Question

Assume that the following conditions exist :

a. All banks are fully loaned up - there are no excess reserves, and desired excess reserves are always zero.

b. The money multiplier is $3$.

c. The planned investment schedule is such that at a $6$percent rate of interest, the investment is $\backslash (1200$billion; at 5 percent, investment is $\backslash )1225$billion

d. The investment multiplier is $3$.

e. The initial equilibrium level of real GDP is $\backslash (18$trillion.

f. The equilibrium rate of interest is $6$percent.

Now the Fed engages in expansionary monetary policy. It buys $\backslash )1$billion worth of bonds, which increases the money supply, which in turn lowers the market rate of interest by $1$percentage point. Determine how much money supply must have increased, and then trace out the numerical consequences of the associated reduction in interest rates on all the other variables mentioned.

Short answer

Bonds bought of $\$1$ billion Increase inmoney supply by $\$3$billion, decrease interest rate by $1\%\hspace{0.17em}$& increases investmentby $\$25$billion, and raisesincome by $\$75$ billion

Step-by-step solution

Investment Multiplier 

Change in investment due to change in interest rates can be calculated by =

$(1225-1200)/(6-5)$. So, $1\%$change in interest rates leads to $\$25$billion change in investment.

Investment multiplier shows multiple times increase in income due to change in income.

Formula = Change in Income/ Change in Investment

So, change in Income =$3x25=\$75$ billion

Money Multiplier Concept 

Money multiplier shows the multiple times increase in money supply due to change in government monetary policy (FOMC bonds buying here).

Money Multiplier = Money supply change / Monetary policy change (bonds' purchase)

As money multiplier = $3$, bonds purchase value = $\$1$billion

So, $3$= Money supply change /$1$

Money supply change = $3x1=\$3$billion dollars