If the money supply is growing at 8 the real rate of growth

If the money supply is growing at 8%, the real rate of growth of GDP is 2%, and financial innovations are reducing the demand for money by 0.5% per year, what should the long-run inflation rate be?

Solution

According to the quantity theory of money:

Money supply (M) x Velocity of money (V) = Price level (P) x Real GDP (Y)

So,

Change in M + Change in V = Change in P (Inflation rate) + Change in Y

Here,

8% - 0.5%** = Inflation Rate + 2%

Inflation rate = (8 - 0.5 - 2)% = 5.5%

** If demand for money reduces by 0.5%, it means that transacitons velocity of money reduces by the same percentage. So, change in V = - 0.5%