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The Local Bifurcation of Ramsey Equilibrium

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  • Becker, Robert A
  • Foias, Ciprian

Abstract

The elasticity of substitution has been proposed as one factor in the generation of aggregate fluctuations in dynamic models with incomplete markets. We study the existence of periodic solutions in a one-sector neoclassical capital accumulation model under borrowing constraints with infinitely-lived heterogeneous agents. A dynamical system representing an equilibrium profile with only the most patient agent holding capital is analyzed when capital income is not an increasing function of total capital. Conditions for the linear approximation system at a steady state to have an eigenvalue of -1 are found. A one-parameter family of maps based on a perturbation of the production function is introduced and the dynamical system is reduced to 1 dimension via an application of a center manifold theorem. Conditions for a stable flip bifurcation are shown to hold at the steady state.

Suggested Citation

  • Becker, Robert A & Foias, Ciprian, 1994. "The Local Bifurcation of Ramsey Equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(5), pages 719-744, August.
  • Handle: RePEc:spr:joecth:v:4:y:1994:i:5:p:719-44
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    1. Itoh Hideshi, 1993. "Coalitions, Incentives, and Risk Sharing," Journal of Economic Theory, Elsevier, vol. 60(2), pages 410-427, August.
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    3. Jewitt, Ian, 1988. "Justifying the First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 56(5), pages 1177-1190, September.
    4. Dilip Mookherjee, 1984. "Optimal Incentive Schemes with Many Agents," Review of Economic Studies, Oxford University Press, vol. 51(3), pages 433-446.
    5. Paul R. Milgrom, 1981. "Good News and Bad News: Representation Theorems and Applications," Bell Journal of Economics, The RAND Corporation, vol. 12(2), pages 380-391, Autumn.
    6. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
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