On Ramsey´s conjecture
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.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Bewley, Truman, 1982. "An integration of equilibrium theory and turnpike theory," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 233-267, September.
- 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.
- Truman Bewley, 2010. "An Integration of Equilibrium Theory and Turnpike Theory," Levine's Working Paper Archive 1381, David K. Levine.
- 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.
- Sorger, Gerhard, 1994. "On the Structure of Ramsey Equilibrium: Cycles, Indeterminacy, and Sunspots," Economic Theory, Springer, vol. 4(5), pages 745-64, August.
- 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.
- Robert A. Becker & Tapan Mitra, 2011.
"Efficient Ramsey Equilbria,"
Caepr Working Papers
2011-009, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
- 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.
- Becker, R.C. & Foias, C., 1992.
"The Local Bifurcation of Ramsey Equilibrium,"
92-002, Indiana - Center for Econometric Model Research.
- Becker, Robert A. & Foias, Ciprian, 1987. "A characterization of Ramsey equilibrium," Journal of Economic Theory, Elsevier, vol. 41(1), pages 173-184, February.
When requesting a correction, please mention this item's handle: RePEc:vie:viennp:1301. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Paper Administrator)
If references are entirely missing, you can add them using this form.