Assume a hypothetical economy in which the velocity is constant at 2 and real GD
ID: 1195420 • Letter: A
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. Using the equation of exchange, compute the price level in each year. Compute the inflation rate for each year. Explain why inflation varies, even though the money supply rises by $100 each year. If the central bank wanted to keep inflation at zero, what should it have done to the money supply each year? If the central bank wanted to keep inflation at 10% each year, what money supply should it have targeted in each year?
Explanation / Answer
MV = PY. Here M is a measure of the money supply, V its velocity, and nominal GDP is written as the product of the overall price level (P) with real GDP (Y). Substituting values for each year:
First year: 1000*2 = P*4000
P = 2000/4000 = 0.5
Second year: 1100*2 = P*4000
P = 2200/4000 = 0.55
Third year: 1200*2 = P*4000
P = 2400/4000 = 0.6
Fourth year: 1300*2 = P*4000
P = 2600/4000 = 0.65.
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Computing inflation rate assuming first year as base year:
Inflation rate during II year: 0.55 - 0.5 / 0.5 = 10%
Inflation rate during III year: 0.60 - 0.50 / 0.50 = 20%
Inflation rate during IV year: 0.65 - 0.50 / 0.50 = 30%
The inflation varies though the increase is only $100 each year because it is calculated on the base year (first year) so the increase in price is set and compared to the base year.
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To keep the inflation at zero, the central bank should downsize the money supply each year based on the value of the first year.
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The money should have been constantly maintained at $1000 each year, as the velocity and GDP are pegged at 2 and $4000 respectively.
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