Maurice Potron Research Paper

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Father Maurice Potron, a French Jesuit and a graduate of France’s prestigious École Polytechnique with a Ph.D. in mathematics,  published  major,  but  surprisingly little known,  mathematical-economic  papers  between  1911 and 1941. His writings include three major findings.

First, in mathematics, he published a demonstration about the existence of solutions of nonnegative matrixes (or “linear substitutions” as he called them) as early as 1911,  before Ferdinand Georg Frobenius (1849–1917) did so in 1912. In 1908 and 1909 Oskar Perron (1880–1975) and Frobenius had only demonstrated theorems related to strictly positive matrixes.

Second, in the same paper, Potron, while trying to reconcile social justice (“fair” price, “fair” wage) and economic interdependencies, was the first to apply PerronFrobenius’s theorems on a Leontief-type model, in order to find the conditions for the existence of a fair economic equilibrium, a “satisfactory economic regime” in Potron’s words, allowing simultaneous adequacy between the consumption  structure  and  that  of production  and  work capacities, and adequacy between price and wage levels. As far as we know, nobody had used Perron-Frobenius’s theorem in economics before World War II (1939–1945).

Third, in 1912 Potron laid the foundations of future input-output  analysis, offering a detailed study of the expenses supported by his baker to produce a two-kilogram loaf of bread. The extension of such a study to other industries would allow precise calculation of the “effective satisfactory regime  of  production-consumption   and prices-wages” (Potron  1912,  p.  19).  Indeed,  he  used matrixes  to  describe the  economic  interdependency between products and branches. The concept of a “technical coefficient” was used in 1912 to promote a central planning office whose mission would be to organize the economy according to social Catholic doctrine. Thus, the invention of input-output  matrixes is undoubtedly due not  to  Wassily Leontief  (1906–1999)  but  to  Potron (1912), since Leontief ’s “The Balance of the Economy of the USSR” was published in 1925 and The Structure of the American Economy, his greatest book, in 1941. The existence of a “calculations bureau” (bureau  des calculs) would constitute the only way to achieve a “satisfactory regime.” This concern led Potron to put forward, in 1936, the use of Gauss-Lanczos’s iterative method in order to help the planning  office deal with  the  huge dimensions of the matrix, a method widely used in algorithms today.

As early as 1912, Potron introduced the number of working days per year as a relevant parameter of the viability of an economic system. He was also concerned with the possibility of demand inadequacy: in what has been called Potron’s law, he shows how an increase in demand will raise general activity and revenue. Since he lacked academic training in economics, Potron’s economic approach is mainly explained by his intellectual and social environment (Abraham-Frois and Lendjel 2004). Catholic doctrine (as expressed in 1891 in Pope Leo XIII’s encyclical Rerum Novarum on the rights and duties of capital and labor)  and  the  network  of  Catholic  social reformers (mainly Potron’s father, Auguste Potron, as well as Henry Pupey Girard, Gustave Desbuquois, and Joseph Zamanski) led him to formulate original propositions in economics, with his own terminology and cumbersome mathematical notations. But this singularity denied him access to academia and to any audience of economists. In the last years of his life, neither his links with X-crise, a French association constituted between 1931 and 1939 by engineering graduates of France’s École Polytechnique to deal  with  the  global  economic  crisis (Fischman  and Lendjel 2000), nor his membership in the Econometric Society (since 1938), nor  even his participation at the eighth International Congress of Mathematics at Oslo in 1936 (probably with the help of Norwegian economist Ragnar Frisch [1895–1973]) provided him with any recognition. This has only come recently.


  1. Abraham-Frois, Gilbert, and Emeric 2001. Une première application du théorème de Perron-Frobenius à l’économie: L’Abbé Potron comme précurseur. Revue d’economie politique 111 (4): 639–666.
  2. Abraham-Frois, Gilbert, and Emeric 2004. Les oeuvres economiques de l’Abbé Potron. Paris: L’Harmattan.
  3. Abraham-Frois, Gilbert, and Emeric 2005. Father Potron’s Early Contribution to Input-Output Analysis. Fifteenth Input-Output Conference, Beijing, June-July.
  4. Fischman, Marianne, and Emeric 2000. La contribution d’X-crise à l’émergence de l’économétrie en France dans les années trente. Revue Européenne  des sciences sociales 38 (118): 115–134.
  5. Potron, M 1911. Application aux problèmes de la “production suffisante” et du “salaire vital” de quelques propriétés des substitutions linéaires à coefficients = 0 et leur application aux problèmes de la production et des salaires. Comptes rendus de l’Académie des Sciences 53: 1129–1131. Reprinted in Abraham-Frois and Lendjel (2004).
  6. Potron, M 1912. Possibilité et détermination du juste prix et du juste salaire. Le mouvement social 73 (4): 289–316. Reprinted in Abraham-Frois and Lendjel (2004).
  7. Potron, M 1913. Quelques propriétés des substitutions linéaires à coefficients ≥ 0 et leur application aux problèmes de la production et des salaires. Annales scientifiques de l’École Normale 30: 53–76. Reprinted in Abraham-Frois and Lendjel (2004).
  8. Potron, M 1936. L’aspect mathématique de certains problèmes économiques. Paris: Author. Reprinted in AbrahamFrois and Lendjel (2004).

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