The Equation of Exchange

THE purpose of this paper is to propose a revised form of the equation of exchange -a form which (it is claimed) combines the advantages of both the Fisher equation and the type adopted by the Cambridge school. The main difference between these is, of course, that the former deals with transactions over a period of time, the latter with resources at a moment of time. Fisher's equation is more immediately intelligible but is unable to allow adequately for the fact that the quantities it relates may change within the period under consideration. The Cambridge equations escape this difficulty and are more readily translatable into demand and supply terms; but they are to that extent unrealistic and are not readily susceptible of numerical expression. § I. Two preliminary difficulties must be noticed. First, there is a troublesome ambiguity as to the time of V, the of circulation of money, in Fisher's equation (M V=P ).1 In his numerical illustrations and also in the Appendix devoted to its elucidation he is careful to exhibit it as a rate of turnover (my italics); i.e., it has a time dimension of -I-as any concept should.2 On the other hand in deriving the equation from its V is given a time dimension of o. The matrix is that in any period of time-say a year-the value of the goods exchanged against money is equal to the value of the money exchanged against goods. The money side is then split up into the quantity of money, M, and its velocity of circulation, V-the latter being in this context described as simply the quotient obtained

Ambiguity · Circulation (fluid dynamics) · Differential equation · Dimension (graph theory) · Economics · Expression (computer science) · First-order partial differential equation · Fisher's equation · Integro-differential equation · Mathematical analysis · Mathematical economics · Matrix (chemical analysis) · Moment (physics) · Period (music) · Physics · Pure mathematics · Statistics · Time value of money · Value (mathematics) · Computer Science · Economic theories and models · Economic Theory and Institutions · Economic Theory and Policy · Finance · Mathematics