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Differentiability of the Value Function without Interiority Assumptions

  • Manuel Santos

    (Department of Economics, University of Miami)

  • Juan Pablo Rincon-Zapatero

    (Department of Economics, Universidad Carlos III de Madrid)

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 focuss on some examples in which our assumptions are not met and the value function is not differentiable.

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Paper provided by University of Miami, Department of Economics in its series Working Papers with number 0704.

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Length: 36 pages
Date of creation: 09 Aug 2007
Date of revision:
Publication status: Forthcoming: Under Review
Handle: RePEc:mia:wpaper:0704
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