Math. Model. Nat. Phenom.
Volume 14, Number 1, 2019
Economics and the environment: distributed optimal control models
|Number of page(s)||15|
|Published online||02 April 2019|
The optimal population size under pollution and migration externalities: a spatial control approach★
University of Dubai, Dubai Business School,
2 University of Milan, Department of Economics, Management, and Quantitative Methods, Milan, Italy.
3 University of Pisa, Department of Economics and Management, via Cosimo Ridofi 10, Pisa 56124, Italy.
4 University of Cagliari, Department of Economics and Management, Cagliari, Italy.
* Corresponding author: firstname.lastname@example.org
Accepted: 22 January 2019
We analyze the implications of pollution and migration externalities on the optimal population dynamics in a spatial setting. We focus on a framework in which pollution affects the mortality rate and decreases utility, while migration occurs within the spatial economy. Agents optimally determine their fertility rate which, along with pollution-induced mortality and spatial migration, determines the net population growth rate. This setting implies that human population follows an endogenous logistic-type dynamics where fertility choices determine what the optimal limit of human population will be. We compare the decentralized and the centralized outcomes showing that such fertility decisions generally differ, quantifying the extent to which pollution and migration induced externalities matter in determining the difference between the two outcomes. We show that, due to the effects of pollution on utility and mortality, both the optimal fertility rate and the population size are smallest in the centralized economy but migration effects change not only the size of these differences but also their direction, suggesting that the spatial channel is an important mechanism to account for in the process of policymaking.
Mathematics Subject Classification: C60 / J10 / O40 / Q52
Key words: Diffusion / endogenous fertility / pollution-induced mortality / spatial dynamics
© EDP Sciences, 2019
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