Question

The money supply for the United States is approximately $15 trillion, and average real GDP growth is three percent. If velocity decreases from zero to negative two percent, what value of U.S. Treasury Securities should the Fed buy or sell to target two percent inflation if the reserve ratio is ten percent. Report an open market purchase as a positive number, a sale as a negative number, and round to the nearest billion dollars.

Answer 1

According to quantity theory

MV = MY

where M = money supply , V = Velocity , P = Price level and Y = Real GDP

Formula:

% change in (AB) = % change in A + % change in B ------------------------(1)

and % change in (A/B) = % change in A - % change in B

Hence as MV = PY and using (1) we get

% change in (MV) = % change in (PY)

=> % change in M + % change in V = % change in P + % change in Y -------------------(2)

Hence, Given that velocity decreases by 2% => % change in V = -2% and

Average real GDP growth is three percent => % change in Y = 3%

We want inflation rate to be 2% => Inflation rate = % increase in Price level(P) = 2%

Hence, Putting this in (2) we get

% change in M - 2% = 2% + 3%

=> % change in M = 7%.---------------------(3)

Hence In order to  target two percent inflation Money supply should increase by 7%

Hence, Fed should increase Money Supply and as Money Supply = (1/rr)( C + ) assuming Excess reserves = 0 and C= Currency holding = 0

=> Money Supply(M) = (1/rr)R where rr = Required reserve rate = 10% = 0.10 and R = reserves

=> M = (1/0.1)R = 10R

Now Initial M = 15 trillion

=> R = 15 trillion / 10 = 1/5 trillion

From (3) % change in Money supply = 7%

Now New Money supply (M') = 15 trillion + (7/100)*15 trillion

=> M' = 16.05 trillion

Hence 10R' = M' = 16.05 trillion.

Hence, R' = 1.605 trillion

Hence Change in R = 1.605 trillion - 1.5 trillion = (1.605) trillion( = 105 billion)

Hence Reserve should increase by 105 billion.

Hence, As we want reserves to increase and hence Fed should use Open Market Purchase and hence buy securities woth 105 billions.

Hence, Fed should do open market operations = +$105 billions