Which economic theory links money supply growth to inflation in the long run?

The quantity theory of money links sustained money-supply growth to inflation in the long run.

Its basic relationship is commonly expressed as MV = PQ: money supply multiplied by velocity equals the price level multiplied by real output. If velocity and real output are relatively stable, faster growth in the money supply tends to produce a higher price level. The theory therefore concerns long-run monetary relationships rather than claiming that every short-run price movement is caused by money.

The idea has roots in sixteenth-century debates and was developed by economists including David Hume, Irving Fisher, Alfred Marshall, and Milton Friedman. Keynes accepted a long-run version but argued that velocity, output, and money demand could vary substantially in the short run. Modern central banks generally target interest rates and inflation rather than a fixed money-growth rule, because the relationship between monetary aggregates and prices can be unstable.