THE QUANTITY THEORY OF MONEY

Print twice the money and, all else equal, prices double. In the equation of exchange M·V = P·Q, with velocity and real output held fixed, the price level rides one-for-one on the money supply — money is neutral. Rendered, not quoted: the identity, the neutrality experiment, and inflation as money growth minus output growth. These are models of an economy, not investment advice.

source Irving Fisher, The Purchasing Power of Money (Macmillan, 1911) — the equation of exchange. econlib full text AMBER · no DOI, historical text

Blue Team · builds & defends
3

The Model

The equation of exchange is an accounting identity: the money that changes hands equals the money value of what is bought.

M · V = P · Q

M money stock · V velocity (times each unit is spent) · P price level · Q real output (transactions). Solve for the price level: P = M·V / Q.

Fisher's classical closure adds two assumptions: V is set by institutions of payment and Q by real productive capacity — both are fixed with respect to M. Then P is proportional to M, and money is a veil over real trade.

5

The Lineage

Money and prices. Fisher 1911 makes money neutral: double M, double P, with real Q untouched (the classical dichotomy).

  • Growth-rate form → inflation = money growth + velocity growth − real output growth.
  • The monetary side of the-is-lm (the LM curve is money-market equilibrium) and the-phillips-curve (inflation expectations anchor on money growth).

Neighbour in THE FOLD: the-is-lm supplies the demand side; here we supply where the price level comes from.

7

The Witness

Re-runs the full selfcheck() against the live engine on load and after any tamper. Green = every law holds to tolerance; red = a planted or real violation was caught.

witness · booting…

The witness verifies the identity balances, that doubling M doubles P, and that the growth-rate identity holds — headless, no canvas needed.

The Machine
4

Data In in ↓

Set the money stock, velocity, and real output. Growth rates feed the inflation identity.

▼
0

The Panel booting

100 · 2.00 = 4.00 · 50
Price level P = MV/Q
4.00
Nominal output PQ
200.0
Neutrality: double M → P
8.00
Inflation π = gM+gV−gQ forecast·AMBER
2.0%
▼
8

Data Out out ↓

Proven result: with V and Q fixed, the price level is exactly proportional to M — 2M ⇒ 2P, and real output Q is unchanged. Money is neutral in the long run.

—
Red Team · attacks & breaks
1

The Adversary wall

The neutrality result is only as good as its assumptions. Fisher fixes V and Q by fiat.

Real economies violate them: velocity V is not constant (it collapsed in 2008–09 and 2020); money growth can raise real output in the short run when prices and wages are sticky (the whole point of the-is-lm / the-phillips-curve). "Ceteris paribus" hides the transmission lags.

AMBER Rational agents, perfect price flexibility, exogenous V and Q — idealizations. Economics is not physics; MV=PQ is an identity, but the neutrality read of it is a modelling assumption.

2

The Graveyard

  • "Money growth instantly and only raises prices." → In the short run, with sticky prices, it moves output too; neutrality is a long-run claim.
  • "Velocity V is a constant of nature." → V is behavioural and shifts with interest rates, payments tech, and crises.
  • "MV=PQ predicts inflation." → As an identity it always balances; prediction needs a theory of V and Q, marked AMBER.
  • "Double M ⇒ double real output." → No — the classical dichotomy leaves real Q unchanged; only P doubles.
6

The Tamper

Planted void (disclosed): force the price level to scale with M² instead of M. Money stops being neutral — doubling M would quadruple P, and the MV=PQ identity breaks. The Witness (7) catches it live.

This is the same flag selfcheck() sets and clears internally to prove the neutrality test has teeth.