Assume a hypothetical economy in which the velocity is constant at 2 and real GD

Question

Assume a hypothetical economy in which the velocity is constant at 2 and real GDP is always at a constant potential of $4,000. Suppose the money supply is $1,000 in the first year, $1,100 in the second year, $1,200 in the third year, and $1,300 in the fourth year.

a. using the equation of exchange, compute the price level in each year

b. compute the inflation rate for each year

c. explain why inflation varies, even though the money supply rises by $100 each year

d. if the central bank wanted to keep the inflation rate at zero, what should it have done to the money supply each year?

e. if the central bank wanted to keep inflation at 10% each year, what money supply should it have targeted in each year?

Explanation / Answer

Before all calculations, let us know the following symbols:

M = Money Supply

V = Velocity of Money

P = Price Level

Y = Real GDP

P * Y = Nominal GDP

(a) The equation of exchange is : M x V = P x Y

P = MV/Y

So, Price in 1st year: P = 1000 x2/4000 = $0.50

  Price in 2nd year: P = 1100 x2/4000 =$0.55

  Price in 3rd year: P = 1200 x2/4000 =$0.60

  Price in 4th year: P = 1300 x2/4000 =$0.65

(b) let 1st year is the base year.

Therefore, inflation is the growth rate in price level

So, inflation in 2nd year : (0.05/0.50) x100 = 10%

inflation in 3rd year : (0.05/0.55) x100 = 9.09%

inflation in 4th year : (0.05/0.60) x100 = 7.69%

(c)   inflation varies, even though the money supply rises by $100 each year, because the amount of increase in money supply is same but growth rate varies.

(d) to keep the inflation rate at zero, growth of money supply should be zero

(e)  if the central bank wanted to keep inflation at 10% each year, it should have targeted 10 % growth in money supply of previous year?

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