Question

A1. Suppose the Bank of Canada (BOC) buys $10B worth of bonds from the Canadian banking system that operates with a desired reserve ratio of 5%. Immediately after the transaction, the balance sheet of the BOC expands by $10B, while balance sheet of the banking system is the same size, but in the long run, the balance sheet of both the BOC and the banking system expand by $200B.

A2.A given increase in the money supply is more effective at shifting the aggregate demand curve the more interest rate responsive (elastic) is the money demand curve.

Answer 1

Solution -A1:

The banking systems reserve ratio was 5% originally however after the purchase it changes to 36% (=$11B/$30B). Since the banking system only desires a 5% reserve ratio than 5% of $30B will be computed $1.5B. Thus an amount of $9.5B (=11B – 1.5B) will be in excess reserves with 30B in deposits. Now assuming they lend all of it i.e. $9.5B, thus will increases Loans by $9.5B however reduces its cash reserves by the same amount. Thus the target reserve ratio equals 0.05. So total deposits in the banking system will eventually increase by 20 times (= 1/0.05) which equals $200B (= $10B x 20). Hence the balance sheets of the banking system will expand by $200B in the long-duration.

BOC					BS
Assets	Amount	Liabilities	Amount		Assets	Amount	Liabilities
Reserves	5	Deposits	12		Reserves	1	Deposits	20
Loans	10	Capital	3		Loans	24	Capital	5
	15		15			25		25
After purchase					After purchase
Assets	Amount	Liabilities	Amount		Assets	Amount	Liabilities
Reserves	5	Deposits	12		Reserves	11	Deposits	30
Loans	10	Capital	3		Loans	24	Capital	5
	15		15			35		35
					After loan
					Assets	Amount	Liabilities
					Reserves	1.5	Deposits	30
					Loans	33.5	Capital	5
						35		35

From above computations we can conclude that although the long-run part is true, however the immediate effect on the balance sheets is false