Question

The demand for British Pounds in exchange of Canadian Dollars is Qd = 75−10e and the supply is Qs = 45+10e, where e is the nominal exchange rate (Canadian Dollars to buy one British Pound) and Q represents the quantity of British Pounds. Suppose that the Bank of Canada wants to keep the exchange rate Canadian Dollars/Pound between 1.6 and 1.7. Assume that the Bank of Canada makes the minimum intervention to keep the exchange rate within the band. What does the Bank of Canada need to do if it wants to keep the exchange rate within the band?

(a) The Bank of Canada does nothing because the equilibrium nominal exchange rate without intervention is within the band.

(b) The Bank of Canada sells 2 British Pounds.

(c) The Bank of Canada buys 2 British Pounds.

(d) The Bank of Canada buys 5 British Pounds.

Answer 1

First let us see what is the equilibrium exchange rate

Qd = Qs

75 - 10e = 45 + 10e

20e = 30

e = 1.5

This means it will take 1.5 Canadian dollar to buy 1 British pound

Q = 60

But Bank of Canada wants to maintain nominal interest rate in a band of 1.6 to 1.7

So in this case Bank of Canada would interevne so as to increase the exchange rate or would lead to depreciation of its own currency against British pound. Thus Central Bank would create to demand of British pound by purchasing some amount of it.

But the main question is by how much should it create demand?

So first it buys 2 British pound the e will be

77 - 10 e = 45 + 10e

20e = 32

e = 1.6

Which is fair enough in our range

Let us look for if it buy 5 british pound

Then e will be

80 - 10e = 45 + 10e

20e = 35

e = 1.75

Which is outside our range

Thus Central bank would buy 2 British pound

Option b is the right answer