Question

Questions 1 and 2 will use the results of uncovered interest rate parity.  Uncovered interest rate parity states that the domestic return must equal the foreign return (FR), where FR = - i^* + (E^e– E)/E.  This relationship can also be solved for the spot rate, which would yield  E = E^e/ (1 + i  - i^*)   

1.  This question concerns the determination of the foreign return. Assume that the expected exchange rate is equal to 2.5 and that the foreign interest rate is equal to .03.

a.  Calculate the expected foreign return for the following spot exchange rates (E)

i.  2.4

ii.  2.5

iii.  2.6

Be precise, taking your answer out to 3 decimal places.

b.  Now assume that the foreign interest rate increases to .05. Calculate the foreign return for the same three spot rates:  2.4,2.5,2.6.

c.  Now assume that the foreign interest rate is .05 but that the expected exchange rate is 2.55.  Calculate the foreign return for the same three spot rates:  2.4,2.5,2.6.

d.  Plot using graph paper or by computer the foreign return curves in parts a – c.  The foreign return will be on the vertical axis and the spot rate on the horizontal axis. You should have three different foreign return curves.

e.  Suppose the domestic interest rate is .03.  Use your graph to find the equilibrium spot exchange rate in parts a – c.

Hint for problem 1: Follow the same approach as in the beginning of chapter 15, including table 15.1 and figure 15.2.

2.  Suppose money demand can be described as M/P = LY, where L = (.13 – i) and Y =1,000 and i is the nominal interest rate.  Assume that the expected future exchange rate equals 2 and that the foreign interest rate equals .03.

a.  Suppose the price level equals one and the nominal money supply equals 100.  Calculate the nominal interest rate.

b.  Calculate the spot exchange rate according to uncovered interest rate parity

c.  Suppose there is a temporary increase in the  nominal money supply to 120.  Assume that the price level remains at one.  Calculate the new nominal interest rate.

d.  Calculate the new spot exchange rate.  

e.  Show graphically the effect of the change in the money supply on the interest rate and the exchange rate.  It is not necessary to use graph paper but label all axes and curves.

Now assume that the increase in the money supply in part c was permanent, not temporary.  The foreign country interest rate has not changed.

f.  What will be the value of the price level in the long run? (Hint:  assume the quantity theory of money).

g.  What will be the value of the exchange rate in the long run? (Hint:  use your answer in part f and PPP).

h.  Use your graph from part e to show the exchange rate change in the short run from a permanent change in the money supply.

Answer 1

Uncovered Interest rate parity is given by the following relationship

E(S)/S = (1 + i_A) / (1 + i_B)    [Multiplicative Model]

E(S)/S – 1 ? i_A - i_B

Where,

E(S) is the expected spot rate expressed as A/B

i_A and i_B are the returns of the two currencies A and B

a. For solving the problem, I have made use of the Excel. Kindly go through the screenshot. Also note that there are two variants of the model as presented above and I have computed the foreign returns using both for clarification. The one mentioned in the question is an additive model.

b.

c.

d.

Hope it clarifies your query, Thanks.