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Smoothness of the Policy Function in Discrete Time Economic Models


  • Santos, Manuel S


The theory applying to dynamic programming has furnished a useful set of techniques for the analysis of many types of sequential models. This theory, however, has not yielded heretofore much information about the differentiability properties of optimal solutions. This aspect is of particular interest as regards the qualitative analysis of optimal paths, where differentiable methods are often called into play. This paper shows roughly that if the objective is twice continuously differentiable and strongly concave, then any interior optimal path is continuously differentiable with respect to the initial state. Copyright 1991 by The Econometric Society.

Suggested Citation

  • Santos, Manuel S, 1991. "Smoothness of the Policy Function in Discrete Time Economic Models," Econometrica, Econometric Society, vol. 59(5), pages 1365-1382, September.
  • Handle: RePEc:ecm:emetrp:v:59:y:1991:i:5:p:1365-82

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    References listed on IDEAS

    1. Hugo Sonnenschein, 1973. "The Utility Hypothesis and Market Demand Theory," Discussion Papers 51, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March.
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    7. Diewert, W. E., 1977. "Generalized slutsky conditions for aggregate consumer demand functions," Journal of Economic Theory, Elsevier, vol. 15(2), pages 353-362, August.
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    9. Brown, Donald J & Matzkin, Rosa L, 1996. "Testable Restrictions on the Equilibrium Manifold," Econometrica, Econometric Society, vol. 64(6), pages 1249-1262, November.
    10. Sonnenschein, Hugo, 1973. "Do Walras' identity and continuity characterize the class of community excess demand functions?," Journal of Economic Theory, Elsevier, vol. 6(4), pages 345-354, August.
    11. Russell, Thomas & Farris, Frank, 1993. "The geometric structure of some systems of demand equations," Journal of Mathematical Economics, Elsevier, vol. 22(4), pages 309-325.
    12. Mantel, Rolf R., 1976. "Homothetic preferences and community excess demand functions," Journal of Economic Theory, Elsevier, vol. 12(2), pages 197-201, April.
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