Abstract
This work investigates the qualitative and quantitative dynamics of a Solow–Swan growth model with differential savings as proposed by Böhm and Kaas (J Econ Dyn Control 24:965–980, 2000) assuming the shifted Cobb–Douglas (SCD) production function (see Capasso et al. in Nonlinear Anal. 11:3858–3876, 2010) which makes it possible to consider the long-run dynamics of non-developed and developing countries as well as that of developed economies. The resulting model is described by a nonlinear discontinuous map generating both a poverty trap and complex dynamics. Furthermore, multistability phenomena may emerge: besides the “vicious circle of poverty”, long-run behaviours may include boom and bust periods. Complex basins can emerge, hence, economic policies trying to raise the capital per capita may fail and economies may be captured by the poverty trap.
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Andrikopoulos, A., Brox, J., Paraskevopoulos, C.: Interfuel and interfactor substitution in ontario manufacturing, 1962–1982. Appl. Econ. 21, 1–15 (1989)
Azariadis, C., Stachurski, J.: Poverty traps. In: Aghion, P., Steven, D. (eds.) Handbook of Economic Growth, Chapter 5, vol. 1, pp. 294–384. Elsevier, Amsterdam (2005)
Bischi, G., Mammana, C., Gardini, L.: Multistability and cyclic attractors in duopoly games. Chaos Solitons Fractals 11(4), 543–564 (2000)
Böhm, V., Kaas, L.: Differential savings, factor shares, and endogenous growth cycles. J. Econ. Dyn. Control 24, 965–980 (2000)
Brianzoni, S., Mammana, C., Michetti, E.: Complex dynamics in the neoclassical growth model with differential savings and non-constant labor force growth. Stud. Nonlinear Dyn. Econom. 11(3), 1–19 (2007)
Brianzoni, S., Mammana, C., Michetti, E.: Nonlinear dynamics in a business-cycle model with logistic population growth. Chaos Solitons Fractals 40, 717–730 (2009)
Brianzoni, S., Mammana, C., Michetti, E.: Local and global dynamics in a discrete time growth model with nonconcave production function. Discrete Dyn. Nat. Soc. 2012, 1–22 (2012a)
Brianzoni, S., Mammana, C., Michetti, E.: Variable elasticity of substituition in a discrete time Solow–Swan growth model with differential saving. Chaos Solitons Fractals 45, 98–108 (2012b)
Brianzoni, S., Mammana, C., Michetti, E.: Local and global dynamics in a neoclassical growth model with nonconcave production function and nonconstant population growth rate. SIAM J. Appl. Math. 75(1), 61–74 (2015)
Capasso, V., Engbers, R., La Torre, D.: On a spatial solow model with technological diffusion and nonconcave production function. Nonlinear Anal. 11, 3858–3876 (2010)
Cheban, D., Mammana, C., Michetti, E.: Global attractors of quasi-linear non-autonomous difference equations: a growth model with endogenous population growth. Nonlinear Anal. Real World Appl. 14(3), 1716–1731 (2013)
Grassetti, F., Mammana, C., Michetti, E.: Variable elasticity of substitution in the diamond model: dynamics and comparisons. Chaotic Model. Simul. J. 4, 265–275 (2015)
Hamilton, K., Ruta, G., Bolt, K., Markandya, A., Pedroso Galianto, S., Silva, P., Ordoubadi, M.S., Lange, G.M., Tajibaeva, L.: Where Is the Wealth of Nations?. The World Bank, Washington (2005)
Jurgen, A.: Technical change and the elasticity of factor substitution. Technical report. Beitrage der Hochschule Pforzheim, vol. 147 (2014)
Kaldor, N.: Alternative theories of distribution. Rev. Econ. Stud. 23, 83–100 (1956)
Kaldor, N.: A model of economic growth. Econ. J. 67, 591–624 (1957)
Karagiannis, G., Palivos, T., Papageorgiou, C.: Variable elasticity variable elasticity of substitution and economic growth. In: Diebolt, C., Kyrtsou, C. (eds.) New Trends in Macroeconomics, pp. 21–37. Springer, Berlin (2005)
