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On Ramsey´s conjecture

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  • Gerhard Sorger

    ()

  • Tapan Mitra

    ()

Abstract

Studying a one-sector economy populated by finitely many heterogeneous households that are subject to no-borrowing constraints, we confirm a conjecture by Frank P. Ramsey according to which, in the long run, society would be divided into the set of patient households who own the entire capital stock and impatient ones without any physical wealth. More specifically, we prove (i) that there exists a unique steady state equilibrium that is globally asymptotically stable and (ii) that along every equilibrium the most patient household owns the entire capital of the economy after some finite time. Furthermore, we prove that despite the presence of the no-borrowing constraints all equilibria are efficient. Our results are derived for the continuous-time formulation of the model that was originally used by Ramsey, and they stand in stark contrast to results that – over the last three decades – have been found in the discrete-time version of the model.

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Paper provided by University of Vienna, Department of Economics in its series Vienna Economics Papers with number 1301.

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Date of creation: Jan 2013
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Handle: RePEc:vie:viennp:1301

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  1. Bewley, Truman, 1982. "An integration of equilibrium theory and turnpike theory," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 233-267, September.
  2. Becker, Robert A, 1980. "On the Long-Run Steady State in a Simple Dynamic Model of Equilibrium with Heterogeneous Households," The Quarterly Journal of Economics, MIT Press, vol. 95(2), pages 375-82, September.
  3. Rae, John, 1834. "Statement of Some New Principles on the Subject of Political Economy," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, number rae1834.
  4. Becker, Robert & Mitra, Tapan, 2011. "Efficient Ramsey Equilibria," Working Papers 11-02, Cornell University, Center for Analytic Economics.
  5. 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.
  6. Kirill Borissov, 2011. "On equilibrium dynamics with many agents and wages paid ex ante," EUSP Deparment of Economics Working Paper Series Ec-05/11, European University at St. Petersburg, Department of Economics, revised 28 Apr 2011.
  7. Becker, Robert A & Foias, Ciprian, 1994. "The Local Bifurcation of Ramsey Equilibrium," Economic Theory, Springer, vol. 4(5), pages 719-44, August.
  8. Truman Bewley, 2010. "An Integration of Equilibrium Theory and Turnpike Theory," Levine's Working Paper Archive 1381, David K. Levine.
  9. Sorger, Gerhard, 1994. "On the Structure of Ramsey Equilibrium: Cycles, Indeterminacy, and Sunspots," Economic Theory, Springer, vol. 4(5), pages 745-64, August.
  10. Becker, Robert A. & Foias, Ciprian, 1987. "A characterization of Ramsey equilibrium," Journal of Economic Theory, Elsevier, vol. 41(1), pages 173-184, February.
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Cited by:
  1. Kirill Borissov & Ram Sewak Dubey, 2013. "A Characterization of Ramsey Equilibrium in a Model with Limited Borrowing," EUSP Deparment of Economics Working Paper Series Ec-08/13, European University at St. Petersburg, Department of Economics.
  2. Robert Becker & Ram Dubey & Tapan Mitra, 2014. "On Ramsey equilibrium: capital ownership pattern and inefficiency," Economic Theory, Springer, vol. 55(3), pages 565-600, April.

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