Differentiability of the value function without interiority assumptions

Juan Pablo Rincón-Zapatero and Manuel S. Santos

Journal of Economic Theory, 2009, vol. 144, issue 5, 1948-1964

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.

Keywords: Constrained; optimization; Value; and; policy; functions; Differentiability; Envelope; theorem; Shadow; price (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (20)

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Related works:
Working Paper: Differentiability of the value function without interiority assumptions (2007)
Working Paper: Differentiability of the Value Function without Interiority Assumptions (2007)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:144:y:2009:i:5:p:1948-1964

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