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Non-constant discounting in continuous time

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Author Info

  • Karp, Larry

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

Abstract

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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Bibliographic Info

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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Related research

Keywords: equilibrium (economics); markov model; pareto principle;

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References

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  1. Christopher Harris & David Laibson, 1999. "Dynamic Choices of Hyperbolic Consumers," Harvard Institute of Economic Research Working Papers 1886, Harvard - Institute of Economic Research.
  2. Per Krusell & Anthony A Smith, Jr., 2001. "Consumption Savings Decisions with Quasi-Geometric Discounting," NajEcon Working Paper Reviews 625018000000000251, www.najecon.org.
  3. Andrew Caplin & John Leahy, 2001. "The social discount rate," Discussion Paper / Institute for Empirical Macroeconomics 137, Federal Reserve Bank of Minneapolis.
  4. Cropper, Maureen & Laibson, David, 1998. "The implications of hyperbolic discounting for project evaluation," Policy Research Working Paper Series 1943, The World Bank.
  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. 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.
  7. Kamihigashi, Takashi, 2001. "Necessity of Transversality Conditions for Infinite Horizon Problems," Econometrica, Econometric Society, vol. 69(4), pages 995-1012, July.
  8. 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.
  9. 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.
  10. 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.
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