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 $4$.

c. The planned investment schedule is such that at a $4$percent rate of interest, investment is $\backslash (1400$billion. At $5$percent, investment is $\backslash )1380$billion.

d. The investment multiplier is $5$.

e. The initial equilibrium level of real GDP is $\backslash (19$trillion.

f. The equilibrium rate of interest is $4$percent.

Now the Fed engages in contractionary monetary policy. It sells $\backslash )2$billion worth of bonds, which reduces the money supply, which in turn raises the market rate of interest by 1 percentage point. Determine how much the money supply must have decreased, and then trace out numerical consequences of the associated increase in interest rates on all other variables mentioned.

Short answer

Bonds sold of $\$2$billion decrease money supply by $\$8$billion, increase interest rate by 1% & decrease investment by $\$20$billion, and reduce income by $ 100 billion

Step-by-step solution

Investment Multiplier Concept

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

$(1400-1380)/(5-4)$. So, $1\%$change in interest rates leads to$\$20$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 =$5x20$= $\$100$billion

Money Multiplier Concept 

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

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

As money multiplier = $4$, bonds sale value = $\$100$billion dollars

So, $4$= Money supply change / $2$

Money supply change = $4x2=\$8$billion dollars