You are the head of the central bank and you want to maintain a 2.5 percent long-run inflation rate. You are using the quantity theory of money to guide your policy.

If the real GDP per capita growth rate is 1.8 percent, the population grows at an annual rate of 1.0 percent, and velocity is constant, you suggest a money 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 a 2.5 percent long-run inflation rate. You are using the quantity theory of money to guide your policy.

If the real GDP per capita growth rate is 1.8 percent, the population grows at an annual rate of 1.0 percent, and velocity is constant, you suggest a money growth rate of ______ percent.

Round your answer to the nearest tenth of a percent.

BlackTom AI · Accepted Answer

To approach this question, start from the quantity theory of money in growth form: MV = PY, where velocity V is assumed constant. Differentiating with respect to time gives ṁ ≈ ṗ + ẏ − v̇, and with velocity growth v̇ = 0 we obtain γ_M = γ_P + γ_Y, where γ denotes growth rates.

First, determine the growth rate of real GDP (Y). The problem provides real GDP per capita growth at 1.8% and population growth at 1.0%. Real GDP per capita growth plus population growth together imply total real GDP growth: γ_Y = 1.8% + 1.0% = 2.8%.

Next, apply the target long-run inflation rate. The goal is to maintain 2.5% inflation, so γ_P = 2.5%.

Now combine these in the growth form of the quantity equation: γ_M = γ_P + γ_Y = 2.5% + 2.8% = 5.3%.

Finally, round to the nearest tenth of a percent as requested. The money growth rate to target a 2.5% long-run inflation, given the stated growth dynamics and a constant velocity, is 5.3% per year.

If velocity were not constant, the calculation would need to incorporate v̇ (velocity growth), which would modify the relation between money growth and inflation, but under the stated assumption it does not.

So, the required money growth rate is 5.3% under these conditions.

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