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Differentiability of the value function without interiority assumptions

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

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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Christopher Phelan & Ennio Stacchetti, 2001. "Sequential Equilibria in a Ramsey Tax Model," Econometrica, Econometric Society, vol. 69(6), pages 1491-1518, November.
  2. Fernando Alvarez & Urban J. Jermann, 2000. "Efficiency, Equilibrium, and Asset Pricing with Risk of Default," Econometrica, Econometric Society, vol. 68(4), pages 775-798, July.
  3. Narayana Kocherlakota, 2010. "Implications of Efficient Risk Sharing Without Commitment," Levine's Working Paper Archive 2053, David K. Levine.
  4. Thomas, J.P. & Worrall, T., 1991. "Foreign direct investment and the risk of expropriation," Discussion Paper 1991-26, Tilburg University, Center for Economic Research.
  5. Luigi Montrucchio & Fabio Privileggi, 2001. "On Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type," ICER Working Papers - Applied Mathematics Series 05-2001, ICER - International Centre for Economic Research.
  6. Kydland, Finn E. & Prescott, Edward C., 1980. "Dynamic optimal taxation, rational expectations and optimal control," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 79-91, May.
  7. 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.
  8. Thorsten Koeppl, 2004. "Differentiability of the Efficient Frontier when Commitment to Risk Sharing is Limited," Working Papers 1049, Queen's University, Department of Economics.
  9. Thomas, Jonathan & Worrall, Tim, 1988. "Self-enforcing Wage Contracts," Review of Economic Studies, Wiley Blackwell, vol. 55(4), pages 541-54, October.
  10. 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.
  11. 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.
  12. Benveniste, L. M. & Scheinkman, J. A., 1982. "Duality theory for dynamic optimization models of economics: The continuous time case," Journal of Economic Theory, Elsevier, vol. 27(1), pages 1-19, June.
  13. Kehoe, Timothy J & Levine, David K, 1993. "Debt-Constrained Asset Markets," Review of Economic Studies, Wiley Blackwell, vol. 60(4), pages 865-88, October.
  14. Christiano, Lawrence J. & Fisher, Jonas D. M., 2000. "Algorithms for solving dynamic models with occasionally binding constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 24(8), pages 1179-1232, July.
  15. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  16. Manuel S. Santos & Michael Woodford, 1997. "Rational Asset Pricing Bubbles," Econometrica, Econometric Society, vol. 65(1), pages 19-58, January.
  17. Benveniste, L M & Scheinkman, J A, 1979. "On the Differentiability of the Value Function in Dynamic Models of Economics," Econometrica, Econometric Society, vol. 47(3), pages 727-32, May.
  18. Sargent, Thomas J., 1980. ""Tobin's q" and the rate of investment in general equilibrium," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 12(1), pages 107-154, January.
  19. Mirman, Leonard J. & Zilcha, Itzhak, 1975. "On optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 11(3), pages 329-339, December.
  20. Martin L. Weitzman, 1973. "Duality Theory for Infinite Horizon Convex Models," Management Science, INFORMS, vol. 19(7), pages 783-789, March.
  21. Lucas, Robert E, Jr, 1980. "Equilibrium in a Pure Currency Economy," Economic Inquiry, Western Economic Association International, vol. 18(2), pages 203-20, April.
  22. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
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