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

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  • Antoci, Angelo
  • Galeotti, Marcello
  • Russu, Paolo

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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 39079.

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Date of creation: May 2012
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Handle: RePEc:pra:mprapa:39079

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Keywords: global and local indeterminacy; two-sector model; endogenous growth; poverty trap; global analysis;

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  1. Paolo Mattana & Kazuo Nishimura & Tadashi Shigoka, 2009. "Homoclinic bifurcation and global indeterminacy of equilibrium in a two-sector endogenous growth model," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(1), pages 25-47.
  2. Paulo Brito & Alain Venditti, 2009. "Local and global indeterminacy in two-sector models of endogenous growth," Working Papers halshs-00408018, HAL.
  3. Sergey Slobodyan, 2002. "Indeterminacy and Stability in a Modified Romer Model," CERGE-EI Working Papers wp205, The Center for Economic Research and Graduate Education - Economic Institute, Prague.
  4. Antoci, Angelo & Galeotti, Marcello & Russu, Paolo, 2011. "Poverty trap and global indeterminacy in a growth model with open-access natural resources," Journal of Economic Theory, Elsevier, vol. 146(2), pages 569-591, March.
  5. Benhabib Jess & Perli Roberto, 1994. "Uniqueness and Indeterminacy: On the Dynamics of Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 63(1), pages 113-142, June.
  6. Benhabib, Jess & Farmer, Roger E.A., 1999. "Indeterminacy and sunspots in macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 6, pages 387-448 Elsevier.
  7. Tarek Coury & Yi Wen, 2009. "Global indeterminacy in locally determinate real business cycle models," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(1), pages 49-60.
  8. Jess Benhabib & Roger E.A. Farmer, 1992. "Indeterminacy and Increasing Returns," UCLA Economics Working Papers 646, UCLA Department of Economics.
  9. Franz Wirl, 2011. "Conditions for indeterminacy and thresholds in neoclassical growth models," Journal of Economics, Springer, vol. 102(3), pages 193-215, April.
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Cited by:
  1. Carboni, Oliviero A. & Russu, Paolo, 2013. "Linear production function, externalities and indeterminacy in a capital-resource growth model," Journal of Mathematical Economics, Elsevier, vol. 49(5), pages 422-428.
  2. OA. Carboni & P. Russu, 2012. "Global Indeterminacy in a Tourism Sector Model," Working Paper CRENoS 201230, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.

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