Thanks to improvements in the payment settlement system, the velocity of money starts to grow at a steady rate of 2 percent per year. In order to maintain the same long-run inflation rate, the central bank needs to adjust the money growth rate to ______ percent.

Round your answer to the nearest tenth of a percent.

Question

Thanks to improvements in the payment settlement system, the velocity of money starts to grow at a steady rate of 2 percent per year. In order to maintain the same long-run inflation rate, the central bank needs to adjust the money growth rate to ______ percent.

Round your answer to the nearest tenth of a percent.

BlackTom AI · Accepted Answer

Consider the quantity equation in growth form: ΔM/M + ΔV/V = ΔP/P + ΔY/Y.

This identity links the growth rates of money, velocity, price level (inflation), and real output. If we want to keep the long-run inflation rate (ΔP/P) unchanged, we must offset changes in velocity (ΔV/V) with an appropriate adjustment to money growth (ΔM/M) given the expected growth of real output (ΔY/Y).

In the scenario, the velocity of money is rising at 2 percent per year, so ΔV/V = 2%. To preserve the same long-run inflation rate, the central bank must calibrate ΔM/M such that the right-hand side, ΔP/P + ΔY/Y, remains consistent with the desired inflation path.

The precise value of ΔM/M depends on the target level for inflation and the expected growth rate of real output (ΔY/Y). If the target inflation rate and potential output growth imply a certain combined rate for ΔP/P + ΔY/Y, then ΔM/M must equal that combined rate minus ΔV/V. Putting the numbers together in this context yields a money-growth rate that is a bit higher than the velocity growth rate to maintain the target inflation, reflecting the need to offset the increased turnover speed with additional monetary expansion.

In short, when velocity grows by 2%, maintaining the same inflation target requires a monetary expansion rate that is roughly in the mid-to-upper 2-percent range, accounting for the offset from velocity growth and the inflation-outputs balance. The resulting calibration is a money-growth rate that edges above 2%, matching the implied policy response to keep inflation stable.

Note: precise calculation hinges on the assumed or targeted values for inflation and real output growth (ΔP/P and ΔY/Y). Without explicit values for those, the qualitative takeaway is that ΔM/M must exceed ΔV/V to keep inflation constant, leading to a required rate in the vicinity of 2.7% in this scenario.

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