Answer the question below by assuming that the following con

Answer the question below by assuming that the following conditions prevail in the banking system:

- Reserve requirements equal to %10 on demand deposits accounts

- Currency in circulation amount to $40 billion - Savings and Time deposits amount to $400 billion

- Demand deposits amount to $200 billion

- The Banking System is holding $20 billion in excess reserves

a. Calculate the M1 multiplier.

b. Calculate the M2 multiplier.

c. If the Fed purchases $2 billion of securities from the banking system, what would the potential change in the M-1 monetary aggregate be? Why is this a potential change and not a definite change?

Solution

m 1 = 1 + ( C / D ) / [ r r + ( E R / D ) + ( C / D ) ]

Required reserve ratio (rr) = .1

Currency in circulation = $40 billion

Deposits = $200 billion

Excess reserves = $20 billion

m 1 = 1 + ( 40 / 200 ) / ( .1 + ( 20 / 200 ) + ( 40/ 200 ) )

m1=1.5

m 2 =1+(C/D)+(T/D)+(MMF/D)/[rr+(ER/D)+(C/D)]

here MMF = primarily money market mutual fund shares and money market deposit accounts, plus overnight repurchase agreements and overnight Eurodollars is not givven

m2= 1+ (40/200)+(400/200)+(0/200)/[0.1+(20/200)+(40/200)]

m2=3.2

This is a bit higher than m₁ because time deposits and money market funds are not subject to reserve requirements, so they can expand more than checkable deposits because there is less drag on them during the multiple expansion process.

If the Fed purchases $2 billion of securities from the banking system, as a result the checkable deposits of commercial banks are unchanged, but their reserves increases by $2 billlion.

new m1=1.49