You are the head of the central bank and you want to maintain 2.5 percent long-run annual inflation, using the quantity theory of money. If real GDP grows at a rate of 3.0 percent and velocity falls by 1.5 percent per year, you propose a money supply growth rate of _______ percent.

Round your answer to the nearest tenth of a percent.

Question

You are the head of the central bank and you want to maintain 2.5 percent long-run annual inflation, using the quantity theory of money. If real GDP grows at a rate of 3.0 percent and velocity falls by 1.5 percent per year, you propose a money supply growth rate of _______ percent.

Round your answer to the nearest tenth of a percent.

BlackTom AI · Accepted Answer

To determine the required money growth rate using the quantity theory of money, recall the relationship in growth form: 
%ΔM ≈ %ΔP + %ΔY + %ΔV.

Here, the target long-run inflation rate is 2.5%, so %ΔP = 2.5%. The real GDP growth rate is given as 3.0%, so %ΔY = 3.0%. Velocity is stated to fall by 1.5% per year, which means %ΔV = −1.5% (a decline in velocity reduces the needed money growth since money turning over less slowly requires less增加 in money supply to achieve the same nominal spending level).

Plugging these into the formula:
%ΔM = 2.5% + 3.0% + (−1.5%) = 2.5% + 3.0% − 1.5% = 4.0%

Thus, the money supply should grow by about 4.0% per year to maintain 2.5% long-run inflation given the stated real growth and velocity decline.

Note on the provided numerical answer: the given answer (7.0%) does not align with the quantity theory calculation above. The computed requirement using the standard growth form is 4.0%. If there were additional context or a different convention (e.g., rounding rules, alternative model specification, or misinterpretation of velocity change direction), it could yield a different figure, but with the standard formula and the numbers provided, 4.0% is the result.

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