Differentiability of the value function without interiority assumptions

Juan Pablo Rincón-Zapatero, Manuel S. Santos

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1948-1964
Number of pages17
JournalJournal of Economic Theory
Issue number5
StatePublished - Sep 2009


  • Constrained optimization
  • Differentiability
  • Envelope theorem
  • Shadow price
  • Value and policy functions

ASJC Scopus subject areas

  • Economics and Econometrics


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