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Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 536570, 22 pages
http://dx.doi.org/10.1155/2012/536570
Research Article

Local and Global Dynamics in a Discrete Time Growth Model with Nonconcave Production Function

1Dipartimento di Management, Università Politecnica delle Marche, 60121 Ancona, Italy
2Dipartimento di Economia e Diritto, Università di Macerata, 62100 Macerata, Italy

Received 18 July 2012; Accepted 7 November 2012

Academic Editor: Juan J. Nieto

Copyright © 2012 Serena Brianzoni et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. M. Solow, “A contribution to the theory of economic growth,” Quarterly Journal of Economics, vol. 70, pp. 65–94, 1956.
  2. T. W. Swan, “Economic growth and capital accumulation,” Economic Record, vol. 32, pp. 334–361, 1956.
  3. R. Klump and H. Preissler, “CES production functions and economic growth,” Scandinavian Journal of Economics, vol. 102, no. 1, pp. 41–56, 2000. View at Scopus
  4. W. H. Masanjala and C. Papageorgiou, “The solow model with ces technology: nonlinearities and parameter heterogeneity,” Journal of Applied Econometrics, vol. 19, no. 2, pp. 171–201, 2004. View at Publisher · View at Google Scholar · View at Scopus
  5. R. Klump and O. de La Grandville, “Economic growth and the elasticity of substitution: two theorems and some suggestions,” American Economic Review, vol. 90, no. 1, pp. 282–291, 2000. View at Scopus
  6. N. Kaldor, “Alternative theories of distribution,” Review of Economic Studies, vol. 23, pp. 83–100, 1956.
  7. N. Kaldor, “A model of economic growth,” Economic Journal, vol. 67, pp. 591–624, 1957.
  8. L. L. Pasinetti, “Rate of profit and income distribution in relation to the rate of economic growth,” Review of Economic Studies, vol. 29, pp. 267–279, 1962.
  9. P. A. Samuelson and F. Modigliani, “The Pasinetti paradox in neoclassical and more general models,” Review of Economic Studies, vol. 33, pp. 269–301, 1966.
  10. V. Böhm and L. Kaas, “Differential savings, factor shares, and endogenous growth cycles,” Journal of Economic Dynamics and Control, vol. 24, no. 5–7, pp. 965–980, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. S. Brianzoni, C. Mammana, and E. Michetti, “Complex dynamics in the neoclassical growth model with differential savings and non-constant labor force growth,” Studies in Nonlinear Dynamics and Econometrics, vol. 11, no. 3, article 3, 17 pages, 2007. View at Scopus
  12. S. Brianzoni, C. Mammana, and E. Michetti, “Global attractor in solow growth model with differential savings and endogenic labor force growth,” AMSE Periodicals, Modelling Measurement and Control D, vol. 29, no. 2, pp. 19–37, 2008.
  13. S. Brianzoni, C. Mammana, and E. Michetti, “Nonlinear dynamics in a business-cycle model with logistic population growth,” Chaos, Solitons and Fractals, vol. 40, no. 2, pp. 717–730, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. S. Brianzoni, C. Mammana, and E. Michetti, “Variable elasticity of substituition in a discrete time Solow-Swan growth model with differential saving,” Chaos, Solitons and Fractals, vol. 45, pp. 98–108, 2012.
  15. N. S. Revankar, “A class of variable elasticity of substitution production function,” Econometrica, vol. 39, pp. 61–71, 1971.
  16. G. Karagiannis, T. Palivos, and C. Papageorgiou, “Variable elasticity of substitution and economic growth,” in New Trends in Macroeconomics, D. Claude and C. Kyrtsou, Eds., pp. 21–37, Springer, Berlin, Germany, 2005.
  17. R. A. Becker, “Equilibrium dynamics with many agents,” in Handbook of Optimal Growth Theory, R. A. Dana, C. le Van, T. Mitra, and K. Nihimura, Eds., Springer, Berlin, Germany, 2006.
  18. C. W. Clark, “Economically optimal policies for the utilization of biologically renewable resources,” Mathematical Biosciences, vol. 12, pp. 245–260, 1971. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. A. K. Skiba, “Optimal growth with a convex-concave production function,” Econometrica, vol. 46, no. 3, pp. 527–539, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. T. Kamihigashi and S. Roy, “Dynamic optimization with a nonsmooth, nonconvex technology: the case of a linear objective function,” Economic Theory, vol. 29, no. 2, pp. 325–340, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. T. Kamihigashi and S. Roy, “A nonsmooth, nonconvex model of optimal growth,” Journal of Economic Theory, vol. 132, no. 1, pp. 435–460, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. M. Majumdar and T. Mitra, “Dynamic optimization with a nonconvex technology: the case of a linear objective function,” Review of Economic Studies, vol. 50, no. 1, pp. 143–151, 1983. View at Publisher · View at Google Scholar
  23. V. Capasso, R. Engbers, and D. La Torre, “On a spatial Solow model with technological diffusion and nonconcave production function,” Nonlinear Analysis: Real World Applications, vol. 11, no. 5, pp. 3858–3876, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  24. E. Liz, “Complex dynamics of survival and extinction in simple population models with harvesting,” Theoretical Ecology, vol. 3, no. 4, pp. 209–221, 2010. View at Publisher · View at Google Scholar · View at Scopus
  25. C. Mira, L. Gardini, A. Barugola, and J.-C. Cathala, Chaotic Dynamics in Two-Dimensional Noninvertible Maps, vol. 20, World Scientific Publishing, Singapore, 1996. View at Publisher · View at Google Scholar
  26. G. I. Bischi, C. Mammana, and L. Gardini, “Multistability and cyclic attractors in duopoly games,” Chaos, Solitons and Fractals, vol. 11, no. 4, pp. 543–564, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  27. I. Sushko, A. Agliari, and L. Gardini, “Bistability and border-collision bifurcations for a family of unimodal piecewise smooth maps,” Discrete and Continuous Dynamical Systems B, vol. 5, no. 3, pp. 881–897, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  28. G.-I. Bischi, L. Gardini, and C. Mira, “Contact bifurcations related to critical sets and focal points in iterated maps of the plane,” in Proceedings of the International Workshop Future Direction in Difference Equation, vol. 69, pp. 15–50, Vigo, Spain, June 2011. View at Zentralblatt MATH
  29. R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Benjamin, Menlo Park, Calif, USA, 1986.