Dynamic Laws of Returns under Uncertainty

  • King-Tim Mak
Conference paper


The study of the effect of resource constraints (limitations) on production has always been an important topic in the theory of production. Turgot [1967] introduced into economic thought a proposition which has come to be known as the Law of Diminishing Returns at the intensive margin. The original spirit of the law was concerned with the restraint on agricultural production imposed by the scarcity of land. From this viewpoint, the particular formulation of the law in terms of diminishing product increments is nonessential to its significance. In bare form, the issue is: whether a bound on the inputs of a proper subset of factors leads to bounded outputs, when the other inputs may be applied in unlimited amounts. This more basic formulation of the law is described by Menger [1936] as an intersecting assertion.


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  1. Eichhorn, W.: Deduktion der Ertragsgesetze aus Prämissen. Zeitschrift für Nationalökonomie 28, 1968, 191–205.Google Scholar
  2. Eichhorn, W.: Functional Equations in Economics. Reading, MA, 1978.Google Scholar
  3. Färe, R.: Strong Limitationality of Essential Proper Subsets of Factors of Production. Zeitschrift für Nationalökonomie 32, 1972, 417–424.Google Scholar
  4. Färe, R.: A Dynamic Formulation of the Law of Diminishing Returns. Symposium on Production Theory. Stockholm 1978.Google Scholar
  5. Färe, R.: Laws of Diminishing Returns. Vol. 176, Lecture Notes in Economics and Mathematical Systems. Berlin 1980.CrossRefGoogle Scholar
  6. Mak, K.: A Stochastic Theory of Production Correspondences. ORC 81–6, Operations Research Center, University of California, Berkeley, 1981.Google Scholar
  7. Mak, K.: A Functional Inequality, with Applications to Production Theory. Quantitative Studies on Production and Prices. Ed. by W. Eichhorn et al. Würzburg-Wien 1982 (this volume).Google Scholar
  8. Menger, K.: Bemerkungen zu den Ertragsgesetzen. Zeitschrift für Nationalökonomie 7, 1936, 25–56.Google Scholar
  9. Menger, K.: Weitere Bemerkungen zu den Ertragsgesetzen. Zeitschrift für Nationalökonomie 7, 1936, 388–397.Google Scholar
  10. Menger, K.: The Logic of the Laws of Returns. A Study in Metaeconomics. Economic Activity Analysis. Ed. by O. Morgenstern. New York 1954.Google Scholar
  11. Radner, R.: Competitive Equilibrium Under Uncertainty. Econometrica 36, 1968, 31–58.CrossRefGoogle Scholar
  12. Shephard, R.W.: The Notion of a Production Function. Unternehmensforschung 11, 1967, 209–232.Google Scholar
  13. Shephard, R.W.: Theory of Cost and Production Functions. Princeton, N.J., 1970a.Google Scholar
  14. Shephard, R.W.: Proof of the Law of Diminishing Returns. Zeitschrift für Nationalökonomie 30, 1970b, 7–34.Google Scholar
  15. Shephard, R.W., and R. Färe: The Law of Diminishing Returns. Zeitschrift für Nationalökonomie 34, 1974, 69–90.Google Scholar
  16. Shephard, R.W., : Dynamic Theory of Production Correspondences. Vol. 50, Mathematical Systems in Economics. Meisenheim 1980.Google Scholar
  17. Turgor, A.R.J.: Sur le Memoire de M. de Saint-Puruvy. Oeuvres de Turgot. Ed. by Daire, Vol. 1, Paris 1967, 418–483.Google Scholar
  18. Yosida, K.: Functional Analysis. 2nd Ed. Berlin 1968.CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 1983

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  • King-Tim Mak

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