Skip to main content
SpringerLink
Log in

Economic Characterization of Reciprocal Isoperimetric Control Problems

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Jehle, G. A., Advanced Microeconomic Theory, Prentice Hall, Englewood Cliffs, New Jersey, 1991.

    Google Scholar 

  2. LaFrance, J. T., and Barney, L. D., The Envelope Theorem in Dynamic Optimization, Journal of Economic Dynamics and Control, Vol. 15, pp. 355-385, 1991.

    Google Scholar 

  3. Caputo, M. R., The Slutsky Matrix and Homogeneity in Intertemporal Consumer Theory, Journal of Economics, Vol. 60, pp. 255-279, 1994.

    Google Scholar 

  4. Clegg, J. C., Calculus of Variations, Interscience, New York, New York, 1967.

    Google Scholar 

  5. Kamien, M. I., and Schwartz, N. L., Patent Life and R&D Rivalry, American Economic Review, Vol. 64, pp. 183-187, 1974.

    Google Scholar 

  6. Hadley, G., and Kemp, M. C., Variational Methods in Economics, North Holland, Amsterdam, Netherlands, 1971.

    Google Scholar 

  7. Caputo, M. R., How to Do Comparative Dynamics on the Back of An Envelope in Optimal Control Theory, Journal of Economic Dynamics and Control, Vol. 14, pp. 655-683, 1990.

    Google Scholar 

  8. Steinberg, A. M., and Stalford, H. L., On Existence of Optimal Controls, Journal of Optimization Theory and Applications, Vol. 11, pp. 266-273, 1973.

    Google Scholar 

  9. Seierstad, A., and SydsÆter, K., Optimal Control Theory with Economic Applications, Elsevier Science, Amsterdam, Netherlands, 1987.

    Google Scholar 

  10. Hartman, P., Ordinary Differential Equations, 2nd Edition, Birkhäuser, Boston, Massachusetts, 1982.

    Google Scholar 

  11. Caputo, M. R., New Qualitative Properties in the Competitive Nonrenewable Resource Extracting Model of the Firm, International Economic Review, Vol. 31, pp. 829-839, 1990.

    Google Scholar 

  12. Gale, D., and NikaidÔ, H., The Jacobian Matrix and Global Univalence of Mappings, Mathematische Annalen, Vol. 159, pp. 81-93, 1965.

    Google Scholar 

  13. Silberberg, E., and Walker, D. A., A Modern Analysis of Giffen's Paradox, International Economic Review, Vol. 25, pp. 687-694, 1984.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Agricultural and Resource Economics, University of California, Davis, and Member, Giannini Foundation of Agricultural Economics, Professor

    M. R. Caputo

Authors
  1. M. R. Caputo
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Caputo, M.R. Economic Characterization of Reciprocal Isoperimetric Control Problems. Journal of Optimization Theory and Applications 98, 325–350 (1998). https://doi.org/10.1023/A:1022685417012

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1022685417012

Search

Navigation