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Differentiability of the value function without interiority assumptions

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Juan Pablo Rincon-Zapatero
Manuel S. Santos

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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 show that the value function is continuously differentiable. We then discuss this result in the context of several economic models.

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Paper provided by Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we071405.

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Date of creation: Mar 2007
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Handle: RePEc:cte:werepe:we071405

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  1. Zhigang Feng & Jianjun Miao & Adrian Peralta-Alva & Manual Santos, 2009. "Numerical Simulation of Nonoptimal Dynamic Equilibrium Models," Working Papers 0912, University of Miami, Department of Economics. [Downloadable!]
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