Question

Suppose that each $0.1$percentage point decrease in the equilibrium interest rate induces a $\backslash (10$billion increase in real planned investment spending by businesses. In addition, the investment multiplier is equal to $5$, and the money multiplier is equal to $4$. Furthermore, every $\backslash )20$billion increase in money supply brings about $0.1$percentage point reduction 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 increase if the Federal Reserve desires to bring about a $\$100$billion increase in equilibrium real GDP ?

b. How much must he 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) ?

Short answer

Change in investment needed = $\$20billion$

Change in money supply needed = $\$20billion$

Amount of open market operations, bonds bought =$\$20billion$

Step-by-step solution

Investment Multiplier Concept

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

Formula = Change in Income/ Change in Investment

As multiplier = $5$, desired change in income = $100$

So, $5$= $100$/ Change in investment

Hence, change in investment needed =$100/5=\$20$billion

Money Supply, Interest Rate & Investment Elasticity 

As $0.1\%$decrease in equilibrium interest rate leads to $\$10$billion increase in real planned investment. So, 0.2% increase in interest rate will lead to required $\$20$billion dollars increase in investment

As $0.1\%$change in interest rate is led by $\$20$billion change in money supply. So, $0.2\%$increase in interest rates needed can be achieved by $\$40$billion increase in money supply.

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 = $4$, needed money supply change = $\$40$billion

So, $4=40$/ Monetary policy bonds purchase

Monetary policy bonds purchase = $40/4$

Monetary policy bonds' purchase = $\$10$billion