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Differentiability of the value function without interiority assumptions

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  • Rincón-Zapatero, Juan Pablo
  • Santos, Manuel S.

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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 144 (2009)
Issue (Month): 5 (September)
Pages: 1948-1964

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Handle: RePEc:eee:jetheo:v:144:y:2009:i:5:p:1948-1964

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Web page: http://www.elsevier.com/locate/inca/622869

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

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Cited by:
  1. Pontus Rendahl, 2013. "Inequality Constraints and Euler Equation based Solution Methods," Cambridge Working Papers in Economics 1320, Faculty of Economics, University of Cambridge.
  2. Zhigang Feng & Jianjun Miao & Adrian Peralta‐Alva & Manuel S. Santos, 2014. "Numerical Simulation Of Nonoptimal Dynamic Equilibrium Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55, pages 83-110, 02.
  3. 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.
  4. 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.
  5. Bruno Strulovici & Martin Szydlowski, 2012. "On the Smoothness of Value Functions," Discussion Papers 1542, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

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