equation of exchange (MV = PQ)
Picture every coin and banknote in an economy as a worker who can be "spent" again and again over a year. If you add up the total value of everything bought in a year, there are two ways to count it: by how much money there is times how often each unit is spent, or by how many goods were sold times their average price. Both routes must reach the same total — that simple bookkeeping identity is the equation of exchange.
The equation of exchange is written MV = PQ. M is the money supply (how much money exists), V is velocity (how many times, on average, each unit of money is spent in a year), P is the price level, and Q is real output (the quantity of goods and services produced). The left side, MV, is total spending; the right side, PQ, is the money value of everything sold — the same thing measured two ways, so the equation is always true by definition. Rearranged, it says the price level P = MV / Q.
Because it always holds, the equation of exchange is an identity, not a theory — it explains nothing on its own. It becomes the quantity theory of money only when you add assumptions: that velocity V is stable and output Q is near its maximum. Then it predicts that increases in M flow straight into higher P (inflation). Its great value is as a clear framework: it shows inflation can come from more money, faster spending, or fewer goods — and forces you to ask which is moving in any given case.
Suppose an economy has 1,000 dollars of money (M) that each changes hands 5 times a year (V), so total spending is 5,000 dollars. If 500 goods (Q) are sold, the average price (P) must be 5,000 / 500 = 10 dollars. Double M to 2,000 with V and Q unchanged, and P doubles to 20.
MV = PQ: total spending must equal the money value of all sales.
MV = PQ is always true by definition, so it predicts nothing by itself. It only yields the quantity theory once you assume velocity (V) and output (Q) are stable.