Question

The money supply for the United States is approximately $15 trillion. What value of U.S. Treasury debt should the Fed buy or sell in order to reduce the money supply by 5% if the reserve ratio is 10%? Report an open market purchase as a positive number, an open market sale as a negative number, and round to the nearest whole billion dollars.

Answer 1

Formula:

In Simple terms when there is no excess reserves and People holds no currency

Money Supply(Ms) = (1/rr)(Monetary Base) where Monetary Base = C + R where C = amount of currency people holds = 0 and R = Reserves and rr = required reserve ratio = 0.10

=> Ms = (1/0.10)(C + R) =10( 0 + R ) = 10R

Given Money supply is 15 trillion

Hence Ms = 15 trillion = 10R => R = 1.5 trillion

Now we want Money supply to decrease by 5%. Hence New money supply = 15 trillion - (5/100)* 15 trillion

=> New money supply(Ms') = 14.25 trillion.

Hence Ms' = 10R'

=> 14.25 trillion = 10R'

=> R' = 1.425 trillion

Hence Change in Reserves Required = 1.425 trillion - 1.5 trillion = -0.075 trillion ( = - 75 billion)

Hence In order to reduce money supply by 5% Reserves should change by -75 billion

Hence In order to reduce reserves and hence Fed should sell debts and hence Use open market Sale and hence Fed has to sell $75 billion of US debts.

Hence Open Market Operation = -$75 billion

Hence Open Market Operation = -$75 billion