A Functional Inequality and the Law of Diminishing Returns

  • King-Tim Mak
Conference paper


Functional equations have always been an important area in mathematics, and have found much applications in the physical sciences. Functional equations have become a useful technique in economic analysis; for example, in the study of aggregation, technical progress, structures of utility functions, price indices and scaling of production, etc. [see Eichhorn].


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  1. Eichhorn, W.: Functional Equations in Economics. Reading, MA, 1978.Google Scholar
  2. Färe, R., and R. W. Shephard: Ray-homothetic Production Functions. Econometrica 45, 1977, 133–146.CrossRefGoogle Scholar
  3. Mak, K.: General Homothetic Production Correspondences. ORC 80–7, Operations Research Center, University of California, Berkeley 1980.Google Scholar
  4. Mak, K.: Dynamic Laws of Returns under Uncertainty. Quantitative Studies on Production and Prices. Ed. by W. Eichhorn et al. Würzburg-Wien 1982 (this volume).Google Scholar
  5. Radner, R.: Dynamic Programming of Economic Growth. Activity Analysis in the Theory of Growth and Planning. Ed. by E. Malinvaud and M.O.L. Bacharach. New York 1967.Google Scholar
  6. Shephard, R. W.: Proof of the Law of Diminishing Returns. Zeitschrift für Nationalökonomie 30, 1970, 7–34.Google Scholar
  7. Shephard, R. W.: Semi-homogeneous Production Functions and Scaling of Production. Lecture Notes in Economics and Mathematical Systems 99, Berlin 1974.Google Scholar

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© Springer-Verlag Berlin Heidelberg 1983

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  • King-Tim Mak

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