be 2.02 dollars for a euro.

What is the current exchange rate today (April 23, 2020), right after the reductions in the interest rates? Has the dollar depreciated or appreciated between April 22 and April 23? Why? Is your answer consistent with the textbook’s claim that a reduction in the interest rate on dollar deposits should cause a depreciation of the dollar?

Illustrate your answer, using a new graph with the rates of return (in dollars terms) on the horizontal axis, and the exchange rate on the vertical axis.

c) What is the effect of the change in the exchange rate above (from April 22 to April 23, 2020) on exports of American goods to Europe? And on exports of European goods to the United States? Explain. (You don’t need to provide numbers, only the general direction of the changes: going up or going down). Who will benefit and who will lose from these changes in the United States?

d) Now, assume American exporters successfully lobby the Federal Reserve, and convince it to adopt a new monetary policy that will boost American exports. Thus, on April 24 the Federal Reserve decides to change the interest rate on dollar deposit once again, with the objective to cause a 1% depreciation of the dollar with respect to the euro (that is, a 1% increase in the amount of dollars required to buy a euro). Assume that the European Central Bank does not react to the new actions by the Federal Reserve, and that investors’ expectations about the future value of the euro remain unchanged (that is, they expect that the exchange rate on April 24, 2021 will be 2.02 dollars for a euro). What interest rate should the Federal Reserve select in order to achieve its objective? Explain.

Illustrate your answer, using a new graph with the rates of return (in dollars terms as usual) on the horizontal axis, and the exchange rate on the vertical axis.

e) Now assume that, unlike in part d), investors, when they hear that the Federal Reserve intends to devaluate the dollar today, also adjust their expectations about the future: now, they expect that the exchange rate on April 24, 2021 will be 2.0402 rather than 2.02. What interest rate should the Federal Reserve select now, on April 24, 2020, in order to achieve its goal of depreciating the dollar by 1% from April 23 to April 24? Explain (no need to illustrate this answer graphically, just give the answer in words).

Answer 1

Forward Exchange rate ($ per euro)= Spot exchange rate ($ per euro) (1+domestic interest rate) / (1+foreign interest rate)

a. $2.02/euro= Spot exchange rate (1+0.02) / 1+0.02

Spot exchange rate= $2.02/euro

b) Domestic interest rate changes to 0.01

Foreign interest rate changes to 0.

$2.02/euro= Spot exchange rate (1+0.01) / (1+0)

Spot exchange rate= $2/euro

Here $ appreciated with fall in domestic interest rate and foreign exchange rate.

No, Answer is not consistent with the textbook’s claim that a reduction in the interest rate on dollar deposits should cause a depreciation of the dollar because here fall foreign interest rate is higher than the fall in domestic interest rate.

c) This appreciation of dollar and fall in exchange rate cause rise in exports of Europe to US because now goods from Europe become cheaper for people in US and on the other hand the exports of US to Europe decreases because for people in Europe the American goods become expensive.

d) If there is a 1% depreciation in Exchange rate dur to new monetary policy then new exchange rate is $2/euro+$2/euro(0.01)= $2.02/euro

$2.02/euro= $2.02/euro (1+domestic interest rate) / (1+0)

1= 1+ domestic interest rate

Domestic interest rate = 0%

If domestic interest rate become 0% then it will cause a 1% increase in exchange rate from $2/euro to $2.02/euro.

e) Spot exchange rate = $2.02/euro

Forward exchange rate= $2.0402/euro

Foreign exchange rate = 0

$2.0402/euro=$2.02/euro (1+domestic interest rate) / (1+0)

1.01-1= domestic interest rate

0.01= 1%= domestic interest rate