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Decisions in Economics and Finance

, Volume 27, Issue 1, pp 1–34 | Cite as

On the smoothness of optimal paths

  • Joël Blot
  • Bertrand Crettez
Article

Abstract

The aim of this paper is to study the differentiability property of optimal paths in dynamic economic models. We address this problem from the point of view of the differential calculus in sequence spaces which are infinite-dimensional Banach spaces. We assume that the return or utility function is concave, and that optimal paths are interior and bounded. We study the C r differentiability of optimal paths vis-à-vis different parameters. These parameters are: the initial vector of capital stock, the discount rate and a parameter which lies in a Banach space (which could be the utility function itself). The method consists of applying an implicit function theorem on the Euler–Lagrange equation. In order to do this, we make use of classical conditions (i.e., the dominant diagonal block assumption) and we provide new ones.

Mathematics Subject Classification (2000): 90A16, 49K40, 93C55

Journal of Economic Literature Classification: C161, D99, O41

Keywords

Banach Space Utility Function Capital Stock Optimal Path Lagrange Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  • Joël Blot
    • 1
  • Bertrand Crettez
    • 1
  1. 1.CERMSEM, University of Paris 1 Panthéon-Sorbonne, Maison des Sciences Economiques 

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