Abstract
Based on a general mathematical model of a technology, implying certain properties for the production function, weak and strong forms of a physical law of diminishing returns are derived. It is also shown that the classical forms of this law hold if the technology is homogeneous (degree one) and the production possibility sets of the technology are strictly convex, but the latter property violates an essential property of a technology, namely that these sets have bounded efficient subsets.
Similar content being viewed by others
References
K. J. Arrow, E. Barankin, and D. Blackwell: Admissable Points of Convex Sets, Contributions to the Theory of Games, Vol. II, Princeton University Press (1953).
K. J. Arrow, H. B. Chenery, B. S. Minhas, and R. M. Solow: Capital-Labor Substitution and Economic Efficiency, The Review of Economics and StatisticsXLIII (August 1961), pp. 225–250.
C. Berge: Topological Spaces, New York, p. 163, (1963).
C. W. Cobb, and P. H. Douglas: A Theory of Production, The American Economic Review, Papers and Proceedings18 (1926), pp. 139–165.
W. Eichhorn: Deduktion der Ertragsgesetze aus Prämissen, Zeitschrift für Nationalökonomie28 (1968), pp. 191–205.
K. Menger: The Logic of the Laws of Return, A Study in MetaEconomics, Economic Activity Analysis, Part III, edited by Oskar Morgenstern, John Wiley and Sons, New York, (1954). Originally published as two papers: Bemerkungen zu den Ertragsgesetzen, Zeitschrift für NationalökonomieVII (1936), pp. 25–26, and: Weitere Bemerkungen zu den Ertragsgesetzen, ibid, pp. 388–397.
J. S. Mill: Principles of Political Economy, Vol. I, (1848). Revised Edition, Book I, Chapter XII, New York, (1900).
W. Rudin: Principles of Mathematical Analysis, Chapters 3, New York, (1964).
P. A. Samuelson: Economics, Part I, Chapter 2, B, Sixth Edition, McGraw-Hill, New York, (1964).
J. A. Schumpeter: History of Economic Analysis, Part II, Chapters, 2 (b), Oxford University Press, New York, (1966).
R. W. Shephard: The Notion of a Production Function, Unternehmensforschung, Vol. 2, No. 4, pp. 209–232, (1967).
R. W. Shephard: Theory of Cost and Production Functions, submitted to Princeton University Press, (June 1969).
J. R. A. Turgot: Observations sur le Memoire de M. Saint-Péravy, (1767), in Oeuvres de Turgot, Ed. Daire, Vol. 1, pp. 418–433, Paris, (1844).
H. Uzawa: Production Functions with Constant Elasticities of Substitution, Review of Economic Studies, Vol. 30, No. 4, (October 1962).
W. Wittmann: Produktionstheorie, Chapter IV, Springer-Verlag, Berlin-Heidelberg-New York, (1968).
Author information
Authors and Affiliations
Additional information
Dedicated to my friend Oskar Morgenstern who called this issue to my attention and urged me to work on it.
Rights and permissions
About this article
Cite this article
Shephard, R.W. Proof of the law of diminishing returns. Zeitschr. f. Nationalökonomie 30, 7–34 (1970). https://doi.org/10.1007/BF01289990
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01289990