Question

Suppose that a bank has a required reserve ratio (target reserve ratio) of 10%, reserves of $2.2 billion, loans of $17.8 billion, deposits of $20 billion, and no other liabilities or assets.

a. (4 points) What is the amount of loans at equilibrium?

b. (4 points) Suppose that the Bank of Canada’s currency issue (legal tender) is $52 billion, private bank deposits at the Bank of Canada are $2 billion, currency in circulation is $36 billion, and the target reserve ratio (required reserve ratio) of banks is 12.5%. What is money supply at equilibrium?

c. (7 points) Suppose that the Bank of Canada sells bonds to combat inflation. What is the effect of the sale of bonds on the equilibrium interest rate, the level of investment, and aggregate expenditure and GDP in the short-run? Show graphically. Use the subscript ‘0’ to represent the original equilibrium and ‘1’ to represent subsequent changes.

Answer 1

(a)

In equilibrium,

Required reserve ($B) = Deposit x Reserve ratio = 20 x 10% = 2

Excess reserves ($B) = Deposit - Required reserves = 20 - 2 = 18

Amount of loan ($B) = Excess reserves = 18

(b)

Monetary base (MB) ($B) = Currency in circulation + Reserves = 36 + 2 = 38

Money supply ($B) = MB / Reserve ratio = 38 / 0.125 = 304

(c)

Sale of bonds lowers money supply, shifting money supply curve leftward, increasing interest rate and decreasing quantity of money.

In following graph, MD0 and MS0 are initial money demand and supply curves, intersecting at point A with initial interest rate r0 and quantity of money M0. When MS0 shifts left to MS1, it intersects MD0 at point B with higher interest rate r1 and lower quantity of money M1.

Higher interest rate lowers investment. Decrease in investment decreases aggregate demand, shifting AD curve leftward, decreasing both price level and real GDP in short run.

In following graph, initial equilibrium is at point A where AD0 (aggregate demand) and SRAS0 (short-run aggregate supply) curves intersect with initial equilibrium price level P0 and initial equilibrium real GDP Y0. When aggregate demand decreases, it shifts AD0 leftward to AD1, intersecting SRAS0 at point B with lower price level P0 and lower real GDP Y0.