Question

True or False?

Suppose that the real interest rate is 3 percent. The money supply is currently growing by 7 percent per year and real GDP is growing by 2 percent per year. If the Fed permanently reduces the growth rate of the money supply to 6 percent, the nominal interest rate will fall to 1 percent. (Hint: Since the change in the money growth rate is permanent, it will permanently change the inflation; people will then adjust their expectations of inflation to be consistent with this permanent change.)

Answer 1

FALSE.

As per quantity theory,

Money supply (M) x Velocity (V) = Price level (P) x Real GDP (Y)

Change in M + Change in V = Change in P (Inflation) + Change in Y

Assuming V remains unchanged, Change in V = 0

Change in M = Inflation + Change in Y

Inflation = Change in M - Change in Y

When Money supply grows at 7% & real GDP grows at 2%,

Inflation = 7% - 2% = 5%

Nominal interest rate = Real interest rate + Inflation rate = 3% + 5% = 8%

When Money supply grows at 6% & real GDP grows at 2%,

Inflation = 6% - 2% = 4%

Nominal interest rate = Real interest rate + Inflation rate = 3% + 4% = 7%

Nominal interest rate falls to 7%, that is, it falls by (8% - 7%) = 1%.