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A characterization of Ramsey equilibrium in a model with limited borrowing

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  • Borissov, Kirill
  • Dubey, Ram Sewak

Abstract

This paper considers a one-sector economic growth model with several infinitely-lived heterogeneous households, who differ both in the discount factors as well as preferences over consumption. Unlike the extreme form of borrowing constraint observed in the classical Ramsey model, recently surveyed in Becker (2006), we allow limited borrowing by the households and prove the existence of a perfect foresight equilibrium. We also show that irrespective of production technology employed by the firms, the capital stock sequence converges to the steady state stock and from some time onward all impatient households are in the maximum borrowing state, whereas the most patient household owns entire capital stock and the debts of all other households.

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  • 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.
    • Handle: RePEc:eee:mateco:v:56:y:2015:i:c:p:67-78
    DOI: 10.1016/j.jmateco.2014.12.004
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    1. Robert Becker & Ram Dubey & Tapan Mitra, 2014. "On Ramsey equilibrium: capital ownership pattern and inefficiency," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 565-600, April.
    2. Mitra, Tapan & Sorger, Gerhard, 2013. "On Ramseyʼs conjecture," Journal of Economic Theory, Elsevier, vol. 148(5), pages 1953-1976.
    3. Kirill Borissov, 2011. "On Equilibrium Dynamics with Many Agents and Wages Paid ex ante," EUSP Department of Economics Working Paper Series 2011/05, European University at St. Petersburg, Department of Economics, revised 28 Apr 2011.
    4. 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), vol. 58(2), pages 329-353, February.
    5. Le Van, Cuong & Nguyen, Manh-Hung & Vailakis, Yiannis, 2007. "Equilibrium dynamics in an aggregative model of capital accumulation with heterogeneous agents and elastic labor," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 287-317, April.
    6. Becker, Robert A. & Mitra, Tapan, 2012. "Efficient Ramsey Equilibria," Macroeconomic Dynamics, Cambridge University Press, vol. 16(S1), pages 18-32, April.
    7. 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.
    8. Becker, Robert A. & Foias, Ciprian, 1987. "A characterization of Ramsey equilibrium," Journal of Economic Theory, Elsevier, vol. 41(1), pages 173-184, February.
    9. Kirill Borissov, 2011. "On Equilibrium Dynamics with Many Agents and Wages Paid ex ante," EUSP Department of Economics Working Paper Series Ec-05/11, European University at St. Petersburg, Department of Economics, revised 28 Apr 2011.
    10. Robert A. Becker, 1980. "On the Long-Run Steady State in a Simple Dynamic Model of Equilibrium with Heterogeneous Households," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 95(2), pages 375-382.
    11. Rose-Anne Dana & Cuong Le Van & Tapan Mitra & Kazuo Nishimura (ed.), 2006. "Handbook on Optimal Growth 1," Springer Books, Springer, number 978-3-540-32310-5, November.
    12. Robert Becker & Ram Dubey & Tapan Mitra, 2014. "On Ramsey equilibrium: capital ownership pattern and inefficiency," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 565-600, April.
    13. Robert A. Becker, 2006. "Equilibrium Dynamics with Many Agents," Springer Books, in: Rose-Anne Dana & Cuong Le Van & Tapan Mitra & Kazuo Nishimura (ed.), Handbook on Optimal Growth 1, chapter 13, pages 385-442, Springer.
    14. Bewley, Truman, 1982. "An integration of equilibrium theory and turnpike theory," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 233-267, September.
    15. Mitra, Tapan & Sorger, Gerhard, 2013. "On Ramseyʼs conjecture," Journal of Economic Theory, Elsevier, vol. 148(5), pages 1953-1976.
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    Cited by:

    1. Axelrod, David, 2017. "Optimizing Discount Rates: Expressing Preferences for Sustainable Outcomes in Present Value Calculations," MPRA Paper 84408, University Library of Munich, Germany.
    2. Boucekkine, Raouf & Nishimura, Kazuo & Venditti, Alain, 2015. "Introduction to financial frictions and debt constraints," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 271-275.
    3. Borissov, Kirill & Dubey, Ram Sewak, 2020. "Growth with many agents and wages paid ex ante," Economic Modelling, Elsevier, vol. 89(C), pages 101-107.
    4. Emmanuelle Augeraud-Véron & Raouf Boucekkine & Fausto Gozzi & Alain Venditti, 2024. "Fifty years of mathematical growth theory: Classical topics and new trends," AMSE Working Papers 2406, Aix-Marseille School of Economics, France.
    5. 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.
    6. Kirill Borissov & Joseph Hanna & Stéphane Lambrecht, 2019. "Public goods, voting, and growth," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 21(6), pages 1221-1265, December.
    7. Borissov, K. & Pakhnin, M., 2018. "A Division of Society into the Rich and the Poor: Some Approaches to Modeling," Journal of the New Economic Association, New Economic Association, vol. 40(4), pages 32-59.
    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.

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    More about this item

    Keywords

    Convergence; Existence; Growth; Heterogeneous agent; Limited borrowing; Turnpike property;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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