Quantity Theory of Money

Every dollar of spending in the economy is somebody handing over money — so total spending can be counted two ways. Count the goods side: price level times real output ($PY$, nominal GDP). Count the money side: the stock of money times how many times each dollar changed hands ($MV$). Two counts of the same flow must be equal: $MV = PY$, an identity as unarguable as double-entry bookkeeping.

The theory enters with an assumption: if velocity is stable and output is set by real forces, then printing money can only show up in one place — prices. That is the intellectual backbone of "inflation is always and everywhere a monetary phenomenon."

Define velocity as the number of times the average dollar is spent on final output in a year. Then by construction:

As an identity it is true by definition. It becomes a theory of inflation by holding $V$ and $Y$ steady and reading it in growth rates:

— money growth beyond real growth (with stable velocity) becomes inflation, one-for-one.

Relating money supply, velocity and nominal GDP — computing velocity from the other two, or reasoning about money growth and inflation.

The identity is bulletproof; the theory is not: velocity moves — it collapsed during the 2008–2020 QE era, which is why tripling the monetary base produced no proportional inflation, embarrassing simple monetarism. Output is not fixed in recessions either. The theory works best in the long run and at extremes (hyperinflations honor it faithfully); quarter-to-quarter it is a weak forecaster.

The idea runs from David Hume's 1752 essays through Irving Fisher's equation of exchange (1911) — who gave it the MV = PT algebra — to Milton Friedman, whose monetarism made it the battle flag of 20th-century macro and the basis for the money-targeting experiments of 1979–82 under Volcker. Velocity's instability after the 1980s humbled strict monetarism, but the identity still frames every hyperinflation post-mortem (Weimar, Zimbabwe, Venezuela) and every QE debate.