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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. We begin with a discrete stage model and take the limit as the length of the stage goes to 0 to obtain the DPE corresponding to the continuous time problem. We characterize the multiplicity of equilibria under non-constant discounting and discuss the relation between a given equilibrium of that model and the unique equilibrium of a related problem with constant discounting. We calculate the bounds of the set of candidate steady states and we Pareto rank the equilibria.

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Paper provided by Department of Agricultural & Resource Economics, UC Berkeley in its series Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series with number qt7pr05084.

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Date of creation: 05 Jan 2004
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Handle: RePEc:cdl:agrebk:qt7pr05084
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  1. Per Krusell & Anthony A. Smith, Jr., 2003. "Consumption--Savings Decisions with Quasi--Geometric Discounting," Econometrica, Econometric Society, vol. 71(1), pages 365-375, January.
  2. 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.
  3. Kamihigashi, Takashi, 2001. "Necessity of Transversality Conditions for Infinite Horizon Problems," Econometrica, Econometric Society, vol. 69(4), pages 995-1012, July.
  4. Andrew Caplin & John Leahy, 2004. "The Social Discount Rate," Journal of Political Economy, University of Chicago Press, vol. 112(6), pages 1257-1268, December.
  5. 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.
  6. 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.
  7. Christopher Harris & David Laibson, 1999. "Dynamic Choices of Hyperbolic Consumers," Harvard Institute of Economic Research Working Papers 1886, Harvard - Institute of Economic Research.
  8. Karp, Larry, 2005. "Global warming and hyperbolic discounting," Journal of Public Economics, Elsevier, vol. 89(2-3), pages 261-282, February.
  9. Cropper, Maureen & Laibson, David, 1998. "The implications of hyperbolic discounting for project evaluation," Policy Research Working Paper Series 1943, The World Bank.
  10. 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.
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