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Two Theorems on Generalized Diminishing Returns and their Applications to Economic Analysis

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  • NGO VAN LONG

Abstract

Under certain weak assumptions such as free disposal and non‐satiety, it is shown that the concavity of utility and of technology implies that the maximum value of the set of all attainable programmes is a concave function of the initial capital stocks. For time‐independent problems, this implies that along an optimal path, as a capital stock is accumulated, its shadow price falls. The usefulness of the theorems is demonstrated in a number of examples, including Kemp's cake‐eating problem and Forster's pollution‐control problem.

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  • Ngo Van Long, 1979. "Two Theorems on Generalized Diminishing Returns and their Applications to Economic Analysis," The Economic Record, The Economic Society of Australia, vol. 55(1), pages 58-63, March.
    • Handle: RePEc:bla:ecorec:v:55:y:1979:i:1:p:58-63
    DOI: 10.1111/j.1475-4932.1979.tb02202.x
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    References listed on IDEAS

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    1. Hadley, G. & Kemp, M. C., 1971. "Variational Methods in Economics," Elsevier Monographs, Elsevier, edition 1, number 9780720436013 edited by Bliss, C. J..
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    Cited by:

    1. Figuières, Charles & Long, Ngo Van & Tidball, Mabel, 2017. "The MBR intertemporal choice criterion and Rawls’ just savings principle," Mathematical Social Sciences, Elsevier, vol. 85(C), pages 11-22.
    2. Charles Figuieres & Ngo Van Long & Mabel Tidball, 2016. "The Mixed Bentham-Rawls Intertemporal Choice Criterion and Rawls’ Just Savings Principle," CIRANO Working Papers 2016s-49, CIRANO.
    3. Ngo Long & Vincent Martinet, 2018. "Combining rights and welfarism: a new approach to intertemporal evaluation of social alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(1), pages 35-64, January.
    4. Ly Dai Hung, 2022. "Fast and Sustainable Development Space: An Integrated Approach," Journal of Asian Economic Integration, , vol. 4(1), pages 72-91, April.
    5. Hartwick, John M. & Van Long, Ngo & Tian, Huilan, 2001. "Deforestation and Development in a Small Open Economy," Journal of Environmental Economics and Management, Elsevier, vol. 41(3), pages 235-251, May.

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