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Economic Characterization of Reciprocal Isoperimetric Control Problems

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  • M. R. Caputo

    (University of California, Davis, and Member, Giannini Foundation of Agricultural Economics)

Abstract

Fundamental identities between the optimal solution functions and optimal value functions for reciprocal pairs of isoperimetric control problems are established in a simple, direct, and economically intuitive fashion. The relationships between the derivatives of the aforementioned functions, the objects of interest in qualitative economic analysis, are shown to follow as a corollary to the identities. The theorem and corollary are applied to the nonrenewable resource extracting model of the firm, where an economic interpretation of them is given, and where new and original comparative dynamics results are derived in a general fashion, without the aid of a phase diagram or specific functional forms.

Suggested Citation

  • M. R. Caputo, 1998. "Economic Characterization of Reciprocal Isoperimetric Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 325-350, August.
    • Handle: RePEc:spr:joptap:v:98:y:1998:i:2:d:10.1023_a:1022685417012
    DOI: 10.1023/A:1022685417012
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    References listed on IDEAS

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    1. Caputo, Michael R., 1990. "A qualitative characterization of the competitive nonrenewable resource extracting firm," Journal of Environmental Economics and Management, Elsevier, vol. 18(3), pages 206-226, May.
    2. LaFrance, Jeffrey T. & Barney, L. Dwayne, 1991. "The envelope theorem in dynamic optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 15(2), pages 355-385, April.
    3. Caputo, Michael R., 1990. "How to do comparative dynamics on the back of an envelope in optimal control theory," Journal of Economic Dynamics and Control, Elsevier, vol. 14(3-4), pages 655-683, October.
    4. Michael Caputo, 1994. "The Slutsky matrix and homogeneity in intertemporal consumer theory," Journal of Economics, Springer, vol. 60(3), pages 255-279, October.
    5. Caputo, Michael R, 1990. "New Qualitative Properties in the Competitive Nonrenewable Resource Extracting Model of the Firm," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(4), pages 829-839, November.
    6. Kamien, Morton I & Schwartz, Nancy L, 1974. "Patent Life and R & D Rivalry," American Economic Review, American Economic Association, vol. 64(1), pages 183-187, March.
    7. Silberberg, Eugene & Walker, Donald A, 1984. "A Modern Analysis of Giffen's Paradox," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(3), pages 687-694, October.
    8. 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. Savin Treanţă, 2022. "Lagrange-Hamilton Approach in Optimization Problems with Isoperimetric-Type Constraints," Journal of Optimization Theory and Applications, Springer, vol. 194(2), pages 508-520, August.
    2. Akpalu, Wisdom & Vondolia, Godwin K., 2012. "Bioeconomic model of spatial fishery management in developing countries," Environment and Development Economics, Cambridge University Press, vol. 17(2), pages 145-161, April.
    3. M. R. Caputo, 1999. "Economic Characterization of Reciprocal Isoperimetric Control Problems Revisited," Journal of Optimization Theory and Applications, Springer, vol. 101(3), pages 723-730, June.
    4. L. Grosset & B. Viscolani, 2006. "Reciprocal Optimal Control Problems and the Associated Pareto Frontier," Journal of Optimization Theory and Applications, Springer, vol. 130(1), pages 113-123, July.
    5. Akpalu, Wisdom & Parks, Peter J., 2007. "Natural resource use conflict: gold mining in tropical rainforest in Ghana," Environment and Development Economics, Cambridge University Press, vol. 12(1), pages 55-72, February.

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