Question

# During 2017, the growth rate in output (real GDP) was 3.2%, and the growth rate in...

During 2017, the growth rate in output (real GDP) was 3.2%, and the growth rate in the money supply (M1) was 5.9%. If velocity was constant, what should the inflation rate have been?

Suppose that we discover that the inflation rate during 2017was 2.9%. What does that tell us about velocity in 2017? Be specific.

Ans.
a) From the Quantity theory of Money,

Nominal Money Supply (M) * Velocity of money (V) = Price level (P) * Real output (Y)

Taking natural log (ln) on both the sides, we get,

lnM + lnV = lnP + lnY

[ln(A*B) = lnA + lnB]

Differentiation of above equation with respect to time t, we get,

dM/dt * 1/M + dV/dt * 1/V = dP/dt * 1/P + dY/dt * 1/Y

=> %Change in M + %Change in V = %Change in P + %Change in Y

We have, %Change in M = 5.9%
% Change in V = 0 (Because velocity is constant)

%Change in P = inflation = ?

%Chnage in Y = 3.2%

=> %Change in P = Inflation Rate = 5.9 - 3.2 = 2.7%

b) If Inflation is 2.9% then,

%Change in V = 5.9 - 3.2 - 2.9 = -0.2%

Thus, the volocity of money decreased by 0.2% in 2017 as compared to the previous period.

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