A multiple criteria economic growth model with environmental quality and logistic population behaviour with variable carrying capacity

We propose a new dynamic (macro)economic model that describes the interaction between physical capital, environmental quality and population dynamics. With respect to other models in literature, our formulation describes the effects of environmental quality on the carrying capacity of a logistic population growth model, and it aims at quantifying the environmental effects on public health. We then present a multiple criteria optimal control problem with finite horizon. Using a scalarization technique and an innovative algorithm based on the numerical solution of forward–backward differential equations, we determine the optimal trajectories of the state and control variables and then an approximation of the Pareto frontier.