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Differentiability of the value function without interiority assumptions

  • Juan Pablo Rincon-Zapatero
  • Manuel S. Santos

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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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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  11. Martin L. Weitzman, 1973. "Duality Theory for Infinite Horizon Convex Models," Management Science, INFORMS, vol. 19(7), pages 783-789, March.
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  16. Hopenhayn, Hugo A & Nicolini, Juan Pablo, 1997. "Optimal Unemployment Insurance," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 412-38, April.
  17. Amir, Rabah & Mirman, Leonard J & Perkins, William R, 1991. "One-Sector Nonclassical Optimal Growth: Optimality Conditions and Comparative Dynamics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(3), pages 625-44, August.
  18. Thomas J. Sargent, 1979. ""Tobin's Q" and the rate of investment in general equilibrium," Staff Report 40, Federal Reserve Bank of Minneapolis.
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