Question

# 2. Suppose that in the U.S., the income velocity of money (V) is constant. Suppose, too,...

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?

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%)

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