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Optimal Growth with Heterogeneous Agents and the Twisted Turnpike: An Example

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  • Robert Becker

    () (Indiana University)

Abstract

The dynamics of a welfare maximizing, heterogeneous agent, one sector optimal Ramsey model is analyzed assuming two agents, each with a distinct discount factor and log utility. Production is Cobb-Douglas. Explicit time varying policy functions are derived, one for each period. A Twisted Turnpike Property and eventually monotone dynamics are demonstrated to govern the evolution of the economy’s aggregate capital stock.

Suggested Citation

  • Robert Becker, 2011. "Optimal Growth with Heterogeneous Agents and the Twisted Turnpike: An Example," Caepr Working Papers 2011-008, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
  • Handle: RePEc:inu:caeprp:2011-008
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    References listed on IDEAS

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    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), pages 743-771.
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    3. Kehoe, Timothy J., 1991. "Computation and multiplicity of equilibria," Handbook of Mathematical Economics,in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 38, pages 2049-2144 Elsevier.
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    5. Bliss, C. J., 1975. "Capital Theory and the Distribution of Income," Elsevier Monographs, Elsevier, edition 1, number 9780720436044 edited by Bliss, C. J..
    6. Coles, Jeffrey Link, 1985. "Equilibrium Turnpike Theory with Constant Returns to Scale and Possible Heterogeneous Discount Factors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(3), pages 671-679, October.
    7. Hansen, Lars Peter & Jagannathan, Ravi, 1997. " Assessing Specification Errors in Stochastic Discount Factor Models," Journal of Finance, American Finance Association, vol. 52(2), pages 557-590, June.
    8. Timothy J. Kehoe & David K. Levine, 1982. "Comparitive Statics and Perfect Foresight in Infinite Horizon Economies," UCLA Economics Working Papers 259, UCLA Department of Economics.
    9. Kehoe, Timothy J. & Levine, David K. & Romer, Paul M., 1990. "Determinacy of equilibria in dynamic models with finitely many consumers," Journal of Economic Theory, Elsevier, vol. 50(1), pages 1-21, February.
    10. Takashi Kamihigashi, 2007. "On the Principle of Optimality for Nonstationary Deterministic Dynamic Programming," Discussion Paper Series 200, Research Institute for Economics & Business Administration, Kobe University.
    11. Dur n, Jorge & Le Van, Cuong, 2003. "Simple Proof Of Existence Of Equilibrium In A One-Sector Growth Model With Bounded Or Unbounded Returns From Below," Macroeconomic Dynamics, Cambridge University Press, pages 317-332.
    12. Rader, Trout, 1972. "Theory of General Economic Equilibrium," Elsevier Monographs, Elsevier, edition 1, number 9780125750400.
    13. Becker, Robert A. & Foias, Ciprian, 1987. "A characterization of Ramsey equilibrium," Journal of Economic Theory, Elsevier, vol. 41(1), pages 173-184, February.
    14. Coles, Jeffrey L., 1986. "Equilibrium turnpike theory with time-separable utility," Journal of Economic Dynamics and Control, Elsevier, vol. 10(3), pages 367-394, September.
    15. Kehoe, Timothy J & Levine, David K, 1985. "Comparative Statics and Perfect Foresight in Infinite Horizon Economies," Econometrica, Econometric Society, vol. 53(2), pages 433-453, March.
    16. Takashi Kamihigashi, 2008. "On the principle of optimality for nonstationary deterministic dynamic programming," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(4), pages 519-525.
    17. Bliss, Christopher, 1999. "The Real Rate of Interest: A Theoretical Analysis," Oxford Review of Economic Policy, Oxford University Press, vol. 15(2), pages 46-58, Summer.
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    Citations

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    Cited by:

    1. Drugeon, Jean-Pierre & Wigniolle, Bertrand, 2016. "On time-consistent policy rules for heterogeneous discounting programs," Journal of Mathematical Economics, Elsevier, pages 174-187.
    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. KONDO Atsumasa, "undated". "The Role of Productivity Growth Rates for Rising Inequality in an Economy with Heterogeneous Agents," ESRI Discussion paper series 326, Economic and Social Research Institute (ESRI).
    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. 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.
    7. repec:ipg:wpaper:201404 is not listed on IDEAS
    8. Lilia Maliar & Serguei Maliar, 2016. "Ruling Out Multiplicity of Smooth Equilibria in Dynamic Games: A Hyperbolic Discounting Example," Dynamic Games and Applications, Springer, vol. 6(2), pages 243-261, June.
    9. 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.
    10. repec:hal:psewpa:halshs-00793530 is not listed on IDEAS
    11. repec:ipg:wpaper:2013-004 is not listed on IDEAS
    12. Stefano Bosi & Thomas Seegmuller, 2013. "Rational bubbles and expectation-driven fluctuations," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(1), pages 69-83, March.
    13. repec:ipg:wpaper:4 is not listed on IDEAS
    14. Jean-Pierre Drugeon & Bertrand Wigniolle, 2017. "On Time-Consistent Collective Choice with Heterogeneous Quasi- Hyperbolic Discounting," PSE Working Papers halshs-01662833, HAL.

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