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Non-Constant Discounting in Continuous Time

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Author Info
Larry Karp (University of California, Berkeley and Giannini Foundation)

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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. 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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File URL: http://repositories.cdlib.org/cgi/viewcontent.cgi?article=1062&context=are_ucb
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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 969.

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Date of creation: 05 Jan 2004
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Handle: RePEc:cdl:agrebk:969

Note: oai:cdlib1:are_ucb-1062
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Related research
Keywords: hyperbolic discounting time consistency Markov equilibria non-uniqueness observational equivalence Pareto efficiency

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  1. Karp, Larry, 2005. "Global warming and hyperbolic discounting," Journal of Public Economics, Elsevier, vol. 89(2-3), pages 261-282, February. [Downloadable!] (restricted)
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  2. Diamond, Peter & Koszegi, Botond, 2003. "Quasi-hyperbolic discounting and retirement," Journal of Public Economics, Elsevier, vol. 87(9-10), pages 1839-1872, September. [Downloadable!] (restricted)
  3. Cropper, Maureen & Laibson, David, 1998. "The implications of hyperbolic discounting for project evaluation," Policy Research Working Paper Series 1943, The World Bank. [Downloadable!]
  4. 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. [Downloadable!] (restricted)
  5. Krusell, Per & Smith Jr., Anthony A, 2001. "Consumption-Savings Decisions with Quasi-Geometric Discounting," CEPR Discussion Papers 2651, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  6. Harris, Christopher & Laibson, David, 2001. "Dynamic Choices of Hyperbolic Consumers," Econometrica, Econometric Society, vol. 69(4), pages 935-57, July.
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  7. 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. [Downloadable!] (restricted)
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