Money Velocity MV=PY

MV = PY: the quantity equation of money

Few identities in economics are older than the quantity equation of money, M · V = P · Y. Irving Fisher gave it its modern form in 1911, in The Purchasing Power of Money. Read left to right: M is the money supply (currency plus deposits), V is the income velocity of money, meaning how many times each unit changes hands over a year, P is the general price level, and Y is real output, or real GDP.

Solve for velocity and you get V = (P · Y) / M, which is just nominal GDP divided by the money stock. This same equation underpins monetarism (Milton Friedman, 1956). The argument runs like this: when V and Y stay reasonably steady over the long run, faster money growth feeds more or less straight into inflation. That is where Friedman’s line that “inflation is always and everywhere a monetary phenomenon” comes from.

Applications

Economists reach for it when they want to study quantitative easing (QE), the demand for money, or how a given monetary policy regime behaves. The Banco Central do Brasil reports several monetary aggregates: M1 (currency plus demand deposits), M2 (M1 plus savings and private securities), M3 (M2 plus fund quotas) and M4 (M3 plus public securities). Each one carries its own velocity.

FAQ

Is velocity really stable? Not over short horizons. It moves with interest rates, with payment technology like Pix and cards, with confidence, and with crises. The long-run picture is steadier, though QE after 2008 broke the old relationship across the advanced economies.

Why did US velocity collapse after 2008? The Fed pushed M2 up sharply through QE, but the banks parked most of that liquidity as excess reserves rather than lending it out. So M climbed while P · Y failed to keep pace, and V fell as a result.

Does the equation work for crypto? Up to a point. Tokenomics borrows it to model token velocity, but there is no clear “real GDP” sitting behind a token, which makes estimating the numbers in practice quite hard.