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On Ramsey equilibrium: capital ownership pattern and inefficiency

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  • Robert Becker
  • Ram Dubey
  • Tapan Mitra

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. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joecth:v:55:y:2014:i:3:p:565-600
    DOI: 10.1007/s00199-013-0767-x
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    1. Mitra, Tapan & Sorger, Gerhard, 2013. "On Ramseyʼs conjecture," Journal of Economic Theory, Elsevier, vol. 148(5), pages 1953-1976.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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, Department of Economics, Indiana University Bloomington.
    7. Becker, Robert A. & Mitra, Tapan, 2012. "Efficient Ramsey Equilibria," Macroeconomic Dynamics, Cambridge University Press, vol. 16(S1), pages 18-32, April.
    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. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Mitra, Tapan & Sorger, Gerhard, 2013. "On Ramseyʼs conjecture," Journal of Economic Theory, Elsevier, vol. 148(5), pages 1953-1976.
    14. 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.
    15. Cuong Le Van & Yiannis Vailakis, 2003. "Existence of a competitive equilibrium in a one sector growth model with heterogeneous agents and irreversible investment," Post-Print halshs-00119095, HAL.
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    Cited by:

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    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), vol. 58(2), pages 329-353, February.
    3. Mitra, Tapan & Sorger, Gerhard, 2013. "On Ramseyʼs conjecture," Journal of Economic Theory, Elsevier, vol. 148(5), pages 1953-1976.
    4. 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.
    5. Ngoc‐Sang Pham & Hien Pham, 2021. "Effects of credit limit on efficiency and welfare in a simple general equilibrium model," International Journal of Economic Theory, The International Society for Economic Theory, vol. 17(4), pages 446-470, December.
    6. Ngoc-Sang Pham, 2023. "Some Lectures on Macroeconomics," Working Papers hal-04366349, HAL.
    7. Stefano Bosi & Cuong Le Van & Ngoc-Sang Pham, 2017. "Rational Land and Housing Bubbles in Infinite-Horizon Economies," Studies in Economic Theory, in: Kazuo Nishimura & Alain Venditti & Nicholas C. Yannelis (ed.), Sunspots and Non-Linear Dynamics, chapter 0, pages 203-230, Springer.
    8. 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.
    9. Anna Castañer & Jesús Marín-Solano & Carmen Ribas, 2021. "A time consistent dynamic bargaining procedure in differential games with hterogeneous discounting," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 555-584, June.
    10. 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.
    11. 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.
    12. Luis Alcalá & Fernando Tohmé & Carlos Dabús, 2019. "Strategic Growth with Recursive Preferences: Decreasing Marginal Impatience," Dynamic Games and Applications, Springer, vol. 9(2), pages 314-365, June.
    13. Borissov, Kirill & Dubey, Ram Sewak, 2020. "Growth with many agents and wages paid ex ante," Economic Modelling, Elsevier, vol. 89(C), pages 101-107.
    14. 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.
    15. 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, Department of Economics, Indiana University Bloomington.
    16. 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.
    17. Pham, Ngoc-Sang, 2018. "Credit limits and heterogeneity in general equilibrium models with a finite number of agents," MPRA Paper 88736, University Library of Munich, Germany.
    18. 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

    Cass criteria; Efficiency; Maximal income monotonicity; Period three Ramsey equilibrium cycle; Weak turnpike property; Approximate CES function; C61; D61; D90; O41;
    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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