Quantity Theory of Money
Solve the equation of exchange, M × V = P × Q, for money supply, velocity, the price level, or real output from the other three.
With V and Q held fixed, a larger money supply raises the price level — the theory’s inflation channel.
The equation of exchange states M × V = P × Q: money supply times velocity equals the price level times real output, where P × Q is nominal GDP. With M = 1,000, V = 2 and Q = 400, the price level is P = (1,000 × 2) ÷ 400 = 5. Rearrange it to isolate any one of the four variables.
The equation of exchange
The quantity theory of money is built on an identity called the equation of exchange: the total money spent in an economy over a period, money supply (M) multiplied by the velocity of money (V), must equal the total value of what was bought, the price level (P) multiplied by real output (Q). Because P × Q is nominal GDP, the identity says spending equals income — it holds true by definition.
Monetarism turns that identity into a theory by adding an assumption: in the long run, velocity is fairly stable and real output is set by the economy’s productive capacity, not by the money supply. If V and Q barely move, then any sustained increase in M must show up as a higher price level P. That is the quantity theory’s central prediction — money growth in excess of output growth feeds through to inflation.
M = money supply, V = velocity, P = price level, Q = real output. P × Q = nominal GDP. Rearranged: M = P×Q ÷ V, V = P×Q ÷ M, P = M×V ÷ Q, Q = M×V ÷ P.
Worked example
Suppose the money supply is 1,000, velocity is 2, and real output is 400. Solve for the price level.
- 1 Write down the equation. M × V = P × Q. To find the price level, rearrange to P = M × V ÷ Q.
- 2 Compute total spending (M × V). M × V = 1,000 × 2 = 2,000 — the total value of transactions, which equals nominal GDP.
- 3 Divide by real output. P = 2,000 ÷ 400 = 5. The price level is 5.
- 4 Check with nominal GDP. P × Q = 5 × 400 = 2,000 = M × V. ✓ Both sides of the identity match.
The four variables and how to isolate each
Each variable is found by rearranging M × V = P × Q. P × Q is nominal GDP; M × V is total spending.
| Variable | Meaning | Isolate it with |
|---|---|---|
| M — money supply | Quantity of money in circulation. | M = P × Q ÷ V |
| V — velocity | Times each unit of money is spent per period. | V = P × Q ÷ M |
| P — price level | Average price index (e.g. GDP deflator ÷ 100). | P = M × V ÷ Q |
| Q — real output | Real GDP, the quantity of goods and services. | Q = M × V ÷ P |
Reading the results
The equation is an identity; the theory is an assumption. M × V = P × Q is always true because velocity is defined as nominal GDP ÷ money supply. The quantity theory’s predictive claim — that money growth causes inflation — rests on V and Q being stable, which holds better over long horizons than quarter to quarter.
Watch your units. P is a price index, not a dollar amount, so P × Q lands in the same nominal-GDP units as M × V. If velocity comes out implausibly high or low, check that M and P × Q are measured over the same period and in the same currency.