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Differentiability of the value function without interiority assumptions

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  • Rincón-Zapatero, Juan Pablo
  • Santos, Manuel S.

Abstract

This paper studies first-order differentiability properties of the value function in concave dynamic programs. Motivated by economic considerations, we dispense with commonly imposed interiority assumptions. We suppose that the correspondence of feasible choices varies with the vector of state variables, and we allow the optimal solution to belong to the boundary of this correspondence. Under minimal assumptions we prove that the value function is continuously differentiable. We then discuss this result in the context of some economic models, and focus on some examples in which our assumptions are not met and the value function is not differentiable.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 144 (2009)
Issue (Month): 5 (September)
Pages: 1948-1964

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Handle: RePEc:eee:jetheo:v:144:y:2009:i:5:p:1948-1964

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: Constrained optimization Value and policy functions Differentiability Envelope theorem Shadow price;

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Cited by:
  1. Sickles, Robin C. & Williams, Jenny, 2008. "Turning from crime: A dynamic perspective," Journal of Econometrics, Elsevier, vol. 145(1-2), pages 158-173, July.
  2. Strulovici, Bruno & Szydlowski, Martin, 2012. "On the Smoothness of Value Functions," MPRA Paper 36326, University Library of Munich, Germany, revised 31 Jan 2012.
  3. Rincón-Zapatero, Juan Pablo & Santos, Manuel S., 2012. "Differentiability of the value function in continuous-time economic models," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/15635, Universidad Carlos III de Madrid.
  4. Zhigang Feng & Manuel Santos & Adrian Peralta-Alva & Jianjun Miao, 2009. "Numerical Simulation of Nonoptimal Dynamic Equilibrium Models," 2009 Meeting Papers 541, Society for Economic Dynamics.

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