How to Use the Equation of Exchange
The equation of exchange states that the money supply times velocity equals the price level times real output: M × V = P × Q.
The Equation of Exchange formula
Calculator
Enter M, V and real output for the level form, plus growth rates to get inflation from the growth form.
M1 or M2, whichever the question hands you.
How many times the average dollar is spent on final goods in a year.
Output at base-year prices. Nominal GDP divided by Q gives the price level.
Used only by the growth form at the bottom.
The quantity theory assumes velocity is stable, which means 0 here.
Real GDP growth. It absorbs part of the money growth before prices move.
$4 trillion of money turning over 5 times a year buys $20 trillion of final output, which is P times Q.
- Price level (P)
- 1.11
- Price index (P × 100)
- 111
- Inflation from the growth form
- 4%
- Price change reading
- Inflation
Nominal GDP divided by real output gives P of 1.11, so prices sit 11.1% away from the base year.
The same price level written the way an index is quoted, with the base year at 100.
Money growth of 6% plus velocity growth of 0% minus output growth of 2% leaves 4% for prices.
How to calculate Equation of Exchange, step by step
- 1Label the four terms. M is the money supply, V is velocity, P is the price level, and Q is real output.
- 2Recognize nominal GDP. The right side, P × Q, is simply nominal GDP, which is why the relationship holds as an identity.
- 3Solve for the missing term. Divide both sides by whatever multiplies the unknown, for example P = (M × V) ÷ Q.
- 4Switch to the growth form for rates. Percentage changes add up: %ΔM + %ΔV ≈ %ΔP + %ΔQ, which turns money growth questions into inflation answers.
Worked example: Equation of Exchange
With a money supply of $4 trillion and velocity of 5, nominal GDP = M × V = $20 trillion. If real output is $18 trillion, then P = 20 ÷ 18 ≈ 1.11, a price index of about 111. In growth terms, if M rises 6% while V holds steady and real output grows 2%, inflation ≈ 6% + 0% − 2% = 4%.
Equation of Exchange questions
Is the equation of exchange the same as the quantity theory of money?
No. The equation is an identity that always holds, while the quantity theory adds the assumption that V and Q are stable, which turns money growth directly into inflation.
How do you get velocity out of it?
Rearrange to V = (P × Q) ÷ M, that is nominal GDP divided by the money supply.
What does it predict about money growth in the long run?
With velocity and real output unchanged, a given percentage rise in M raises the price level by that same percentage and leaves real output alone.
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