The Analysis of Linear Economic Systems
Father Maurice Potron’s Pioneering Works
Edited by Christian Bidard, Guido Erreygers
Routledge – 2010
Maurice Potron (1872-1942), a French Jesuit mathematician, constructed and analyzed a highly original, but virtually unknown economic model. This book presents translated versions of all his economic writings, preceded by a long introduction which sketches his life and environment based on extensive archival research and family documents.
Potron had no education in economics and almost no contact with the economists of his time. His primary source of inspiration was the social doctrine of the Church, which had been updated at the end of the nineteenth century. Faced with the ‘economic evils’ of his time, he reacted by utilizing his talents as a mathematician and an engineer to invent and formalize a general disaggregated model in which production, employment, prices and wages are the main unknowns. He introduced four basic principles or normative conditions (‘sufficient production’, the ‘right to rest’, ‘justice in exchange’, and the ‘right to live’) to define satisfactory regimes of production and labour on the one hand, and of prices and wages on the other. He studied the conditions for the existence of these regimes, both on the quantity side and the value side, and he explored the way to implement them.
This book makes it clear that Potron was the first author to develop a full input-output model, to use the Perron-Frobenius theorem in economics, to state a duality result, and to formulate the Hawkins-Simon condition. These are all techniques which now belong to the standard toolkit of economists. This book will be of interest to Economics postgraduate students and researchers, and will be essential reading for courses dealing with the history of mathematical economics in general, and linear production theory in particular.
Foreword Paul Anthony Samuelson Church, Society and Economics: An Introduction to the Life and Work of Maurice Potron Christian Bidard and Guido Erreygers 1. Abstract of a study on just prices and wages 2. With regard to a mathematical contribution to the study of the problems of production and wages 3. Some properties of linear substitutions with coefficients ≥0 and their application to the problems of production and wages 4. Application to the problems of "sufficient production" and the "living wage" of some properties of linear substitutions with coefficients ≥0 5. Possibility and determination of the just price and the just wage 6. Mathematical contribution to the study of the problems of production and of wages 7. Relations between the question of unemployment and those of the just price and the just wage 8. Some properties of linear substitutions with coefficients ≥0 and their application to the problems of production and of wages 9. Mathematical contribution to the study of the equilibrium between production and consumption 10. The scientific organization of labour - The "Taylor system" 11. On some conditions of economic equilibrium. Letter of M. Potron (90) to R. Gibrat (22) 12. On the economic equilibria 13. Communication made at the Oslo Congress 14. The mathematical aspect of some economic problems in relation to some recent results of the theory of nonnegative matrices. Lectures given at the Catholic Institute of Paris 15. On nonnegative matrices 16. On nonnegative matrices and positive solutions to certain linear systems 17. Letter on industrial statistics Appendix I: Alfred Barriol, "Obituary. Maurice Potron (1872-1942)" Appendix II: Alfred Barriol, "[Report on] L.aspect mathématique de certains problèmes économiques" Appendix III: Michel Vittrant, "[Report on] Le problème de la manne des Hébreux" The Potron Bibliography
Christian Bidard is Professor of Economics at the University of Paris Ouest, France.
Guido Erreygers is Professor of Economics at the University of Antwerp, Belgium.