Question

You have learned that money velocity is rather stable. Assume for simplicity that the velocity is constant (the quantity theory of money). Explain how the growth in the money supply and inflation are related.

Answer 1

According to quantity equation we have :

MV = PY where M = Money supply, V = velocity of money and is constant(assumed), P = Price level and Y = Real Output which we consider to be dependent on factors of production and hence we consider it to be independent of Money supply(like in a long run where all inputs are fully employed).

So If M changes Y will remain same and as V is constant and hence V will also remain same.

Formula :

% change in (AB) = % change in A + % change in B

So, MV = PY => % change in (MV) = % change in (PY)

=> % change in M + % change in V = % change in P + % change in Y.

As discussed above, If M changes Y will remain same and as V is constant and hence V will also remain same

=> % change in V = 0 and % change in Y = 0

=> % change in M + 0 = % change in P + 0

=> % change in M = % change in P and as % change in P = Inflation rate(note negative inflation is known as deflation)

=> Growth rate of money supply = Inflation rate.

Hence, Growth rate of money supply is equal to inflation rate.