Question

1. Use the quantity theory of money equation to address the following questions. Use the following as initial values: M = $4 trillion, V = 3, P = 1, Y = $12 trillion. (2 points) MV = PY a. All other things being equal, by how much will nominal GDP expand if the central bank increases the money supply to $4.2 trillion and velocity remains constant? Show your work and explain your answer. b. Reset your values to the initial condition. Suppose that real GDP and velocity do not change when the central bank increases the money supply from $4 trillion to $4.2 trillion. Calculate the rate of inflation that results from the increase in the money supply. Show your work and explain (recall that the rate of inflation is the % change in the price level). c. Reset your values to the initial condition. Suppose that when the central bank changes the supply of money from $4 trillion to $4.2 trillion that real GDP increases from $12 trillion to 12.25 trillion. Calculate the rate of inflation under this scenario if velocity remains constant. Show your work. Compare this rate of inflation to the one you just calculated, and explain.

Answer #1

MV = PY [Where Y: Real GDP and PY: Nominal GDP]

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

(a) Increase in M = ($4.2 trillion / $4 trillion) - 1 = 1.05 - 1 = 0.05 = 5%

5% + 0% = % Change in P (Inflation) + % Change in Y

% Change in Nominal GDP = 5%

(b) Increase in M = ($4.2 trillion / $4 trillion) - 1 = 1.05 - 1 = 0.05 = 5%

5% + 0% = Inflation + 0%

Inflation = 5%

(c) Increase in Y = ($12.25 trillion / $12 trillion) - 1 = 1.0208 - 1 = 0.0208 = 2.08%

5% + 0% = Inflation + 2.08%

Inflation = 5% - 2.08% = 2.92%

In this case, inflation rate is lower than the rate computed in part (b), because in part (b), entire increase in price level was due to an increase in money supply. But in this case output has increased, lowering price level due to higher aggreate supply, decreasing inflation rate.

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