Quantity Theory of Money explains a relationship between the quantity of money and the price level. In its simple form, more money leads to proportionately higher prices if velocity and real output remain unchanged. Those conditions separate a useful explanation from the misleading rule that more money always means an equally large price rise.
In our market, the same monetary unit can be used repeatedly during a period. The relationship is written M × V = P × Y: M is money quantity, V its velocity, P the price level and Y the real volume of goods and services produced. P times Y is their value at current prices. If we define velocity as V = PY/M, the equation is an accounting identity: both sides must agree. It does not tell us which variable caused the others to change. This version concerns final production, not every transfer or trade in existing assets. For example, we do not add the value of flour used to bake a loaf again on top of the full price of the loaf sold. [3]
To infer what prices will do, we must specify how people and producers behave. The International Monetary Fund (IMF) explanation assumes relatively stable V. In their 2010 paper, economists Bennett T. McCallum and Edward Nelson discuss a long-run proportional price response to a money-stock change originating outside the model, with the relevant other conditions held unchanged. This is a conditional theoretical relationship, not a forecast from every observed monetary increase; the authors do not speak for the institution’s entire policy either. If V or Y changes, the price outcome can differ. The equation itself makes neither variable stable. [1] [2]
Take our own small model: M = 100, V = 2 and Y = 100 give P = 2. If M rises to 110 with everything else unchanged, P becomes 2.2, a rise of 10%. If Y also rises to 110 alongside money, P stays at 2. With Y = 100, a fall in V to 20/11 can preserve that price level too. These are alternative assumptions, not three simultaneous predictions. The second case resembles a market receiving more goods as well; the third, people holding relatively more money and using it less for purchases. [3]
Keep V unchanged and let money grow by 10% and real output by 4%. The exact price change in this model is (1.10/1.04 − 1) × 100 ≈ 5.77%, not exactly 6%. We divide the new monetary amount by the new output volume, so simply subtracting ordinary percentages is insufficient. The calculation 10 − 4 = 6 is an approximation used for small changes. The discrepancy matters more with larger movements. An exact expression uses ratios of growth factors; for readers using advanced mathematics, the relationship can be added exactly in logarithmic changes, not ordinary percentage changes. [3]
Velocity is not a universal constant that can be attached to any chart. The economic database FRED calculates the US M2V series from nominal gross domestic product (GDP) and the average M2 stock. Nominal GDP values the final goods and services produced in the economy at the prices of the period. You cannot use this velocity with the monetary base instead of M2: Monetary Base covers different money from Broad Money, a wider grouping of currency, eligible deposits and other liquid instruments. Currency, period and annualisation must also match. Always read Velocity of Money alongside its methodology. A statistical redefinition can change calculated velocity even when people’s purchasing behaviour has not changed at all. [4]
A business with idle machinery and the ability to hire workers may meet some extra demand by producing more. St. Louis Fed uses this distinction to explain short and long horizons: Y may initially rise, whereas with capacity fully utilised, extra spending more readily feeds into P. V may change too. This explanation does not promise an exact path next month or a date by which the economy will adjust. Long-run monetary neutrality in certain models means that changing money quantity alone does not permanently raise real output; it does not imply a painless transition. [3]
The Bank of England, the UK’s central bank, explains that a commercial bank usually creates a new deposit when it makes a loan. Repayment of principal, the loan amount still owed excluding interest, reduces money created in this way. The stock M can therefore respond to credit demand and economic activity, rather than merely determine their direction. Observing money and prices rising together does not by itself establish the cause. Here, reserves mean banks’ account balances at the central bank. Customer deposits are amounts a bank owes its customers. These are different things, and there is no mechanical fixed multiple automatically turning each increase in reserve balances into a set amount of loans. When applying the theory, ask where the monetary change comes from as well. [5]
Bitcoin has predetermined rules for creating new bitcoin units (BTC) and a limit of roughly 21 million BTC. This matters for supply, but does not make demand constant. In a hypothetical economy pricing its production in BTC, P would describe goods prices in bitcoin, not automatically the dollar price of a bitcoin. Limited supply alone determines neither V, Y nor BTC/USD. An exchange-rate estimate would need a defined market, demand for holding BTC and other assumptions. Purchasing Power means what your money can buy. The equation alone does not predict how it will change or guarantee that it will rise. [6]
For the clearest picture, read this entry together with Velocity of Money, Monetary Base, Broad Money, Purchasing Power. The reverse links also lead from Velocity of Money.