Question

2. Suppose that in the U.S., the income velocity of money (V) is constant. Suppose, too, that every year, real GDP grows by 2.5 percent (%∆Y/year = 0.025) and the supply of money grows by 10 percent (%∆M/year = 0.10).

a. According to the Quantity Theory of Money, what would be the growth rate of nominal GDP = P×Y? Hint: %∆(X×Y) = %∆X + %∆Y.

b. In that case, what would be the inflation rate (i.e. %∆P/year)?

c. If the central bank wants the inflation rate to be 0%, what money supply growth rate (i.e. - %∆M per year) should it set?

Answer 1

As it is given that,

velocity of money (V) is constant, So %∆V = 0.

Real GDP growth (%∆Y) = 0.025 and Money growth (%∆M) = 0.10.

a) According to the Quantity theory of Money,

MV = PY

%∆M + % ∆V = % ∆P + %∆Y

%∆M + %∆V = growth rate of nominal GDP --- (1)

[ Because Nominal GDP = P*Y, so growth rate of nominal GDP = % ∆P + %∆Y ]

Put values in (1), we get

10% + 0% = growth rate of nominal GDP

growth rate of nominal GDP = 10% (0.1)

b) In this case the inflation rate i.e. %∆P per year is equal to 7.5% 0r 0.075.

Explanation:

growth rate of nominal GDP = % ∆P + %∆Y

Put values, we get

10% = %∆P + 2.5%

% ∆P ( inflation) = 10% -2.5% = 7.5%

c) If central bank wants to the inflation rate to 0%, then it should set money supply growth rate equal to 2.5%.

%∆M + % ∆V = % ∆P + %∆Y

%∆M + 0% = 0% + 2.5%

%∆M =2.5%

( it should reduce money supply by 10-2.5% = 7.5%)