How to Calculate the Velocity of Money (MV = PQ)
Velocity of money equals nominal GDP divided by the money supply: V = (P × Q) ÷ M, from the quantity theory equation MV = PQ.
Formula
M × V = P × Q (quantity theory of money), so V = (P × Q) ÷ M = nominal GDP ÷ money supply
Steps
- 1Find nominal GDP. P × Q — the price level times real output, i.e., GDP in current dollars.
- 2Find the money supply. Usually M1 or M2, as given in the problem.
- 3Divide. V = nominal GDP ÷ M — how many times the average dollar is spent on final goods per year.
Worked example
If nominal GDP is $20 trillion and the money supply is $4 trillion, V = 20 ÷ 4 = 5: the average dollar changes hands five times a year.
Frequently asked questions
What does the quantity theory of money predict?
If V and Q are stable, MV = PQ implies that growth in the money supply translates into proportional growth in the price level — the monetarist case that inflation is a monetary phenomenon in the long run.
Can you rearrange MV = PQ for any variable?
Yes — given any three of M, V, P, and Q you can solve for the fourth. For example, P = MV ÷ Q gives the price level.
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