Suppose that each $0.1$percentage point increase in the equilibrium interest rate induces a $\backslash (5$billion decrease in real planned investment spending by businesses. In addition, the investment multiplier is equal to $4$, and the money multiplier is equal to $3$. Furthermore, every $\backslash )9$billion decrease in money supply brings about $0.1$-percentage-point increase in the equilibrium interest rate. Use this information to answer the following questions under the assumption that all other things are equal.

a. How much must real planned investment decrease if the Federal Reserve desires to bring about an $\$80$billion decrease in equilibrium real GDP ?

b. How much must the money supply change for the Fed to induce the change in real planned investment calculated in part (a)?

c. What dollar amount of open market operations must the Fed undertake to bring about the money supply change calculated in part (b) ?

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

Formula = Change in Income/ Change in Investment

As multiplier = $4$, desired change in income = $-80$

So, $4$= $-80$/ Change in investment

Hence, change in investment needed = $-80/4=\$20$billion

As $0.1\%$decrease in equilibrium interest rate leads to $\$5$billion increase in real planned investment. So, 0.4% decrease in interest rate will lead to required $\$20$billion dollars decrease in investment

As $0.1\%$change in interest rate is led by $\$9$billion increase in money supply. So, decrease in interest rates needed can be achieved by $\$36$billion decrease in money supply.

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 = $3$, needed money supply change = $36$billion

So, $3=36$/ Monetary policy open market operations amount

Monetary policy OMO amount = $36/3$

Monetary policy open market bonds' purchase = $\$12$billion