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Saddles, Indeterminacy and Bifurcations in an Overlapping Generations Economy with a Renewable Resource

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Listed:
  • Erkki Koskela
  • Markku Ollikainen
  • Mikko Puhakka

Abstract

We incorporate a renewable resource into an overlapping generations model with standard, well-behaved utility and constant returns to scale production functions. Besides being a factor of production the resource serves as a store of value. We characterize dynamics, efficiency and stability of steady state equilibria and show that the nature of steady state equilibrium depends on the value of the intertemporal elasticity of substitution in consumption. In particular, if that elasticity is at least half, but not exactly one, stationary equilibria are saddle points. The stationary equilibrium is stable when the intertemporal elasticity of substitution is unity. For smaller values of that elasticity we use a parametric example to demonstrate the existence of stable equilibria (indeterminacy) and a subcritical flip bifurcation. Hence, an overlapping generations economy with a renewable resource can display cycles and indeterminacy even in the absence of externalities or imperfect competition.

Suggested Citation

  • Erkki Koskela & Markku Ollikainen & Mikko Puhakka, 2000. "Saddles, Indeterminacy and Bifurcations in an Overlapping Generations Economy with a Renewable Resource," CESifo Working Paper Series 298, CESifo Group Munich.
  • Handle: RePEc:ces:ceswps:_298
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    File URL: http://www.cesifo-group.de/DocDL/cesifo_wp298.pdf
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    References listed on IDEAS

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    1. Cass, David, 1972. "On capital overaccumulation in the aggregative, neoclassical model of economic growth: A complete characterization," Journal of Economic Theory, Elsevier, vol. 4(2), pages 200-223, April.
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    3. Kemp, Murray C & Long, Ngo Van, 1979. "The Under- Exploitation of Natural Resources: A Model with Overlapping Generations," The Economic Record, The Economic Society of Australia, vol. 55(150), pages 214-221, September.
    4. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
    5. Mourmouras, Alex, 1993. "Conservationist government policies and intergenerational equity in an overlapping generations model with renewable resources," Journal of Public Economics, Elsevier, vol. 51(2), pages 249-268, June.
    6. Olson, Lars J. & Knapp, Keith C., 1997. "Exhaustible Resource Allocation in an Overlapping Generations Economy," Journal of Environmental Economics and Management, Elsevier, vol. 32(3), pages 277-292, March.
    7. Grandmont, Jean-Michel, 1998. "Introduction to Market Psychology and Nonlinear Endogenous Business Cycles," Journal of Economic Theory, Elsevier, vol. 80(1), pages 1-13, May.
    8. Gregroy Amacher & Richard Brazee & Erkki Koskela & Markku Ollikainen, 1999. "Taxation, Bequests, and Short and Long Run Timber Supplies: An Overlapping Generations Problem," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 13(3), pages 269-288, April.
    9. Farmer, Roger E. A., 1986. "Deficits and cycles," Journal of Economic Theory, Elsevier, vol. 40(1), pages 77-88, October.
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    More about this item

    Keywords

    Overlapping generations; renewable resources; bifurcations;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • Q20 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - General

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