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On Ramsey Equilibrium: Capital Ownership Pattern and Inefficiency

Author

Listed:
  • Robert Becker

    () (Indiana University)

  • Ram Sewak Dubey

    () (Montclair State University)

  • Tapan Mitra

    () (Cornell University)

Abstract

We provide a sufficient condition on the production function under which eventually the most patient household owns the entire capital stock in every Ramsey Equilibrium, called the turnpike property. This generalizes the result in the literature which establishes the turnpike property using the capital income monotonicity condition. We then provide an example of a Ramsey Equilibrium in which the most patient household reaches a no capital position infinitely often. This is a strong refutation of the turnpike property on Ramsey equilibria. We also show that the constructed Ramsey equilibrium is inefficient in terms of the aggregate consumption stream that it provides.

Suggested Citation

  • Robert Becker & Ram Sewak Dubey & Tapan Mitra, 2012. "On Ramsey Equilibrium: Capital Ownership Pattern and Inefficiency," Caepr Working Papers 2012-007, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
  • Handle: RePEc:inu:caeprp:2012-007
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    File URL: http://www.iub.edu/~caepr/RePEc/PDF/2012/CAEPR2012-007.pdf
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    References listed on IDEAS

    as
    1. Cuong Le Van & Yiannis Vailakis, 2003. "Existence of a competitive equilibrium in a one sector growth model with heterogeneous agents and irreversible investment," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(4), pages 743-771, November.
    2. 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.
    3. 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.
    4. Mitra, Tapan & Sorger, Gerhard, 2013. "On Ramseyʼs conjecture," Journal of Economic Theory, Elsevier, vol. 148(5), pages 1953-1976.
    5. 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.
    6. 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.
    7. Becker, Robert A & Boyd, John H, III & Foias, Ciprian, 1991. "The Existence of Ramsey Equilibrium," Econometrica, Econometric Society, vol. 59(2), pages 441-460, March.
    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. Sorger, Gerhard, 1994. "On the Structure of Ramsey Equilibrium: Cycles, Indeterminacy, and Sunspots," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(5), pages 745-764, August.
    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, Oxford University Press, vol. 95(2), pages 375-382.
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    Cited by:

    1. 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.
    2. Bosi, Stefano & Le Van, Cuong & Pham, Ngoc-Sang, 2017. "Asset bubbles and efficiency in a generalized two-sector model," Mathematical Social Sciences, Elsevier, vol. 88(C), pages 37-48.
    3. Engelbert Dockner & Florian Wagener, 2014. "Markov perfect Nash equilibria in models with a single capital stock," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(3), pages 585-625, August.
    4. Mitra, Tapan & Sorger, Gerhard, 2013. "On Ramseyʼs conjecture," Journal of Economic Theory, Elsevier, vol. 148(5), pages 1953-1976.
    5. 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.
    6. 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.
    7. 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.
    8. Stefano Bosi & Cuong Le Van & Ngoc-Sang Pham, 2016. "Rational land and housing bubbles in infinite-horizon economies," Documents de travail du Centre d'Economie de la Sorbonne 16027, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    9. Jean-Pierre Drugeon & Bertrand Wigniolle, 2017. "On impatience, temptation and Ramsey’s conjecture," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 73-98, January.
    10. 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.
    11. Cuong Le Van & Ngoc-Sang Pham, 2016. "Intertemporal equilibrium with financial asset and physical capital," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 155-199, June.
    12. repec:ipg:wpaper:2013-004 is not listed on IDEAS
    13. repec:ipg:wpaper:4 is not listed on IDEAS
    14. Luis Alcala & Fernando Tohme & Carlos Dabus, 2016. "Strategic Growth with Recursive Preferences: Decreasing Marginal Impatience," Papers 1608.06959, arXiv.org.
    15. repec:hal:journl:halshs-01314609 is not listed on IDEAS

    More about this item

    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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