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

Antoci, Angelo and Galeotti, Marcello and Russu, Paolo (2012): Global analysis and indeterminacy in a two-sector growth model with human capital.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: global and local indeterminacy; two-sector model; endogenous growth; poverty trap; global analysis
• Subjects: O - Economic Development, Innovation, Technological Change, and Growth > O4 - Economic Growth and Aggregate Productivity > O41 - One, Two, and Multisector Growth Models; O - Economic Development, Innovation, Technological Change, and Growth > O1 - Economic Development > O10 - General; E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy > E24 - Employment ; Unemployment ; Wages ; Intergenerational Income Distribution ; Aggregate Human Capital ; Aggregate Labor Productivity; C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods; D - Microeconomics > D9 - Intertemporal Choice > D90 - General; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis

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