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Differentiability of the value function without interiority assumptions

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  • Juan Pablo Rincon-Zapatero
  • Manuel S. Santos

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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File URL: http://e-archivo.uc3m.es/bitstream/10016/668/1/we071405.pdf
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Bibliographic Info

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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Keywords: Constrained optimization; Value and policy functions; Differentiability; Envelope theorem; Shadow price;

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Cited by:
  1. Jaime McGovern & Olivier Morand & Kevin Reffett, 2013. "Computing minimal state space recursive equilibrium in OLG models with stochastic production," Economic Theory, Springer, vol. 54(3), pages 623-674, November.
  2. Zhigang Feng & Manuel Santos & Adrian Peralta-Alva & Jianjun Miao, 2009. "Numerical Simulation of Nonoptimal Dynamic Equilibrium Models," 2009 Meeting Papers 541, Society for Economic Dynamics.
  3. Pontus Rendahl, 2013. "Inequality Constraints and Euler Equation based Solution Methods," Cambridge Working Papers in Economics 1320, Faculty of Economics, University of Cambridge.
  4. Strulovici, Bruno & Szydlowski, Martin, 2012. "On the Smoothness of Value Functions," MPRA Paper 36326, University Library of Munich, Germany, revised 31 Jan 2012.
  5. Robin C. Sickles & Jenny Williams, 1999. "Turning from Crime: A Dynamic Perspective," School of Economics Working Papers 1999-08, University of Adelaide, School of Economics.

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