Abstract
The purpose of this paper is to highlight certain features of a dynamic optimisation problem in an economic growth model with environmental negative externalities that gives rise to a two-dimensional dynamical system. In particular, it is demonstrated that the dynamics of the model, which is based on a production function with perfect substitutability (perfect substitution technologies), admits a locally attracting equilibrium with a basin of attraction that may be considerably large, as it can extend up to the boundary of the system phase plane. Moreover, this model exhibits global indeterminacy because either equilibrium of the system can be selected according to agent expectation. Formulas for the calculation of the bifurcation coefficients of the system are derived, and a result on the existence of limit cycles is obtained. A numerical example is given to illustrate the results.
Highlights
Equilibrium selection in dynamic optimisation models with externalities may depend on the expectations of economic agents rather than the history of the economy, as pointed out in [22] and [28]
The purpose of this paper is to highlight certain features of a dynamic optimisation problem in an economic growth model with environmental negative externalities that gives rise to a two-dimensional dynamical system
It is demonstrated that the dynamics of the model, which is based on a production function with perfect substitutability, admits a locally attracting equilibrium with a basin of attraction that may be considerably large, as it can extend up to the boundary of the system phase plane
Summary
Equilibrium selection in dynamic optimisation models with externalities may depend on the expectations of economic agents rather than the history of the economy, as pointed out in [22] and [28]. In [2], the authors assumed that the production technology is represented by the Cobb– Douglas function Y (t) = K(t)αL(t)βE(t)γ with α+β +γ < 1 and α, β, γ > 0, whereas in the present study, a linear production function (perfect substitution technologies) is proposed This production function with perfect substitutability allows the investigation of system complexity. It is possible to determine the range of the continuum of initial values Li0 such that the trajectories form (K0, E0, Li0) approach a stable equilibrium; see Section 4.3.
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