Mathematical analysis of an economic growth model with perfect-substitution technologies
Paolo Russu
University of Sassari
Published 2020-01-10


dynamic optimisation problem
economic growth model
environmental economics
Hopf bifurcation
Poincaré compactification

How to Cite

Russu P. (2020) “Mathematical analysis of an economic growth model with perfect-substitution technologies”, Nonlinear Analysis: Modelling and Control, 25(1), pp. 84–107. doi: 10.15388/namc.2020.25.15733.


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.

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