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Differentiability of the Value Function without Interiority Assumptions

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  • Manuel Santos

    (Department of Economics, University of Miami)

  • Juan Pablo Rincon-Zapatero

    (Department of Economics, 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 focuss on some examples in which our assumptions are not met and the value function is not differentiable.

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Bibliographic Info

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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Keywords: Constrained optimization; value and policy functions; differentiability; envelope theorem; shadow price;

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References

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  1. David Cass, 2006. "Competitive Equilibrium with Incomplete Financial Markets," PIER Working Paper Archive 06-010, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
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Cited by:
  1. Strulovici, Bruno & Szydlowski, Martin, 2012. "On the Smoothness of Value Functions," MPRA Paper 36326, University Library of Munich, Germany, revised 31 Jan 2012.
  2. 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.
  3. Zhigang Feng & Jianjun Miao & Adrian Peralta-Alva & Manuel S. Santos, 2009. "Numerical simulation of nonoptimal dynamic equilibrium models," Working Papers 2009-018, Federal Reserve Bank of St. Louis.
  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. Pontus Rendahl, 2013. "Inequality Constraints and Euler Equation based Solution Methods," Cambridge Working Papers in Economics 1320, Faculty of Economics, University of Cambridge.

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