Question

1. Suppose that the velocity of circulation of money is constant and real GDP is growing at 2 percent a year.

a) To achieve an inflation target of 2 percent a year, at what rate would the central bank (Bank of Canada) grow the quantity of money?

b) At what growth rate of the quantity of money would deflation be created?

Answer 1

Answer

(a)

According to quantity theory of money MV = PY

where M = quantity of money, V = velocity and is constant, P = Price level and Y = Real GDP

Formula :

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

Thus using above formula and quantity equation we have :

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

Velocity is constant => % change in V = 0, % change in P = Inflation rate(If P increases and If P decreases we called it deflation rate) = 2%(target), % change in Y = 2%

=> % change in M + 0 = 2% + 2% = 4%

Hence, the central bank should grow the quantity of money by 4%.

(b)

Now, we want deflation to occur means we want to decrease price level i.e. we want % change in P < 0

So using (a) and above information we have :

% change in M + 0 = % change in P + 2%

=> % change in P = % change in M - 2% < 0 => % change in M < 2%

Hence Deflation will be created for all growth rate of Money < 2%.