Question

. Based on the quantity theory of money, write the expression for the long-run rate of inflation. Be sure to apply the growth rate rules in deriving your answer.

Answer 1

Quantity equation is given by:

MV = PY

where M = money supply

P = price level

V = velocity of money

Y = Real GDP

According to quantity theory of money Velocity is constant and as Real GDP depends on factors of production and hence in the long run Real GDP is assumed to be constant because in a Long run factors are fully employed and because of this economy is always at its full employment level and Real GDP = Potential GDP(or full employment output) and is constant.

Mathematically:

Growth rule:

Growth rate of (XY) = Growth rate of (X) + Growth rate of (Y)

As MV = PY

=> Growth rate of (MV) = Growth rate of (PY)

=> Growth rate of (M) + Growth rate of (V) = Growth rate of (P) + Growth rate of (P) -----------------------------------(2)

According to quantity equation discussed above Velocity(V) is constant and Real GDP(Y) is constant in the long run

=> Growth rate of (V) = 0 and Growth rate of (Y) = 0

So (2) becomes

Growth rate of (M) + 0 = Growth rate of (P) + 0

=> Growth rate of (P) = Growth rate of money supply

As growth rate of Price level is also known as Inflation rate

=> Growth rate of (P) = = Rate of Inflation = Growth rate of money supply

Hence, Long run rate of inflation = Growth rate of money supply