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Equilibria in Altruistic Economic Growth Models

Author

Listed:
  • Łukasz Balbus

    (University of Zielona Góra)

  • Anna Jaśkiewicz

    (Wrocław University of Science and Technology)

  • Andrzej S. Nowak

    (University of Zielona Góra)

Abstract

In this paper, we consider a stochastic economic growth model in the form of an intergenerational dynamic game. Both paternalistic and non-paternalistic components are present in the model. Under very general assumptions allowing for unbounded utility functions and weakly continuous transitions, we establish the existence of Markov perfect equilibria that consist of a consumption strategy and an indirect utility function. In the pure paternalistic case, we obtain new results on equilibria. An important point of our contribution is that we make no separability assumptions on the utility functions of generations.

Suggested Citation

  • Łukasz Balbus & Anna Jaśkiewicz & Andrzej S. Nowak, 2020. "Equilibria in Altruistic Economic Growth Models," Dynamic Games and Applications, Springer, vol. 10(1), pages 1-18, March.
  • Handle: RePEc:spr:dyngam:v:10:y:2020:i:1:d:10.1007_s13235-019-00305-3
    DOI: 10.1007/s13235-019-00305-3
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    References listed on IDEAS

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    1. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2013. "A constructive geometrical approach to the uniqueness of Markov stationary equilibrium in stochastic games of intergenerational altruism," Journal of Economic Dynamics and Control, Elsevier, vol. 37(5), pages 1019-1039.
    2. Barro, Robert J, 1974. "Are Government Bonds Net Wealth?," Journal of Political Economy, University of Chicago Press, vol. 82(6), pages 1095-1117, Nov.-Dec..
    3. Loury, Glenn C, 1981. "Intergenerational Transfers and the Distribution of Earnings," Econometrica, Econometric Society, vol. 49(4), pages 843-867, June.
    4. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    5. Hori, Hajime, 1997. "Dynamic Allocation in an Altruistic Overlapping Generations Economy," Journal of Economic Theory, Elsevier, vol. 73(2), pages 292-315, April.
    6. E. S. Phelps & R. A. Pollak, 1968. "On Second-Best National Saving and Game-Equilibrium Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 185-199.
    7. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    8. Jorge Durán, 2003. "Discounting long run average growth in stochastic dynamic programs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(2), pages 395-413, September.
    9. Jorge DurÂn, 2000. "On dynamic programming with unbounded returns," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(2), pages 339-352.
    10. Anna Jaśkiewicz & Andrzej Nowak, 2011. "Stochastic Games with Unbounded Payoffs: Applications to Robust Control in Economics," Dynamic Games and Applications, Springer, vol. 1(2), pages 253-279, June.
    11. Wolfgang Leininger, 1986. "The Existence of Perfect Equilibria in a Model of Growth with Altruism between Generations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(3), pages 349-367.
    12. Simone Galperti & Bruno Strulovici, 2017. "A Theory of Intergenerational Altruism," Econometrica, Econometric Society, vol. 85, pages 1175-1218, July.
    13. Dutta, Prajit K & Sundaram, Rangarajan, 1992. "Markovian Equilibrium in a Class of Stochastic Games: Existence Theorems for Discounted and Undiscounted Models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(2), pages 197-214, April.
    14. Sundaram, Rangarajan K., 1989. "Perfect equilibrium in non-randomized strategies in a class of symmetric dynamic games," Journal of Economic Theory, Elsevier, vol. 47(1), pages 153-177, February.
    15. 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.
    16. Ray, Debraj, 1987. "Nonpaternalistic intergenerational altruism," Journal of Economic Theory, Elsevier, vol. 41(1), pages 112-132, February.
    17. Boud, John III, 1990. "Recursive utility and the Ramsey problem," Journal of Economic Theory, Elsevier, vol. 50(2), pages 326-345, April.
    18. Balbus, Łukasz & Jaśkiewicz, Anna & Nowak, Andrzej S., 2016. "Non-paternalistic intergenerational altruism revisited," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 27-33.
    19. Matthew O. Jackson & Andrew McLennan (ed.), 2008. "Foundations in Microeconomic Theory," Springer Books, Springer, number 978-3-540-74057-5, November.
    20. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, November.
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