Optimal population growth as an endogenous discounting problem: The Ramsey case



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Boucekkine, Raouf and Martínez Gonzalo, Blanca and Ruiz Tamarit, J. Ramón (2017) Optimal population growth as an endogenous discounting problem: The Ramsey case. [ AMSE Working Papers; nº 1731, ]

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This paper revisits the optimal population size problem in a continuous time Ramsey setting with costly child rearing and both intergenerational and intertemporal altruism. The social welfare functions considered range from the Millian to the Benthamite. When population growth is endogenized, the associated optimal control problem involves an endogenous effective discount rate depending on past and current population growth rates, which makes preferences intertemporally dependent. We tackle this problem by using an appropriate maximum principle. Then we study the stationary solutions (balanced growth paths) and show the existence of two admissible solutions except in the Millian case. We prove that only one is optimal. Comparative statics and transitional dynamics are numerically derived in the general case.

Item Type:Working Paper or Technical Report
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Capítulo de libro:
Boucekkine R., Martínez B., Ruiz-Tamarit J.R. (2018) Optimal Population Growth as an Endogenous Discounting Problem: The Ramsey Case. In: Feichtinger G., Kovacevic R., Tragler G. (eds) Control Systems and Mathematical Methods in Economics. Lecture Notes in Economics and Mathematical Systems, vol 687. Springer, Cham

Uncontrolled Keywords:Optimal population size, Population ethics, Optimal growth, Endogenous discounting, Optimal demographic transitions
Subjects:Sciences > Statistics > Mathematical optimization
Social sciences > Sociology > Demography
Social sciences > Economics > Economic development
JEL:C61, C62, J1, O41
Series Name:AMSE Working Papers
ID Code:60768
Deposited On:04 Jun 2020 11:29
Last Modified:04 Jun 2020 11:29

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