Question

Assume that currency (C) is $ 20 billion and reserves (R) are $ 10 billion, the reserve-deposit ratio (rr ) is 0.1, and the currency-deposit ratio (cr) is 0.2. The current price level is P = 120. 1) What is the monetary base? What is the amount of demand deposits? What is the money multiplier? What is the money supply? Show your work. 2) The central bank wishes to increase the money supply by 10% . Calculate the dollar amount of open market operations (i.e., increase in the monetary base) necessary to meet the target. Describe in words how the FOMC would do this

Answer 1

1) Monetary base (B) = C + R

B = $20 billion + $10 billion = $30 billion

2) Demand deposits

First we write the currency-deposit ratio equation:

CR = C/D

0.2 = $20 bilion/D

D*0.2 = $20 billion/D*D

0.2D = $20 billion

0.2D*10 = $20 billion *10

2D = $200 billion

D = $200 billion / 2

D = $100 billion

Which is consistent with the currency-deposit ratio of 0.2 because currency is $ 20 billion and deposits are $ 100 billion.

3) Money multiplier (m)

m = cr + 1/ cr + rr

m = 0.2 + 1/0.2 + 0.1

m = 4

4) Money Supply (M)

M = m x B

M = 4 x $30 billion

M = $120 billion

5) Increase in monetary base for a 10% increase in money supply:

ΔM = ΔR * m

10%ΔM = ΔR * 4

10%/4 = ΔR * 4/4

0.025 = ΔR

ΔR = 2.5%

The FOMC needs to increase banks reserves by 2.5%, in order to increase the money supply by 10%.

The FOMC would do this by buying US Treasury notes in the Open Market. The dollars it would use to buy these notes enter the monetary base in the form of excess reserves, and commercial banks then would use these excess reserves to make loans, and this would ultimately increase the money supply.