The eighteenth century: a marriage not consumated

The making of economics in the eighteenth century was accompanied by enthusiasm for mathematics and some attempts at formalization. Most of the latter seem naive today; they mainly used elementary arithmetic and few went as far as to apply some algebra.

Other contributions made more advanced use of mathematics. In 1772, Paolo Frisi endeavoured to complete Verri’s price formula with an optimization calculation, using differentials and even - barely ten years after their introduction into mathematics - Lagrange multipliers. In France, Achilles-Nicolas Isnard (1781 [2009]) represented the economy as a system of simultaneous equations which, despite some rough simplifica­tions that ensured tractability, prefigures later efforts to account for interdependencies across markets (Van den Berg 2006). Charles-Franςois Bicquilley’s 1804 attempt to formulate a wide-ranging mathematical theory of the economy that could cover a range of aspects - from market price determination to insurance - is unique for its extensive use of probability theory (Crepel 1998). There are even outliers, most prominently Daniel Bernoulli who, as early as 1738, relied on the theory of functions to anticipate what would be later known as expected utility theory and provided a first version of the decreasing marginal utility principle.

The success of all these attempts was, however, limited. One reason is that many of them dealt with circumscribed questions, without developing a comprehensive approach to individual behaviour or market coordination. For all its originality, Bernoulli’s for­malization simply related utility to monetary income, where the latter is first allocated to buy the most necessary things, then the less and less necessary, until the superflu­ous ones; that is, wealth can satisfy a series of hierarchically ordered needs, an idea that others had already expressed at the time (though only verbally). It does not prove decreasing marginal utility for one good only and does not open the way to a general theory of utility; therefore, it cannot constitute the basis of a theory of demand, let alone of market price formation.

Another reason is the imperfect correspondence between economic principles and mathematical symbols or equations. Italian writers’ ratio of the number of buyers to sellers is a clear example of how mathematics had an evocative, illustrative function but did not serve as a guide for building compelling arguments. Even Frisi’s differential cal­culus, in the absence of a theory of economic behaviour backing his calculations, turned out to provide little, if any, economic insight (Tubaro 2002).

Reactions to these attempts were varied, but rarely enthusiastic. Vehement attacks were directed against Frisi’s mathematics, and Verri dropped the mathematical notes from subsequent editions of his book. Bicquilley and Isnard were less overtly criticized but fell rapidly into oblivion; and Bernoulli’s formalization found an echo among mathematicians but, until more than a century later, contributed very little to econo­mists’ debates on utility.