Question

Suppose that each 0.1 percentage point increase in equilibrium interest rate induces a $4 billion decrease in real planned investment spending by businesses. In addition, the investment multiplier is equal to 3, and the money multiplier is equal to 4. Furthermore, every $10 billion decrease in the money supply brings about a 0.1 percentage point increase in the equilibrium interest rate. Use this information to answer the following question under the assumption that all other things are equal. If actual GDP is $500 billion and potential GDP is $440 billion, then which of the following is the correct policy for the Fed?

Answer is: Sell $12.5 billion in bonds, but how do you get this answer?

Answer 1

Output gap ($ Billion) = Actual GDP - Potential GDP = 500 - 440 = 60

Since output gap is positive, aggregate demand (AD) has to be reduced to close the gap, which can be done by decreasing money supply.

Since investment multiplier = 3,

Required decrease in investment to lower AD by $60 billion = $60 billion / 3 = $20 billion

A $4 billion decrease in investment means, interest rate falls by 0.1%. Therefore,

$20 billion decrease in investment means, interest rate falls by (0.1 x 20/4)% = 0.5%.

When interest rate increases by 0.1%, money supply decreases by $10 billion. So,

When interest rate increases by 0.5%, money supply decreases by ($10 x 0.5/0.1) billion = $50 billion.

Since money multiplier = 4,

Required open market sale of bonds = Required decrease in money supply / money multiplier = $50 billion / 4

= $12.5 billion

(Note that money supply can be decreased by open market sale of bonds by central bank)