Ramsey’s Conjecture in a Stochastically Growing Economy

  • Tamotsu NakamuraEmail author


Becker (1980) confirms Ramsey’s conjecture (Ramsey 1928) in a discrete-time model by proving that the most patient individuals own the entire capital of the economy, while others consume their wage income in the long-run.



The author would like to thank Professors Kentaro Iwatsubo, Tetsugen Haruyama, Daishin Yasui and seminar participants at the Kobe University. The financial support of Grants-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (15K03431 and 17K18564) is gratefully acknowledged. The usual disclaimer applies.


  1. Becker, R.A. 1980. On the long-run steady state in a simple dynamic model of equilibrium with heterogeneous households. Quarterly Journal of Econonomics 95 (2): 375–82.CrossRefGoogle Scholar
  2. Becker, R.A., and I. Zilcha. 1997. Stationary Ramsey equilibria under uncertainty. Journal of Economic Theory 75: 122–140.CrossRefGoogle Scholar
  3. Boyd III, J.H., 2000. Sustained growth with heterogeneous households, International Florida University.
  4. Duffie, D., and L.G. Epstein. 1992. Stochastic differential utility. Econometrica 60 (2): 353–94.CrossRefGoogle Scholar
  5. Epstein, L.G., and S.E. Zin. 1989. Substitution, risk aversion, and the temporal behavior of consumption and asset returns: a theoretical framework. Econometrica 57: 937–969.CrossRefGoogle Scholar
  6. Epstein, L.G., and S.E. Zin. 1991. Substitution, risk aversion, and the temporal behavior of consumption and asset returns: an empirical analysis. Journal of Political Economy 99: 263–286.CrossRefGoogle Scholar
  7. Kreps, D.M., and E.L. Porteus. 1978. Temporal resolution of uncertainty and dynamic choice theory. Econometrica 46: 185–200.CrossRefGoogle Scholar
  8. Kreps, D.M., and E.L. Porteus. 1979. Dynamic choice theory and dynamic programming. Econometrica 47: 91–100.CrossRefGoogle Scholar
  9. Mitra, T., and G. Sorger. 2013. On Ramsey’s conjecture. Journal of Economic Theory 148 (5): 1953–1976.CrossRefGoogle Scholar
  10. Nakamura, T. 2014. On Ramsey’s conjecture with AK technology. Economics Bulletin 34 (2): 875–884.Google Scholar
  11. Obstfeld, M. 1994a. Evaluating risky consumption paths: the role of inter temporal substitutability. European Economic Review 38: 1471–1486.CrossRefGoogle Scholar
  12. Obstfeld, M. 1994b. Risk-taking, global diversification, and growth. American Economic Review 84: 1310–1329.Google Scholar
  13. Ramsey, F.P. 1928. A mathematical theory of saving. Economic Journal 38: 543–559.CrossRefGoogle Scholar
  14. Weil, Philippe. 1989. The equity puzzle and the risk-free puzzle. Journal of Monetary Economics 24: 401–421.CrossRefGoogle Scholar
  15. Smith, W.T. 1996a. Feasibility and transversality conditions for models of portfolio choice with non-expected utility in continuous time. Economics Letters 53 (2): 123–31.CrossRefGoogle Scholar
  16. Smith, W.T. 1996b. Taxes, uncertainty, and long-term growth. European Economic Review 40 (8): 1647–64.CrossRefGoogle Scholar
  17. Stokey, N., and R.E. Lucas Jr. 1989. Recursive methods in economic dynamics. Harvard University Press.Google Scholar

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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Kobe UniversityKobeJapan

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