2020, issue 2, p. 86-99

Received 03.05.2020; Revised 21.05.2020; Accepted 30.06.2020

Published 24.07.2020; First Online 27.07.2020


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MSC 90B30, 91B34, 91B64, JEL C02, E23, D57

Sraffa and Leontief Revisited: Mathematical Methods and Models of a Circular Economy

J.-F. Emmenegger * ORCID ID favicon Big,   D. Chable ,   H.A. Nour Eldin,   H. Knolle

* Correspondence: This email address is being protected from spambots. You need JavaScript enabled to view it.


Introduction. Sometimes new results in one scientific field can help to study quite other branches. In the new book we observe application of various mathematical methods to study circular economics.

The purpose of the paper is to give information about the new book “SRAFFA AND LEONTIEF REVISITED: Mathematical methods and models of a circular economy”. The academic editor Walter de Gruyter-Oldenbourg has published this monography in January 2020 in English language.

Results. This book contributes to the increasing call for a comprehensive perception of economic production processes. The book is dedicated to Wassily Leontief’s concept of Input-Output Analysis and to Piero Sraffa's seminal book “Production of Commodities by Means of Commodities”. Single product and joint production industries of a circular economy are described, consequently using matrix algebra. The central role of the Perron-Frobenius Theorem for non-negative matrices, specially Perron-Frobenius eigenvalues and eigenvectors is revealed as a common basis of Sraffa’s and Leontief’s approaches and applied to clarify the basic economic assumptions which are inherent to economic production processes.

Conclusions. The book addresses young researchers wishing to explore the foundations of circular economy, practitioners wishing to examine the potential of Sraffa’s price models in connection to Leontief’s Input-Output analysis. Advanced undergraduate, graduate, PhD students and their instructors in economics, political science or applied mathematics, who seek to understand Sraffa and the recent developments of the circular economy of inter industrial and national economy will find numerous examples with complete solutions, presented by a rich, formal, mathematical methodology, revealing the economic content of the results. Detailed examples and visualizing graphs are presented for applications of various mathematical methods.


Keywords: Input-Output analysis, circular economy, Perron-Frobenius Theorem, non-negative matrix.


Cite as: Emmenegger J.-F., Chable D., Nour Eldin H.A., Knolle H. Sraffa and Leontief Revisited: Mathematical Methods and Models of a Circular Economy. Cybernetics and Computer Technologies. 2020. 2. P. 86–99. https://doi.org/10.34229/2707-451X.20.2.9



           1.     Emmenegger J.-F., Chable D., Nour Eldin H.A., Knolle H. Sraffa and Leontief Revisited: Mathematical Methods and Models of a Circular Economy. Berlin, Boston. De Gruyter. 2020. 572 p. https://doi.org/10.1515/9783110635096

           2.     Aurez V., Georgeault L. Economie circulaire, Système économique et finitude des ressources. De Boeck Supérieur s. a. Louvain-la-Neuve. 2016 and 2019.

           3.     Leontief W.W. Die Wirtschaft als Kreislauf. Archiv für Sozialwissenschaft und Sozialpolitik. 1928. 60. P. 577–623.

           4.     Sraffa P. Production of commodities by means of commodities. Cambridge. Cambridge University Press. 1960 (and the German edition, Verlag Suhrkamp. 780. 1976, with an appendix of Bertram Schefold).

           5.     Foley D.K. Adam’s Fallacy, A guide to economic Theology. The Belknap Press of Harvard University Press. 2006. https://doi.org/10.4159/9780674027077

           6.     Knolle H. Die Wachstumsgesellschaft, Aufstieg, Niedergang und Veränderung. Köln. PapyRossa. 2016.

           7.     Newman P., Arbor A. Production of commodities by means of commodities. Schweizerische Zeitschrift für Volkswirtschaftslehre und Statistik. 1962. 98. Jg. P. 58–75.

           8.     Gantmacher F.R. Matrizentheorie. Berlin. Springer-Verlag. 1986. https://doi.org/10.1007/978-3-642-71243-2

           9.     Schefold B. “Mr. Sraffa on Joint Production and other Essays”. London: Routledge. 1989. https://doi.org/10.4324/9780203168721



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