**Nicolas-François Canard** was a French mathematician, philosopher and economist. He was one of the pioneers of applying mathematics to economic problems.

- One of the other teachers at the Lycée de Moulins was to have a significant influence on Canard's life.
- This was Joseph Lakanal (1762-1845), the teacher of philosophy, who, like Canard, was in the Fathers of Christian Doctrine.
- Canard, renouncing his ecclesiastical status, took the oath.
- The discussions between members of the Jacobin Club clearly influenced Canard's interests.
- In April 1796 Canard was appointed as professor of mathematics at the École Centrale de Moulins.
- Canard was dismissed from his position of professor of mathematics, having been accused of being a royalist.
- One of his colleagues was appointed to teach mathematics at the École while, after a time, Canard was again allowed to teach at the École Centrale de Moulins, but this time general grammar rather than mathematics.
- In December 1802, the École Centrale de l'Allier was combined with the Lycée de Moulins and, following this change, Canard was appointed as professor of mathematics in March 1803.
- This appointment was carried out by a committee chaired by Jean-Baptiste Delambre and Canard was preferred by the committee to his colleague Noël Baudeux.
- Canard's most important contributions were on mathematical economics where he attempted to use his mathematical skills to attack economic problems such as taxation, supply and demand, pricing and value.
- The first of these was written as consequence of a winning submission Canard made to a prize competition proposed by the French National Institute of Sciences and Arts.
- The topic for the competition was taxation, with the specific question being: "Est-il vrai que, dans un pays agricole, toute espèce d'impôt retombe en dernier terme sur les propriétaires fonciers, et si l'on se décide par l'affirmative, les contributions indirectes retombent-elles sur ces mêmes propriétaires avec une surcharge?" Ⓣ(Is it true that in an agricultural country, any kind of tax falls last term on landowners, and if it is decided in the affirmative, indirect contributions they fall on the same owners with an surcharge?) In fact Canard made a number of both successful and unsuccessful submissions to various competitions proposed by the French National Institute.
- However, the quality of Canard's attempt to apply mathematical techniques, in particular algebraic techniques, to economics has been much criticised.
- The referees of his competition entries pointed out errors in the way that Canard had applied some of his mathematical machinery.
- However, more recent reappraisals of Canard's contributions have shown that his work does have merit for, although there are errors, perhaps these are understandable as he is making a study of an unexplored area.
- Also, it is now possible to see that Canard anticipated some of the ideas which were introduced by later workers.
- To Canard likewise must be attributed the first unequivocal attempt at supply-and-demand analysis.
- Canard developed an equilibrium theory based on the relative bargaining power of buyer and seller, which he related to need and competition.
- (Clearly recognizing the forces of monopoly and monopsony, he nevertheless failed to develop a bilateral monopoly model.) Second, Canard revived Cantillon's 'three rents', and wove them into a general equilibrium conception of the economy, which he used to trace the effects of taxation (in the process, adumbrating the Ricardian theory of land rent).
- Canard argued that the imposition of a new tax produces disequilibrium and sets in motion certain equilibrating adjustments which take time to work themselves through the economy.
- Canard's maxim that 'every old tax is good, every new tax is bad', must be judged in this context.
- Despite this work by Canard and other early writers, Antoine Augustin Cournot is usually considered as writing the first significant work on mathematical economics when he published "Recherches sur les principes mathématiques de la théorie des richesses" Ⓣ(Research on the mathematical principles of the theory of wealth) (1838).

Born 2 December 1754, Sézanne, Haute Marne, France. Died 28 August 1833, Moulins-sur-Allier, Auvergne, France.

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**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive