Quantity Equations: Early History

Abstract

The idea that there exists a relationship between the available quantity of money and the general level of prices was translated into mathematical form in the seventeenth century by John Briscoe in his Discourse on the Late Funds … of 1694 where it was expressed as a relation between the stock of precious metals and the value of commodities exchanged. There was, however, no recognition of the role of the velocity of circulation in Briscoe’s equation. There followed an equation by Henry Lloyd in 1771 in his Essay on the Theory of Money which similarly failed to incorporate any velocity term; perhaps betraying the mercantilist element in their thought. The inclusion of the latter had to await the work of early nineteenth-century writers, and came with the appearance of Klaus Kröncke’s Das Steuerwesen nach seiner Natur und seinen Wirtkungen untersucht (1804), Joseph Lang’s Grundlinien der politischen Arithmetik (1811), Luca Samuele Cagnazzi’s Elementi di Economia Politica (1813), and Samuel Turner’s Letter Addressed to the Right Hon. Robert Peel (1819). In 1840 the probabilist John Lubbock produced what is almost certainly the most sophisticated early version of the quantity equation in his anonymous On Currency where the possibility of differences in the velocity of circulation of different components of the available quantity of money is admitted. This, of course, is the same as recognising a problem as to the definition of the M in modern versions of the equation; something neglected in earlier versions. One might notice the comparatively unsophisticated uses to which these equations were put by their architects, the more so given the sophisticated understanding of monetary theory that existed at the time and which gained expression in the Bullionist controversy and the Banking school–Currency school debates. In this instance, the laws of algebra and those of economics still, it would seem, remained far apart.