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Non-constant discounting in continuous time

  • Karp, Larry

This note derives the dynamic programming equation (DPE) to a differentiable Markov Perfect equilibrium in a problem with non-constant discounting and general functional forms. Beginning with a discrete stage model and taking the limit as the length of the stage goes to 0 leads to the DPE corresponding to the continuous time problem. The note discusses the multiplicity of equilibria under non-constant discounting, calculates the bounds of the set of candidate steady states, and Pareto ranks the equilibria.

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

Volume (Year): 132 (2007)
Issue (Month): 1 (January)
Pages: 557-568

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Handle: RePEc:eee:jetheo:v:132:y:2007:i:1:p:557-568
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  1. Karp, Larry, 2004. "Global Warming and Hyperbolic Discounting," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt5zh730nc, Department of Agricultural & Resource Economics, UC Berkeley.
  2. Andrew Caplin & John Leahy, 2000. "The Social Discount Rate," NBER Working Papers 7983, National Bureau of Economic Research, Inc.
  3. Tsutsui, Shunichi & Mino, Kazuo, 1990. "Nonlinear strategies in dynamic duopolistic competition with sticky prices," Journal of Economic Theory, Elsevier, vol. 52(1), pages 136-161, October.
  4. Per Krusell & Anthony A Smith, Jr., 2001. "Consumption Savings Decisions with Quasi-Geometric Discounting," Levine's Working Paper Archive 625018000000000251, David K. Levine.
  5. Robert J. Barro, 1999. "Ramsey Meets Laibson In The Neoclassical Growth Model," The Quarterly Journal of Economics, MIT Press, vol. 114(4), pages 1125-1152, November.
  6. Kamihigashi, Takashi, 2001. "Necessity of Transversality Conditions for Infinite Horizon Problems," Econometrica, Econometric Society, vol. 69(4), pages 995-1012, July.
  7. Erzo G. J. Luttmer & Thomas Mariotti, 2003. "Subjective Discounting in an Exchange Economy," Journal of Political Economy, University of Chicago Press, vol. 111(5), pages 959-989, October.
  8. Cropper, Maureen & Laibson, David, 1998. "The implications of hyperbolic discounting for project evaluation," Policy Research Working Paper Series 1943, The World Bank.
  9. Christopher Harris & David Laibson, 1999. "Dynamic Choices of Hyperbolic Consumers," Harvard Institute of Economic Research Working Papers 1886, Harvard - Institute of Economic Research.
  10. Li, Chuan-Zhong & Lofgren, Karl-Gustaf, 2000. "Renewable Resources and Economic Sustainability: A Dynamic Analysis with Heterogeneous Time Preferences," Journal of Environmental Economics and Management, Elsevier, vol. 40(3), pages 236-250, November.
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