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Non-constant discounting in continuous time

  • Karp, Larry


    (University of California, Berkeley. Dept of agricultural and resource economics and policy)

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 University of California at Berkeley, Department of Agricultural and Resource Economics and Policy in its series CUDARE Working Paper Series with number 0969.

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Length: 23 pages
Date of creation: 2004
Date of revision:
Handle: RePEc:are:cudare:0969
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  1. Per Krusell & Anthony A. Smith, Jr., . "Consumption-Savings Decisions with Quasi-Geometric Discounting," GSIA Working Papers 2001-05, Carnegie Mellon University, Tepper School of Business.
  2. Karp, Larry, 2005. "Global warming and hyperbolic discounting," Journal of Public Economics, Elsevier, vol. 89(2-3), pages 261-282, February.
  3. 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.
  4. Christopher Harris & David Laibson, 1999. "Dynamic Choices of Hyperbolic Consumers," Harvard Institute of Economic Research Working Papers 1886, Harvard - Institute of Economic Research.
  5. 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.
  6. repec:tpr:qjecon:v:114:y:1999:i:4:p:1125-1152 is not listed on IDEAS
  7. Andrew Caplin & John Leahy, 2001. "The social discount rate," Discussion Paper / Institute for Empirical Macroeconomics 137, Federal Reserve Bank of Minneapolis.
  8. Cropper, Maureen & Laibson, David, 1998. "The implications of hyperbolic discounting for project evaluation," Policy Research Working Paper Series 1943, The World Bank.
  9. Kamihigashi, Takashi, 2001. "Necessity of Transversality Conditions for Infinite Horizon Problems," Econometrica, Econometric Society, vol. 69(4), pages 995-1012, July.
  10. 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.
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