Question

a. Suppose the Fed decides to target the M1 money supply again and that $4.25 trillion is its target. If the required reserve ratio is 0.10, the currency ratio is 0.80 and the excess reserve ratio is 0.30, how large should the Fed make the monetary base?

b. Find the level of required reserves and excess reserves for this economy.

Answer 1

a.

Money supply= Monetary base x Money multiplier

Target money supply= $4.25 trillion

Required reserve= r= 0.10

Currency deposit ratio= c= 0.80

Excess reserve= e= 0.30

Money multiplier= (1+c)/(c+r+e)= 1.80/1.20= 1.5

4.25 trillion = Monetary base x 1.5

Monetary base= 4.25 trillion / 1.5

Monetary base= 2.83 trillion

Fed should make monetary base of $2.83 trillion

b.

For the level of required reserve and excess reserve, find deposit:

Let deposit be y

Monetary base= Currency + Reserve

Monetary base= c(y)+r(y)+e(y)= 0.80y+0.10y+0.30y= 1.20y

$2.83 trillion / 1.20 = y

y= $1.525 trillion   

Amount of required reserve= $1.525 trillion x (r)= $1.525 trillion x 0.10= $0.1525 trillion

Amount of excess reserve= $1.525 trillion x c= $1.525 trillion x 0.30= $0.4575 trillion