Optimal savings and the value of population.

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Optimal savings and the value of population. Abstract Text:

Kenneth J Arrow,Alain Bensoussan,Qi Feng,Suresh P Sethi,Kenneth J Arrow,Alain Bensoussan,Qi Feng,Suresh P Sethi,

We study a model of economic growth in which an exogenously changing population enters in the objective function under total utilitarianism and into the state dynamics as the labor input to the production function. We consider an arbitrary population growth until it reaches a critical level (resp. saturation level) at which point it starts growing exponentially (resp. it stops growing altogether). This requires population as well as capital as state variables. By letting the population variable serve as the surrogate of time, we are still able to depict the optimal path and its convergence to the long-run equilibrium on a two-dimensional phase diagram. The phase diagram consists of a transient curve that reaches the classical curve associated with a positive exponential growth at the time the population reaches the critical level. In the case of an asymptotic population saturation, we expect the transient curve to approach the equilibrium as the population approaches its saturation level. Finally, we characterize the approaches to the classical curve and to the equilibrium.

Optimal savings and the value of population. Publishing Authors By Initials

KJ Arrow,A Bensoussan,Q Feng,SP Sethi,KJ Arrow,A Bensoussan,Q Feng,SP Sethi,

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Optimal savings and the value of population. Journal Published:

PUBLICATION TYPE: Journal Article

Journal: Proceedings of the National Academy of Sciences of

VOLUME: 104

Page Numbers: 18421-6

Journal Abbreviation: Proc. Natl. Acad. Sci. U.S.A.

ISSN: 1091-6490

DAY: 5

MONTH: 11

YEAR: 2007

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LANGUAGE: eng

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AFFILIATION: Department of Economics, Stanford University, Stanford, CA 94305, USA. arrow@stanford.edu

Country: United States

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MEDLINETA: Proc Natl Acad Sci U S A

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