Question

1) The foreign exchange market is in equilibrium when deposits of all currencies offer the same
expected rate of return. The condition that the expected returns on deposits of any two
currencies are equal when measured in the same currency is called the interest parity
condition.
Consider the following two currencies, the dollar ($) and the euro (€). Let R$ and R€
represent the interest rates on dollar deposits and euro deposits respectively and let E$/€
represent the current exchange rate defined in terms of dollars per euro. Further, denote the
expected exchange rate by Ee
$/€
a. Write down the interest rate parity condition for this currency pair using the above
notations.
b. Underline the term representing the return on dollar deposits in part (a). Graph and
label this on a diagram with the vertical axis labelled “Exchange rate (E$/€)”and the
horizontal axis labelled “Rates of returns (in dollar terms)”.
c. Circle the term(s) representing the expected rate of return on euro deposits expressed
in terms of dollars in part (a). Graph and label this on the same diagram in part (b).
d. Indicate with “2” on your diagram the point where no one would be willing to hold
euro deposits and label the corresponding exchange rate as E2
$/€. Explain why that would
be the case using the interest parity condition you have written down in (a). What
happens to the demand for dollars and euros?
e. Similarly, indicate with “3” on your diagram the point where no one would be willing
to hold dollar deposits and label the corresponding exchange rate as E3
$/€. Explain
why that would be the case. What happens to the demand for dollars and euros?

f. Label the point on your diagram where the interest parity condition is satisfied as “1”
and label the exchange rate corresponding to this point as E1
$/€. Explain how points “2”
and “3” are on your diagram would ultimately reach point “1”, with detailed reference to
how the terms in the inequality expression given in slide 14-31 of your lecture handout,
would have a tendency to change.

2 ) You have now graphed and explained the model of exchange rate determination in 3.
Comparative static analysis can now be applied to this simple model.
Use the diagrammatic analysis of foreign exchange equilibrium and explain the effects of a
rise in the interest rate paid on dollar deposits from R1
$ to R2
$.
[Hint: Your answer should include an explanation of what happens to the relative
attractiveness of holding deposits in the two currencies (dollars and euros) at the original
exchange rate E1
$/€ and how the new equilibrium exchange rate E2
$/€ is achieved.]

Answer 1

The equilibrium exchange rate is the interaction of the supply of a currency and the demand for a currency. As in any market, the foreign exchange market will be inequilibrium when the quantity supplied of a currency is equal to the quantity demanded of a currency.

The foreign exchange market is in equilibrium when deposits of all currencies offer the same expected rate of return. The condition that the expected returns on deposits of any two currencies are equal when measured in the same currency is called the interest parity condition.
Consider the following two currencies, the dollar ($) and the euro (€). Let R$ and R€ represent the interest rates on dollar deposits and euro deposits respectively and let E$/€ represent the current exchange rate defined in terms of dollars per euro. Further, denote the expected exchange rate by Ee $/€

a. Write down the interest rate parity condition for this currency pair using the above notations.

Interest rate parity (IRP) is a theory in which the interest rate differential between two countries is equal to the differential between the forward exchange rate and the spot exchange rate. Interest rate parity plays an essential role in foreign exchange markets, connecting interest rates, spot exchange rates and foreign exchange rates.

Interest rate parity is a theory in which the interest rate differential between two countries is equal to the differential between the forward exchange rate and the spot exchange rate.

b. Underline the term representing the return on dollar deposits in part (a). Graph and label this on a diagram with the vertical axis labelled “Exchange rate (E$/€)”and the
horizontal axis labelled “Rates of returns (in dollar terms)”.
c. .........!!!!!

2.

Most of economic theory consists of comparative statics analysis. Comparative Statics is the determination of the changes in the endogenous variables of a model that that will reusult from a change in the exogenous variables or parameters of that model. A crucial bit of information is the sign of the changes in the endogenous variables.

There is very limited opportunity to establish the signs of the impacts of changes in macroeconomics or any field that does not have an explicit maximization or minimization operation involved. But in microeconomics comparative statics is a powerful tool for establishing important deductions of theories.

First consider the case without maximization or minimization being involved, such as occurs in macroeconomics. The simplest case is situation in which one variable y is determined by some variable x. Suppose the value of y is determined as the solution to an equation,

f(x,y) = 0

This equation holds for all valuees of x so it holds that the differential dy and dx satisfy the equation

(∂f/∂y)dy + (∂f/∂x)dx = 0
or equivalently
f_ydy + f_xdx = 0