Optimal Population Growth as an Endogenous Discounting Problem: The Ramsey Case

Raouf Boucekkine (), Blanca Martinez () and José Ruiz-Tamarit

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Abstract: 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.

Keywords: optimal population size; optimal growth; population ethics; endogenous discounting; optimal demographic transitions (search for similar items in EconPapers)
Date: 2017-08
New Economics Papers: this item is included in nep-dge and nep-gro
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01579155v1
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Citations: View citations in EconPapers (2)

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Related works:
Chapter: Optimal Population Growth as an Endogenous Discounting Problem: The Ramsey Case (2018)
Working Paper: Optimal Population Growth as an Endogenous Discounting Problem: The Ramsey Case (2018)
Working Paper: Optimal Population Growth as an Endogenous Discounting Problem: The Ramsey Case (2017)
Working Paper: Optimal population growth as an endogenous discounting problem: The Ramsey case (2017)
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