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Global analysis and indeterminacy in a two-sector growth model with human capital

Angelo Antoci, Marcello Galeotti and Paolo Russu ()

MPRA Paper from University Library of Munich, Germany

Abstract: The purpose of the present paper is to highlight some features of global dynamics of the two-sector growth model with accumulation of human and physical capital analyzed by Brito, P. and Venditti, A. (2010). In particular, we explore two cases where the Brito-Venditti system admits two balanced growth paths each of them corresponding, after a change of variables, to an equilibrium point of a 3-dimensional system. In the former one, the two stationary states have, respectively, a 2-dimensional and a 1-dimensional stable manifold (i.e. they are, in the Brito-Venditti terminology, locally indeterminate of order 2 and determinate, respectively). In the latter case, instead, the stable manifolds of the two equilibria have, respectively, dimension two and three (i.e. they are locally indeterminate of order 2 and 3). In both cases we prove the possible existence of points P such that in any neighborhood of P lying on the plane corresponding to a fixed value of the state variable there exist points Q whose positive trajectories tend to either equilibrium point. Moreover we show examples where the 2-dimensional stable manifold of the order 2 locally indeterminate equilibrium, in the former case, and the basin of the attracting equilibrium, in the latter case, are proven to be both unbounded.

Keywords: global and local indeterminacy; two-sector model; endogenous growth; poverty trap; global analysis (search for similar items in EconPapers)
JEL-codes: O41 O10 E24 C02 D90 C61 (search for similar items in EconPapers)
Date: 2012-05
New Economics Papers: this item is included in nep-dge
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Related works:
Journal Article: Global analysis and indeterminacy in a two-sector growth model with human capital (2014) Downloads
Working Paper: Global Analysis and Indeterminacy in a Two-sector Growth Model with Human Capital (2012) Downloads
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