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Global Analysis and Indeterminacy in a Two-sector Growth Model with Human Capital

  • Angelo Antoci


    (Università degli Studi di Sassari)

  • Marcello Galeotti


    (Università degli Studi di Firenze,)

  • Paolo Russu

    (Università degli Studi di Sassari)

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 and Venditti, which is a specification of the model proposed by Mulligan and Sala-i-Martin. In particular, our analysis focuses on the context in which 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, and proves 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. This implies that equilibrium selection in Brito Venditti system may depend on expectations of economic agents rather than on the history of the economy. That is, economies with identical technologies and preferences, starting from the same initial values of the state variables (history), may follow rather different equilibrium trajectories according to the economic agents' choices of the initial values of the jumping variables (expectations). Moreover we prove that the basins of attraction (two or three dimensional) of locally indeterminate equilibrium points may be very large, as they may extend up to the boundary of the system phase space.

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Paper provided by Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa in its series Working Papers - Economics with number wp2012_14.rdf.

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Length: 31 pages
Date of creation: 2012
Date of revision:
Handle: RePEc:frz:wpaper:wp2012_14.rdf
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  1. 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.
  2. Sergey Slobodyan, 2002. "Indeterminacy and Stability in a Modified Romer Model," CERGE-EI Working Papers wp205, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
  3. Benhabib Jess & Farmer Roger E. A., 1994. "Indeterminacy and Increasing Returns," Journal of Economic Theory, Elsevier, vol. 63(1), pages 19-41, June.
  4. Brito, Paulo & Venditti, Alain, 2010. "Local and global indeterminacy in two-sector models of endogenous growth," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 893-911, September.
  5. 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.
  6. Franz Wirl, 2011. "Conditions for indeterminacy and thresholds in neoclassical growth models," Journal of Economics, Springer, vol. 102(3), pages 193-215, April.
  7. 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.
  8. 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.
  9. 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.
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