Readers of this Review are doubtlessly familiar with the famous equation of exchange, MV=PQ, frequently employed to analyze the price level effects of monetary shocks. One might think the algebraic formulation of the equation is an outgrowth of the 20th century tendency toward mathematical modeling and statistical testing. Indeed, textbooks typically associate the transaction velocity version of the equation with Irving Fisher and the alternative Cambridge cash balance version with A. C. Pigou, two early 20th century proponents of the application of mathematics to economic analysis. The equation, however, is considerably older, as Thomas M. Humphrey demonstrates in "Algebraic Quantity Equations Before Fisher and Pigou."
Humphrey traces the origins and prehistory of the equation in both its variants, showing that Fisher and Pigou were the inheritors of a long tradition. In fact, by 1900 the equation of exchange was over 120 years old and at least nineteen writers in five countries had presented versions of the equation. Certain versions were even more intricate than the equations of Fisher and Pigou. As early as 1771, writers had produced formulas showing that excessive growth of the money stock causes inflation.
Amanda L. Kramer