Indeterminacy, bifurcations and chaos in an overlapping generations model with negative environmental externalities

Abstract

We analyze an overlapping generations model where agent's welfare depends on three goods: leisure, environmental quality and consumption of a private good. We assume that the production process of the private good depletes the natural resource and that the consumption of the private good alleviates the damages due to environmental deterioration. In such context, we show that individuals' reactions to environmental deterioration may lead to complex dynamics, in particular to the rise of periodic orbits and chaos.

Poverty trap and global indeterminacy in a growth model with open-access natural resources

“…Since our system meets the Mangasarian hypotheses, the above conditions plus the limit transversality condition lim t→+∞ Ω(t)K(t)e −θt = 0 are sufficient for solving problem (2). This is the case also if α + β + γ > 1 (remember we assumed α + β < 1), because the stock E is considered as a positive externality in the decision problem of the representative agent.…”

“…We analyze a growth model with environmental externalities, giving rise to a three-dimensional nonlinear dynamic system (the framework is that introduced by Wirl [53]). 2 In particular, we study 1 In the present work we are not dealing with another important problem in economic dynamics, namely the existence of indifference points in an optimal control problem. Starting from these points, several optimal solutions exist, giving rise to the same value of the objective function (see the seminal contributions of Sethi [48], Skiba [49], Dechert and Nishimura [24] and, among the others, the recent works of Hartl et al [27], Caulkins et al [19,20], Wirl and Feichtinger [55], Wagener [50,51]).…”

“…In Meng and Yip [38] indeterminacy is produced by negative capital externalities. In Antoci et al [1] and in Antoci and Sodini [2] negative externalities may generate indeterminacy in an economy where private goods can be consumed as substitutes for free-access environmental goods. The present paper has the following structure.…”

“…Therefore, when multiple Nash equilibrium trajectories exist, starting from the same initial values of the state variables, economic agents may select one which is Pareto-dominated by others, due to coordination problems. 2 Wirl analyzes dynamic optimization problems of competitive agents with one state variable x and one dynamic externality y. Whereas the time evolution of y is affected by agents' choices, the impact due to each single agent is negligible; consequently, the evolution of y is considered as an exogenous datum.…”

Nonlinear Dynamics in an OLG Growth Model with Young and Old Age Labour Supply: The Role of Public Health Expenditure

“…The income of the young is taxed away by the government at the constant rate 1 0 < < τ , which uses the revenues so collected to finance a balanced-budget public health programme (e.g., hospitals, vaccines, scientific research and so on). Individuals consume only when old (see, e.g., Galor and Weil, 1996;Grandmont et al, 1998;Antoci and Sodini, 2009 …”