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Model of neo-Malthusian population anticipating future changes in resources

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  • Michel, Philippe

Abstract

In this paper we develop a class of models to study a population and resource dynamical system in which the decision to give birth is based on a rational far-sighted cost–benefit analysis on what the future of the resource level will be. This leads to consider a system in which a time forward population/resource dynamical system is coupled with a time backward Bellman’s equation (which models the choice of having a child). We construct, from a population model with food consumption, an example, to study the change in time of the fertility rate when a catastrophic change in resource is announced at a given moment, when a birth control policy is announced and we compare these two announcements in case nothing happens. Moreover, we provide, mathematical tools to theoretically and numerically study this complex coupling of time forward and time backward equations.

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  • Michel, Philippe, 2021. "Model of neo-Malthusian population anticipating future changes in resources," Theoretical Population Biology, Elsevier, vol. 140(C), pages 16-31.
    • Handle: RePEc:eee:thpobi:v:140:y:2021:i:c:p:16-31
    DOI: 10.1016/j.tpb.2021.03.002
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