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Non-constant discounting in finite horizon: The free terminal time case

  • Jesus Marin Solano
  • Jorge Navas Rodenes

    (Universitat de Barcelona)

This paper derives the HJB (Hamilton-Jacobi-Bellman) equation for sophisticated agents in a finite horizon dynamic optimization problem with non-constant discounting in a continuous setting, by using a dynamic programming approach. A simple example is used in order to illustrate the applicability of this HJB equation, by suggesting a method for constructing the subgame perfect equilibrium solution to the problem. Conditions for the observational equivalence with an associated problem with constant discounting are analyzed. Special attention is paid to the case of free terminal time. Strotzs model (an eating cake problem of a nonrenewable resource with non-constant discounting) is revisited.

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Paper provided by Universitat de Barcelona. Espai de Recerca en Economia in its series Working Papers in Economics with number 183.

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Length: 29 pages
Date of creation: 2007
Date of revision:
Handle: RePEc:bar:bedcje:2007183
Contact details of provider: Postal: Espai de Recerca en Economia, Facultat de Ciències Econòmiques. Tinent Coronel Valenzuela, Num 1-11 08034 Barcelona. Spain.
Web page: http://www.ere.ub.es

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  1. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
  2. Karp, Larry, 2004. "Non-constant discounting in continuous time," CUDARE Working Paper Series 0969, University of California at Berkeley, Department of Agricultural and Resource Economics and Policy.
  3. Laibson, David I., 1997. "Golden Eggs and Hyperbolic Discounting," Scholarly Articles 4481499, Harvard University Department of Economics.
  4. Karp, Larry, 2005. "Global warming and hyperbolic discounting," Journal of Public Economics, Elsevier, vol. 89(2-3), pages 261-282, February.
  5. Karp, Larry & Tsur, Yacov, 2008. "Time perspective and climate change policy," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt04k4b21g, Department of Agricultural & Resource Economics, UC Berkeley.
  6. Loewenstein, George & Prelec, Drazen, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, MIT Press, vol. 107(2), pages 573-97, May.
  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.
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