Klump, R., de La Grandville, O.: Economic growth and the elasticity of substitution: two theorems and some suggestions. Am. Econ. Rev. 90(1), 282–291 (2000)
Makrooni, R., Khellat, F., Gardini, L.: Border collision and fold bifurcations in a family of one-dimensional discontinuous piecewise smooth maps: divergence and bounded dynamics. J. Differ. Equ. Appl. 21, 791–824 (2015)
Masanjala, W.H., Papageorgiou, C.: The solow model with ces technology: nonlinearities and the solow model with ces technology: Nonlinearities and parameter heterogeneity. J. Appl. Econom. 19(2), 171–201 (2004)
Miyagiwa, K., Papageorgiou, C.: Elasticity of substitution and growth: normalized ces in the diamond model. Econ. Theory 21(1), 155–165 (2003)
Nguyen, S., Streitwieser, M.: Capital-energy substitution revisited: new evidence from micro data. Working Paper, Center for Economic Studies, US Bureau of the Census, vol. 4 (1997)
Papageorgiou, C., Saam, M.: Two-level ces production technology in the solow and diamond growth models. Scand. J. Econ. 110(1), 119–143 (2008)
Pasinetti, L.L.: Rate of profit and income distribution in relation to the rate of economic growth. Rev. Econ. Stud. 29, 267–279 (1962)
Paterson, N.: Elasticities of substitution in computable general equilibrium models. Working Paper, Department of Finance Canada (2012)
Prywas, M.: A nested ces approach to capital-energy substitution. Energy Econ. 8(1), 22–28 (1986)
Revankar, N.S.: Capital-labor substitution, technological change and eco- nomic growth: the U.S. experience, 1929–1953. Metroeconomica 23, 154–176 (1971)
Sato, R., Hoffman, R.F.: Production functions with variable elasticity of factor substitution: some analysis and testing. Rev. Econ. Stat. 50(4), 453–460 (1968)
Schefold, B.: Zero wages–no problem? A reply to mandler. Metroeconomica 56(4), 503–513 (2005)
Solow, R.M.: A contribution to the theory of economic growth. Q. J. Econ. 70, 65–94 (1956)
Stern, D.: Elasticities of substitution and complementarity. Rensselaer Polytechnic Institute, Department of Economics, Rensselaer Working Papers in Economics (0403) (2004)
Sushko, I., Agliari, A., Gardini, L.: Bistability and border-collision bifurcations for a family of unimodal piecewise smooth maps. Discrete Contin. Dyn. Syst. B 5(3), 881–897 (2005)
Swan, T.W.: Economic growth and capital accumulation. Econ. Rec. 32, 334–361 (1956)
Thompson, P., Taylor, T.: The capital-energy substitutability debate: a new look. Rev. Econ. Stat. 77(3), 565–569 (1995)
Tramontana, F., Gardini, L., Agliari, A.: Endogenous cycles in discontinuous growth models. Math. Comput. Simul. 81, 1625–1639 (2011)
Tramontana, F., Westerhoff, F., Gardini, L.: One-dimensional maps with two discontinuity points and three linear branches: mathematical lessons for understanding the dynamics of financial markets. Decis. Econ. Finance 37, 27–51 (2014)
Tramontana, F., Westerhoff, F., Gardini, L.: A simple financial market model with chartists and fundamentalists: market entry levels and discontinuities. Math. Comput. Simul. 108, 16–40 (2015)
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The authors wish to thank the Editor and the two anonymous Referees for their valuable comments and suggestions.
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Grassetti, F., Mammana, C. & Michetti, E. Poverty trap, boom and bust periods and growth. A nonlinear model for non-developed and developing countries. Decisions Econ Finan 41, 145–162 (2018). https://doi.org/10.1007/s10203-018-0211-6
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DOI: https://doi.org/10.1007/s10203-018-0211-6