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Limit of the Solutions for the Finite Horizon Problems as the Optimal Solution to the Infinite Horizon Optimization Problems


  • Dapeng CAI

    (Institute for Advanced Research, Nagoya University, Nagoya, Japan)

  • Takashi Gyoshin NITTA

    (Department of Mathematics, Faculty of Education, Mie University, Tsu, Japan)


We aim to generalize the results of Cai and Nitta (2007) by allowing both the utility and production function to depend on time. We also consider an additional intertemporal optimality criterion. We clarify the conditions under which the limit of the solutions for the finite horizon problems is optimal among all attainable paths for the infinite horizon problems under the overtaking criterion, as well as the conditions under which such a limit is the unique optimum under the sum-of-utilities criterion. The results are applied to a parametric example of the one-sector growth model to examine the impacts of discounting on optimal paths.

Suggested Citation

  • Dapeng CAI & Takashi Gyoshin NITTA, 2008. "Limit of the Solutions for the Finite Horizon Problems as the Optimal Solution to the Infinite Horizon Optimization Problems," Papers 0803.4050,
  • Handle: RePEc:arx:papers:0803.4050

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    References listed on IDEAS

    1. Anderson, Robert M., 1991. "Non-standard analysis with applications to economics," Handbook of Mathematical Economics,in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 39, pages 2145-2208 Elsevier.
    2. Anand, Sudhir & Sen, Amartya, 2000. "Human Development and Economic Sustainability," World Development, Elsevier, vol. 28(12), pages 2029-2049, December.
    3. Cuong Le Van & Lisa Morhaim, 2006. "On optimal growth models when the discount factor is near 1 or equal to 1," International Journal of Economic Theory, The International Society for Economic Theory, vol. 2(1), pages 55-76.
    4. Heal, G., 1998. "Valuing the Future: Economic Theory and Sustainability," Papers 98-10, Columbia - Graduate School of Business.
    5. Michel, Philippe, 1990. "Some Clarifications on the Transversality Condition," Econometrica, Econometric Society, vol. 58(3), pages 705-723, May.
    6. Weitzman, Martin L., 1998. "Why the Far-Distant Future Should Be Discounted at Its Lowest Possible Rate," Journal of Environmental Economics and Management, Elsevier, vol. 36(3), pages 201-208, November.
    7. W. A. Brock, 1970. "On Existence of Weakly Maximal Programmes in a Multi-Sector Economy," Review of Economic Studies, Oxford University Press, vol. 37(2), pages 275-280.
    8. Kamihigashi, Takashi, 2001. "Necessity of Transversality Conditions for Infinite Horizon Problems," Econometrica, Econometric Society, vol. 69(4), pages 995-1012, July.
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