DEPARTMENT OF ECONOMICS All but one: How pioneers of linear economics overlooked Perron-Frobenius mathematics Wilfried Parys UNIVERSITY OF ANTWERP Faculty of Applied Economics City Campus Prinsstraat 13, B.226 B-2000 Antwerp Tel. +32 (0)3 265 40 32 Fax +32 (0)3 265 47 99 www.uantwerpen.be FACULTY OF APPLIED ECONOMICS DEPARTMENT OF ECONOMICS All but one: How pioneers of linear economics overlooked Perron-Frobenius mathematics Wilfried Parys RESEARCH PAPER 2013-030 DECEMBER 2013 University of Antwerp, City Campus, Prinsstraat 13, B-2000 Antwerp, Belgium Research Administration – room B.226 phone: (32) 3 265 40 32 fax: (32) 3 265 47 99 e-mail:
[email protected] The research papers from the Faculty of Applied Economics are also available at www.repec.org (Research Papers in Economics - RePEc) D/2013/1169/030 All but one: How pioneers of linear economics overlooked Perron-Frobenius mathematics Wilfried PARYS Acknowledgements: Previous versions of this paper were presented at the 17th Annual Conference of the European Society for the History of Economic Thought at Kingston University, London, in May 2013, and at the Colloquium on The Pioneers of Linear Models of Production, University of Paris Ouest, Nanterre, in January 2013. I thank the participants of these conferences for their useful comments. I am indebted to Thomas Hawkins for his stimulating communications on Perron- Frobenius since 2005, and for his valuable comments on my January 2013 version. Section 3 benefited from earlier discussions on Potron with Christian Bidard and Guido Erreygers. I am grateful for some interesting remarks by Olav Bjerkholt, Nerio Naldi, Arrigo Opocher, Hans Schneider, and by the late Franz Alt and the late Paul Samuelson.