Quantity Theory of Money
What is Quantity Theory of Money?
The quantity theory of money states that the general price level is directly proportional to the money supply, expressed by the equation MV = PQ.
It is expressed by the equation MV = PQ, where money supply times velocity equals price level times output. The theory assumes velocity and output are stable in the long run, so changes in money supply primarily affect prices, not real output.
Quantity Theory of Money: a worked example
Start with a money supply of M = $800 billion and velocity of V = 6. Nominal output PQ equals 800 x 6 = $4,800 billion. If real output Q is $4,000 billion measured in base year prices, the price level is P = 4,800 / 4,000 = 1.20. Now suppose the money supply grows 9% while velocity holds steady and real output grows 3%. The growth rate version of the equation, %change M + %change V = %change P + %change Q, gives 9% + 0% = %change P + 3%, so inflation runs at roughly 6%. Holding money growth to 3% instead would deliver rough price stability, which is the policy conclusion monetarists draw from the identity.
The mistake students make with quantity theory of money
Q in MV = PQ is real output, not nominal GDP, and substituting nominal GDP for Q counts the price level twice. Nominal GDP is already the product P x Q, so a problem that hands you nominal GDP along with velocity is asking for M, not for Q. The other overreach is treating the equation as proof that money growth is always inflationary. MV = PQ is an identity by construction, and it becomes a theory of inflation only once you assume velocity is stable and output sits at its long run level.
Quantity Theory of Money questions
What does MV = PQ mean?
The equation says money supply times velocity equals the price level times real output. M is the quantity of money, V is how many times the average dollar is spent on final goods in a year, P is the price level, and Q is real output. The right side is nominal GDP, so the equation states that total spending on final goods equals the value of what was sold.
How do you calculate the velocity of money?
Velocity equals nominal GDP divided by the money supply, or V = PQ / M. With nominal output of $4,800 billion and a money supply of $800 billion, velocity is 4,800 / 800 = 6, meaning the average dollar changes hands six times a year buying final goods. Velocity is never observed directly, it is backed out from nominal GDP and the money supply, which is why the equation always balances.
Does the quantity theory of money hold in the short run?
The quantity theory performs best over long horizons. Velocity can swing in the short run when people change how much cash they keep on hand, and output can move when the economy sits below full employment, so extra money may raise real output rather than only prices. Over long stretches output is set by resources and technology, so sustained money growth above output growth shows up mainly as inflation.
Formula / Example
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