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On the Ramsey equilibrium with heterogeneous consumers and endogenous labor supply

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  • Bosi, Stefano
  • Seegmuller, Thomas

Abstract

In this paper, we address the stability issue, stressing the role of labor supply, in a Ramsey model with heterogeneous households subject to borrowing constraints. Making labor supply endogenous leads us to prove the existence of two kinds of steady state: the one where everybody supplies labor, the other where only the most patient agent refrains from working. Going beyond models with inelastic labor supply, we show how preferences of impatient agents affect the saddle-path stability of each type of steady state and the occurrence of endogenous cycles. When their elasticity of intertemporal substitution in consumption exceeds one, instability and cycles are less likely, requiring lower degrees of capital-labor substitution. Conversely, elasticity values below one promote the emergence of fluctuations. We end the paper by showing the existence of the intertemporal equilibrium under market incompleteness, using a local approach based on the first-order conditions.

Suggested Citation

  • Bosi, Stefano & Seegmuller, Thomas, 2010. "On the Ramsey equilibrium with heterogeneous consumers and endogenous labor supply," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 475-492, July.
  • Handle: RePEc:eee:mateco:v:46:y:2010:i:4:p:475-492
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    Citations

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    Cited by:

    1. Nishimura, Kazuo & Nourry, Carine & Seegmuller, Thomas & Venditti, Alain, 2016. "Public Spending As A Source Of Endogenous Business Cycles In A Ramsey Model With Many Agents," Macroeconomic Dynamics, Cambridge University Press, vol. 20(02), pages 504-524, March.
    2. Robert Becker & Stefano Bosi & Cuong Van & Thomas Seegmuller, 2015. "On existence and bubbles of Ramsey equilibrium with borrowing constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 329-353.
    3. repec:hal:journl:halshs-01020635 is not listed on IDEAS
    4. Bosi, Stefano & Ismael, Mohanad & Venditti, Alain, 2016. "Collateral and growth cycles with heterogeneous agents," Journal of Macroeconomics, Elsevier, vol. 48(C), pages 327-350.
    5. repec:hal:journl:halshs-00544332 is not listed on IDEAS
    6. Bosi, Stefano & Seegmuller, Thomas, 2010. "On the role of progressive taxation in a Ramsey model with heterogeneous households," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 977-996, November.
    7. Borissov, Kirill & Dubey, Ram Sewak, 2015. "A characterization of Ramsey equilibrium in a model with limited borrowing," Journal of Mathematical Economics, Elsevier, vol. 56(C), pages 67-78.
    8. Becker, Robert A. & Borissov, Kirill & Dubey, Ram Sewak, 2015. "Ramsey equilibrium with liberal borrowing," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 296-304.
    9. Stefano Bosi & Cuong Le Van, 2011. "On the existence of a Ramsey equilibrium with endogenous labor supply and borrowing constraints," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00612131, HAL.
    10. repec:ipg:wpaper:201404 is not listed on IDEAS
    11. Kazuo Nishimura & Carine Nourry & Thomas Seegmuller & Alain Venditti, 2015. "On the (de)stabilizing effect of public debt in a Ramsey model with heterogeneous agents," International Journal of Economic Theory, The International Society for Economic Theory, vol. 11(1), pages 7-24, March.
    12. repec:hal:journl:halshs-00331299 is not listed on IDEAS
    13. Robert Becker & Stefano Bosi & Cuong Le Van & Thomas Seegmuller, 2012. "On existence, efficiency and bubbles of Ramsey equilibrium with borrowing constraints," Caepr Working Papers 2012-001, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
    14. repec:hal:psewpa:halshs-00793530 is not listed on IDEAS
    15. repec:ipg:wpaper:2013-004 is not listed on IDEAS
    16. Riham BARBAR & Jean-Paul BARINCI, "undated". "Consumption Externalities, Endogenous Discounting, Heterogeneity and Cycles," EcoMod2009 21500008, EcoMod.
    17. Mohanad ISMAEL, "undated". "Social Inequalities and Macroeconomic Instability," EcoMod2009 21500044, EcoMod.
    18. repec:hal:journl:halshs-00612131 is not listed on IDEAS
    19. repec:ipg:wpaper:4 is not listed on IDEAS

    More about this item

    Keywords

    Saddle-path stability Endogenous cycles Heterogeneous agents Endogenous labor supply Borrowing constraint;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D30 - Microeconomics - - Distribution - - - General
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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