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Moving the Goalposts: Differentiability of the Value Function without Interiority Assumptions

Author

Listed:
  • Manuel S. Santos

    (Department of Economics, University of Miami)

  • Juan Pablo Rincon-Zapatero

    (Departamento de Economia, Universidad Carlos III de Madrid)

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.

Suggested Citation

  • Manuel S. Santos & Juan Pablo Rincon-Zapatero, 2007. "Moving the Goalposts: Differentiability of the Value Function without Interiority Assumptions," Working Papers 0614, University of Miami, Department of Economics.
    • Handle: RePEc:mia:wpaper:0614
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    References listed on IDEAS

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