Inflation Simulator: The Quantity Theory of Money, MV=PQ

The equation behind the price level

The quantity theory of money ties the money supply to prices through a simple accounting identity, the equation of exchange: the total money in circulation times how often each unit changes hands must equal total spending, which is also total nominal output.

M * V = P * Q

M = money supply
V = velocity of money  (how many times a unit of currency is spent per period)
P = price level
Q = real output (quantity of goods & services)

Rearranged, P = MV/Q: for a given amount of real output Q, if velocity V is roughly stable, prices P move proportionally with the money supply M. This is the core monetarist claim — "inflation is always and everywhere a monetary phenomenon," in Milton Friedman's phrase — and it holds well as a long-run, average relationship even though V and Q both shift in the short run for reasons that have nothing to do with the money supply.

From the identity to hyperinflation

The equation becomes dangerous when a government finances spending by having the central bank print money rather than borrowing or taxing — monetising the deficit. If M grows faster than real output Q, and V does not fall to compensate, P must rise. In moderate cases this produces ordinary inflation of a few percent; in extreme cases (Weimar Germany 1923, Zimbabwe 2008, Venezuela in the 2010s) it produces hyperinflation, conventionally defined as prices rising more than 50% in a single month. Hyperinflation is self-reinforcing: as money loses value, people spend it faster rather than holding it (velocity V rises), which by the same equation pushes prices up further even without any additional printing, and the government's response — printing yet more money to cover the same real spending — closes a vicious circle.

The Fisher equation: real vs nominal

Inflation also drives a wedge between the nominal interest rate a lender is quoted and the real return they actually get after prices rise, captured by the Fisher equation:

(1 + i) = (1 + r)(1 + pi)          exact form
i  ~=  r + pi                       common approximation, small pi

i  = nominal interest rate
r  = real interest rate
pi = expected inflation rate

Central banks that target inflation are effectively trying to hold expected π stable so that r — the return that actually determines saving and investment decisions — is predictable. When inflation is volatile or expectations become unanchored, lenders demand a larger inflation premium, nominal rates climb, and the economy's ability to plan long-term contracts (mortgages, wages, pensions) degrades.

The Phillips curve trade-off

Central bank policy usually runs into the Phillips curve, the empirical (and short-run) inverse relationship between inflation and unemployment: tightening money supply growth to cool inflation tends to slow the economy and raise unemployment, while looser policy that lowers unemployment tends to push inflation up. The trade-off is not fixed — it shifts with inflation expectations, and in the long run most economists hold that the curve is roughly vertical (unemployment converges to a "natural rate" independent of the average inflation rate) — but in the short run, deciding how quickly to squeeze money-supply growth back down after a period of high inflation is exactly a Phillips-curve trade-off between inflation and employment pain.

What a central bank actually controls

A central bank does not set P directly; it influences M (through interest rates, reserve requirements and asset purchases) and, indirectly, expectations of future π, which feed back into current wage and price setting. The lag between a policy change and its effect on inflation is long and variable — often cited as 12 to 24 months — which is why central banks act on forecasts of where M, V and Q are heading rather than waiting to see today's inflation print before adjusting policy.

Frequently asked questions

Try it live

Everything above runs in your browser — open Inflation Simulator and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.