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On Ramsey´s conjecture

Gerhard Sorger () and Tapan Mitra

Vienna Economics Papers from University of Vienna, Department of Economics

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.

JEL-codes: D61 D91 E21 O41 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-dge and nep-hpe
Date: 2013-01
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