Bifurcations and Chaotic Attractors in an Overlapping Generations Model with Negative Environmental Externalities

  • Angelo Antoci
  • Ahmad NaimzadaEmail author
  • Mauro Sodini


We analyze an overlapping generations model with the following features. There exists a continuum of identical individuals whose welfare depends on leisure, on the stock E of a free access environmental good and on the consumption C of a private good. The private good is produced by a continuum of identical perfectly competitive firms via a constant returns technology (represented by a Cobb–Douglas production function); the representative firm uses physical capitalK and labour L of the representative individual as productive inputs. Each economic agent considers as negligible the negative impact of his choices on the environmental good; this implies that the choices of each agent generate negative externalities on the others.

Following Zhang (1999), Antoci et al. (2007) and Itaya (2008) (among the others), we assume that individuals’ utility function is non separable in E and C; that is, the marginal utility of C depends on the value of E; in particular, we consider both the cases in which marginal utility increases (i.e. C and E are substitutes) and decreases (i.e. C and E are complements) when the value of E decreases.1


Utility Function Chaotic Attractor Economic Agent Negative Externality Private Good 
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  1. Antoci, A. (2009). Environmental degradation as engine of undesirable economic growth via self-protection consumption choices. Ecological Economics, 68, 1385–1397.CrossRefGoogle Scholar
  2. Antoci, A., & Bartolini, S. (1999). Negative externalities as the engine of growth in an evolutionary context (Fondazione Eni Enrico Mattei Working paper 83.99). MilanGoogle Scholar
  3. Antoci, A., & Bartolini, S. (2004). Negative externalities and labor input in an evolutionary game. Environment and Development Economics, 9, 591–562.CrossRefGoogle Scholar
  4. Antoci, A., Galeotti, M., & Russu, P. (2005). Consumption of private goods as substitutes for environmental goods in an economic growth model. Nonlinear Anal-Model Control, 10, 3–34.Google Scholar
  5. Antoci, A., Galeotti, M., & Russu, P. (2007). Undesirable economic growth via economic agents’ self-protection against environmental degradation. Journal of The Franklin Institute, 344, 377–390.CrossRefGoogle Scholar
  6. Antoci, A., Borgesi, S., & Galeotti, M. (2008). Should we replace the environment? Limits of economic growth in the presence of self-protective choices. International Journal of Social Economics, 35, 283–297.CrossRefGoogle Scholar
  7. Bartolini, S., & Bonatti, L. (2002). Environmental and social degradation as the engine of economic growth. Ecological Economics, 43, 1–16.CrossRefGoogle Scholar
  8. Bartolini, S., & Bonatti, L. (2003). Undesirable growth in a model with capital accumulation and environmental assets. Environment and Development Economics, 8, 11–30.Google Scholar
  9. Benhabib, J., & Farmer, R. E. (1999). Indeterminacy and sunspots in macroeconomics. In J. B. Taylor & M. Woodford (Eds.), Handbook of macroeconomics. Amsterdam: North-Holland.Google Scholar
  10. Benhabib, J., Nishimura, K., & Shigoka, T. (2008). Bifurcation and sunspots in the continuous time equilibrium model with capacity utilization. Journal of Economic Theory, 4, 337–355.CrossRefGoogle Scholar
  11. Bennet, R. L., & Farmer, R. E. (2000). Indeterminacy with non-separable utility. Journal of Economic Theory, 93, 118–143.CrossRefGoogle Scholar
  12. Cazzavillan, G., Lloyd-Braga, T., & Pintus, P. (1998). Multiple steady states and endogenous fluctuations with increasing returns to scale in production. Journal of Economic Theory, 80, 60–107.CrossRefGoogle Scholar
  13. Cazzavillan, G. (2001). Indeterminacy and endogenous fluctuations with arbitrarily small externalities. Journal of Economic Theory, 101, 133–157.CrossRefGoogle Scholar
  14. Chen, B. L., & Lee, S. F. (2007). Congestible public goods and local indeterminacy: A two-sector endogenous growth model. Journal of Economic Dynamics and Control, 31, 2486–2518.CrossRefGoogle Scholar
  15. Coury, T., & Wen, Y. (2009). Global indeterminacy in locally determinate real business cycle models. International Journal of Economic Theory, 101, 133–157.Google Scholar
  16. Duranton, G. (2001). Endogenous labour supply, growth and overlapping generations. Journal of Economic Behavior and Organization, 44, 295–314.CrossRefGoogle Scholar
  17. Grandmont, J. M., Pintus, P., & de Vilder, R. (1998). Capital-labor substitution and competitive nonlinear endogenous business cycles. Journal of Economic Theory, 80, 14–59.CrossRefGoogle Scholar
  18. Hueting, R. (1980). New scarcity and economic growth. More welfare through less production? Amsterdam: North Holland.Google Scholar
  19. Itaya, J.-I. (2008). Can environmental taxation stimulate growth? The role of indeterminacy in endogenous growth models with environmental externalities. Journal of Economic Dynamics and Control, 32, 1156–1180.CrossRefGoogle Scholar
  20. Krugman, P. (1991). History versus expectations. Quarterly Journal of Economics, 106, 651–667.CrossRefGoogle Scholar
  21. Leipert, C. (1989). National Income and economic growth: The conceptual side of defensive expenditures. Journal of Economic Issues, 23, 843–856.Google Scholar
  22. Leipert, C., & Simonis, U. E. (1988). Environmental damage – environmental expenditures: Statistical evidence on the federal republic of Germany. International Journal of Social Economics, 15, 37–52.CrossRefGoogle Scholar
  23. Matsuyama, K. (1991). Increasing returns, industrialization, and indeterminacy of equilibrium. Quarterly Journal of Economics, 106, 587–597.CrossRefGoogle Scholar
  24. Meng, Q., & Yip, C. K. (2008). On indeterminacy in one-sector models of the business cycle with factor-generated externalities. Journal of Macroeconomics, 30, 97–110.CrossRefGoogle Scholar
  25. Pintus, P., Sands, D., & deVilder, R. (2000). On the transition from local regular to global irregular fluctuations. Journal of Economic Dynamics and Control, 24, 247–272.CrossRefGoogle Scholar
  26. Reichlin, P. (1986). Equilibrium cycles in an overlapping generations economy with production. Journal of Economic Theory, 40, 89–102.CrossRefGoogle Scholar
  27. Shogren, J. F., & Crocker, T. D. (1991). Cooperative and non-cooperative protection against transferable and filterable externalities. Environmental and Resource Economics, 1, 195–213.CrossRefGoogle Scholar
  28. Zhang, J. (1999). Environmental sustainability, nonlinear dynamics and chaos. Economic Theory, 14, 489–500.CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Dipartimento diMetodi QuantitativiUniversità di Milano-BicoccaMilanoItaly

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