Consider a financial crisis where people stop spending money and hence velocity falls. In particular, suppose velocity falls by a factor of 1/2, i.e., . Suppose potential GDP is growing at 2% per year. If the central bank wants 2% inflation in the long run, by how much should it expand the money supply in this financial crisis?

Question

Consider a financial crisis where people stop spending money and hence velocity falls. In particular, suppose velocity falls by a factor of 1/2, i.e.,  . Suppose potential GDP is growing at 2% per year. If the central bank wants 2% inflation in the long run, by how much should it expand the money supply in this financial crisis?

BlackTom AI · Accepted Answer

We start from the most basic relationship that ties money, velocity, and nominal output: the quantity equation MV = PY. In growth terms, the growth rate of M plus the growth rate of V equals the growth rate of nominal output (which is P times Y).

Step 1: Identify the target nominal growth. If potential GDP (Y) is growing at 2% per year and the central bank aims for 2% inflation in the long run, then nominal GDP (P·Y) must grow by approximately 2% + 2% = 4% per year. This is the desired growth rate of nominal output in the long run.

Step 2: account for the fall in velocity. The problem states velocity falls by a factor of 1/2, i.e., V is reduced by 50%. This corresponds to a change in velocity growth rate, ΔV, of −50% in the relevant period. In growth terms, we use %ΔV = −50%.

Step 3: apply the quantity equation in growth form. We need %ΔM + %ΔV ≈ %Δ(PY) = 4%. Substituting %ΔV = −50%, we get %ΔM − 50% ≈ 4%.

Step 4: solve for %ΔM. Rearranging gives %ΔM ≈ 4% + 50% = 54%.

Conclusion (numerical result): To achieve a 2% inflation long run target given a 50% drop in velocity and 2% potential GDP growth, the central bank should expand the money supply by about 54% in the crisis period. (Thus the required monetary expansion is 54%.)

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