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Differentiability of the value function without interiority assumptions

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Rincón-Zapatero, Juan Pablo
Santos, Manuel S.

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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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Publisher 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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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Zhigang Feng & Jianjun Miao & Adrian Peralta-Alva & Manuel S. Santos, 2009. "Numerical simulation of nonoptimal dynamic equilibrium models," Working Papers 2009-018, Federal Reserve Bank of St. Louis. [Downloadable!]
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