Why do some countries have runaway inflation while others have little? Connect the money supply with real output and inflation.
Key idea
The equation of exchange: $$MV = PY$$ $M$ is the money supply, $V$ is velocity (how many times a dollar is spent on final output in a year), $P$ is the price level and $Y$ is real output, so $PY$ is nominal GDP. In growth rates: $$\%\Delta M + \%\Delta V \approx \%\Delta P + \%\Delta Y$$ If velocity is stable, money growing faster than real output raises prices in the long run.
Why it works
Velocity is defined as $V = \dfrac{PY}{M}$, so $MV = PY$ is true by definition. It becomes a theory when we add an assumption: in the long run, real output is set by resources and technology (LRAS), not by money, and velocity changes slowly. Then extra money cannot buy more real output; it bids up prices. Economists broadly agree that sustained, rapid money growth causes high inflation, and that money is neutral in the long run. How stable velocity is, and so how tightly money growth tracks inflation from year to year, is debated: in some decades velocity has swung a lot.
Worked examples
Worked example: Finding velocity
The money supply is \$5,000 billion and nominal GDP is \$20,000 billion. Find velocity.
- $V = \dfrac{PY}{M} = \dfrac{20{,}000}{5{,}000} = 4$.
- Each dollar is spent on final goods and services about 4 times a year.
Answer: 4
Worked example: Growth rates
Money grows 8% a year, velocity is steady, and real GDP grows 3% a year. About what is inflation?
- $8 + 0 \approx \%\Delta P + 3$.
- Inflation $\approx 8\% - 3\% = 5\%$.
Answer: About 5%
Common mistake
Thinking printing more money makes a country richer in the long run. It raises prices instead, because real output depends on resources and technology. Check: in the long run, which side of $MV = PY$ can money change? With $V$ and $Y$ fixed, only $P$.
See it with real data: M2 growth and CPI inflation on the Economic Data page. Over short periods the link is loose, which is part of the debate about velocity.