Question

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^*)

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

a) In the state of equilibrium, Money Supply = Money Demand

As stated, Money Supply = 100, Money Demand = P * (LY)

Substituting values (Price level is 1 therefore P=1; L=0.13-i; Y=1000), we get the below equation:

==> 100 = 1*(0.13-i)*1000 ==> 0.1 = 0.13 - i

Therefore, i = 0.03

b) Using the uncovered interest rate equation for spot rate, E = Ee / (1 + i - i*)

Substituting values, Ee = 2, i = 0.03, i* = 0.03 (solved in part a)

Spot exchange rate E = 2 / ( 1 + 0.03 - 0.03 ) = 2

c) Only difference between part a and part c is that money supply has been changed to 120 from 100

Using the same equation used in part a, we get

==> 120 = 1 * ( (0.13-i)*1000 ==> 0.12 = 0.13 - i ==> i = 0.01

d) New spot exchange rate E = Ee / (1 + i - i*) = 2 / ( 1 + 0.03 - 0.01) = 2 / 1.02 = 200 / 102 = 100 / 51 = 1.96

e) In this particular example, Money Supply and interest rate relation can be represented by the below equation :

Ms = Md = PLY = 1*(0.13-i)*1000

==> Ms = 1000 (0.13 - i)

This is a downward sloping linear equation with Y intercept value of 130 and X intercept value of 0.13

As money supply decreases, interest rate increases. When money supply increases beyond 130, interest rate becomes negative. When money supply decreases to 0, interest rate is maximum at 13% (0.13)

Money supply and exchange rate are related by the below (as derived in part h,

E = b / (a-Ms)

When money supply is 100, E is 2. When money supply increases to 120, E decreases marginally to 1.96

This is a downward sloping curve with slope infinity at Ms = constant; and as Ms increases, E keeps on decreasing with E approaching zero when Ms is approaching infinity.

f) As per quantity theory of money, price level of goods and services is directly proportional to the amount of money in circulation (money supply)

Therefore, P = k * Ms [P = price level, k = constant, Ms = money supply]

Initial price level is 1 when money supply is 100. Hence, k = 0.01

When, Ms increases to 120 in the long run, price level changes to follows:

Pnew = 0.01 * 120 = 1.2

g) As per Purchasing power parity equation,

E = P1 / P2

Initial values are as follows,

E = 2 (as solved in part b),

P1 = 1

Therefore, initial P2 = P1/E = 0.5

Since there is no change interest rate and Money supply in foreign country; price levels will remain same in foreign country at P2 = 0.5 (as per money demand hypothesis)

Also, P1 has been revised to 1.2 with money supply increasing.

Under revised conditions:

Revised E = P1 revised / P2 ==> 1.2 / 0.5 = 2.4

Hence, the exchange rate has changed from 2 to 2.4

h) As solved earlier,

Short run change will in money supply will marginally affect the exchange rates (2 to 1.96) as they are related by the below equation (inveresly proportional) :

Ms = Md = P(0.13-i)Y = k(0.13 - i) where k = constant (value = P*Y)

Also, i is related to exchange rate as follows ==> i* = 1+i - Ee/E

This implies, in short-run; Ms = k*(0.13-1+i-Ee/E)

As K, i (foreign interest rate), Ee (Future exchange rate) are constants

The equation is of the form ==> Ms = a - b / E where a and b are constants

Or, E = b / (a-Ms)

For long term impact, using PPP

E = P1 / P2

P1 is directly proportional to Money supply

Therefore, E = k*Ms / P2 ==> Ms = (p2/k)*(E)

This is of the form E = k*Ms

I have decribed here the relation between exchange rate change from change in money supply in long run and short run. All three variables, exchange rate, money supply and interest rate cannot be decribed in a single graph.

Clarity in question h will help me respond better.