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At the Origins of Mathematical Economics: The Economics of A. N. Isnard (1748-1803)

Author(s):Van Den Berg, Richard
Reviewer(s):Porter, Theodore M.

Published by EH.NET (June 2006)


Richard van den Berg, editor, At the Origins of Mathematical Economics: The Economics of A. N. Isnard (1748-1803). New York: Routledge, 2005. xvii + 461 pp. $115 (cloth), ISBN: 0-415-30649-3.

Reviewed for EH.NET by Theodore M. Porter, Department of History, UCLA.

This volume consists primarily of selections from the works of the French engineer and economist A. N. Isnard. Almost unknown in his own time, Isnard acquired a modest reputation retrospectively as a pioneer of mathematical economics. He was admired especially by L?on Walras, and William Jaff? attached great importance to Isnard’s Trait? des richesses as source for the mathematical framework of Walras’s theory of general equilibrium. Van den Berg, a lecturer at Kingston University in the U.K., helps to situate Isnard in relation to the economic thought of his own time and place, in critical engagement with such authors as Turgot, Rousseau, and, above all, Quesnay. However, Van den Berg invokes the modern style of economics as the reason to look back to Isnard, who stands justified before history as an avatar of mathematical economics, a precursor.

Isnard’s best-known work is the Trait? des Richesses (Treatise on Wealth), printed in 1781 at the author’s expense, and now rare. Van den Berg here exhumes Isnard’s other economic writings, many of them virtually unknown in our day and perhaps even in his. We have in this book only a fraction of Isnard’s writings; a complete edition would have run to several volumes. Anyone doing serious research on Isnard would have to consult the works in their entirety. Nevertheless, van den Berg has made a good choice, performing his most valuable service by bringing to the attention of economists and historians Isnard’s lesser-known writings. These include the Social Catechism (1784), which defends human dignity and responsibility against radicals such as La Mettrie and the Baron d’Holbach, while at the same time presenting economic motives as properly linked to moral behavior and to sociability. There are some policy pieces from the years of the French Revolution, including, in March of 1789, a defense of a “single tax” on net revenues of agriculture, industry, and commerce (and not alone, as the physiocrats recommended, on land), and another piece on taxation in 1791. Perhaps the most interesting is his “Reflections on the issue of the assignats” (1790), where he addresses in a general way the advantages and dangers of paper money, with clear reference to issues of immediate importance. Isnard rejected any simple quantity theory, as for example that any issuance of paper money leads inevitably to a proportionate inflation of the currency. He was especially concerned with questions of trust: the state should introduce assignats slowly and responsibly so that the public will not lose confidence in them. But cautious moderation was not the way of the Revolution, and Isnard’s worst fears were soon realized.

What does this book tell us about the sources and the character of Isnard’s economic mathematics? Anglophone as well as francophone scholars now know that French engineering corps — such as Ponts et Chauss?es (responsible for transportation networks) and Mines — cultivated, in the nineteenth century and beyond, a quantitative form of economics linked to the administrative and political challenges faced by these powerful state agencies. Several of these engineers, preeminently Jules Dupuit, pursued the economic aspect of these problems well beyond the demands of immediate practicality. Walras’s links to this tradition are also of interest, since he studied as an external student (i.e. he was not destined for service in the state corps) in the School of Mines. However, he chose not to take up the characteristic problems of French engineering economics such as working out a basis for deciding what transportation projects were economically justified and establishing a rational basis for the tolls.

I began with hopes that this volume might reveal interconnections between engineering and economic quantification from before the French Revolution. Van den Berg presents new research in the archives of the Corps des Ponts et Chauss?es, the Archives Nationales, and French regional archives in the Department of the Rhone to reconstruct the trajectory of Isnard’s career as a Ponts engineer. But the excerpted writings, at least, do not address the economics of public works, and the titles of Isnard’s engineering writings refer to arches and locks, with no indication that economics is at issue. Van den Berg is reticent on the connections, if any. He refers often to Isnard as “the engineer,” seeming to imply that his profession was relevant for his economics. For example: “The engineer’s views on taxation are a consistent development of the central notions of his economic theory” (p. 41); “The surprising Cath?chisme social … must be considered as developing parts of the engineer’s ‘science of man'” (p. 51). But no link is shown between his profession and his economic beliefs or style.

Van den Berg may well suppose that engineers can be expected to rely on mathematics in a way that literary economists would not. However, he does not attend to the history of engineering, and for example Antoine Picon’s authoritative L’Invention de l’ing?nieur moderne: L’Ecole des Ponts et Chauss?es, 1747-1851 is missing from his bibliography, as is the extensive scholarship on French mathematics (and sometimes also on economics) by Ivor Grattan-Guinness. One readily learns from research in the history of mathematics, science, and technology that the creation of the Ecole Polytechnique in the mid-1790s was of huge importance for the formation of engineers. The new polytechnic school, with its highly elitist patterns of recruitment and curricular preoccupation with mathematics, created a new sort of engineer, a type that would be rare outside of France until the mid-nineteenth century. Eighteenth-century French engineering used mathematics in a more sparing and more immediately practical way, and it would be interesting to compare Isnard’s economic quantification with contemporary engineering. For a historian, the question is not only whether mathematics was applied to economics, but also what sort of mathematics and how it was used.

It is necessary, then, to examine the role (and not merely to note the presence) of mathematics in Isnard’s economic writings. My impression is that his mathematics is often not very hospitable to what we might call an economic sensibility. Van den Berg refers (p. 34) to assumptions made for “mathematical convenience,” assumptions Isnard knew to be inaccurate. The formulation by Isnard that is sometimes seen as a precursor of general equilibrium mathematics treats the economy as a bookkeeper might. Costs of production, and hence values, are fixed. Economic actors divide their wares into what they need for themselves and what they will offer in trade, rather than letting this division be a function of the price structure. His solutions are reached arithmetically, with perhaps a rudimentary element of algebra. This is the sort of conception that economists nowadays sometimes associate with engineers, though it is far from clear to me that any of Isnard’s contemporaries thought of the economy this way. In his essay on paper money (assignats), Isnard rejects these radical simplifications. A doubling of the quantity of metal, he says, will not necessarily double the value of wheat in the currency of metal. Instead, a “new order” will establish itself “in offers and bids,” a “new order on which the change in value depends” (p. 296).

Van den Berg’s translations are fairly clear and free of anachronistic terms and concepts. Although he relies often on cognates when a different sort of word would be more accurate (for example, he renders confiance too often as “confidence” rather than as “trust”), the volume is a real translation, whose phraseology is almost always idiomatic, if not arresting. It is convenient to have the French on facing pages for comparison. This is, in short, a useful introduction to a mostly unsung economist, and on an appropriate scale. I don’t know how much more singing about Isnard is required.

Theodore M. Porter teaches history of science in the Department of History, UCLA. His books include Trust in Numbers: The Pursuit of Objectivity in Science and Public Life; Karl Pearson: The Scientific Life in a Statistical Age; and (co-edited with Dorothy Ross), The Cambridge History of Science, Volume VII: Modern Social Sciences.

Subject(s):History of Economic Thought; Methodology
Geographic Area(s):Europe
Time Period(s):18th Century