Skip to main content
SpringerLink
Log in

Differentiability of the Value Function of Nonclassical Optimal Growth Models

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

Abstract

We consider an optimal growth (multi-sector) model with nonconvex technology. Using the Clarke results on generalized gradients, we prove that the value function has left and right derivatives with respect to the initial capital stock, without requiring supermodularity assumptions.

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. Cass, D., Optimal Growth in an Aggregative Model of Capital Accumulation, Review of Economic Studies, Vol. 32, pp. 233–240, 1965.

    Google Scholar 

  2. Benveniste, L. M., and Scheinkman, J. A., On the Differentiability of the Value Function in Dynamic Models of Economics, Econometrica, Vol. 47, pp. 727–732, 1979.

    Google Scholar 

  3. Dechert, W. D., and Nishimura, K., A Complete Characterization of Optimal Growth Paths in an Aggregated Model with a Nonconcave Production Function, Journal of Economic Theory, Vol. 31, pp. 332–354, 1983.

    Google Scholar 

  4. Amir, R., Mirman, L. J., and Perkins, W. R., One-Sector Nonclassical Optimal Growth: Optimality Conditions and Comparative Dynamics, International Economic Review, Vol. 32, pp. 625–644, 1991.

    Google Scholar 

  5. Amir, R., Sensitivity Analysis of Multisector Optimal Economic Dynamics, Journal of Mathematical Economics, Vol. 25, pp. 123–141, 1996.

    Google Scholar 

  6. Topkis, D., Minimizing a Submodular Function on a Lattice, Operations Research, Vol. 26, pp. 305–321, 1978.

    Google Scholar 

  7. Athey, S., Monotone Comparative Statistics in Stochastic Optimization Problem, Working Paper, Graduate School of Business, Stanford University, 1995.

  8. Clarke, F. H., Optimization and Nonsmooth Analysis, John Wiley and Sons, New York, New York, 1983.

    Google Scholar 

  9. Berge, C., Espaces Topologiques: Fonctions Multivoques, Dunod, Paris, France, 1959.

    Google Scholar 

  10. Rockafellar, R. T., Convex Analysis, Princeton University Press, Princeton, New Jersey 1972.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Paris-1, Paris, France

    K. Askri (Doctorand)

  2. CNRS, CEPREMAP, Paris, France

    C. Le Van (Director of Research)

Authors
  1. K. Askri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Le Van
    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

Askri, K., Le Van, C. Differentiability of the Value Function of Nonclassical Optimal Growth Models. Journal of Optimization Theory and Applications 97, 591–604 (1998). https://doi.org/10.1023/A:1022690009338

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1022690009338

Search

Navigation