The Genuine Savings Criterion and the Value of Population in an Economy with Endogenous Fertility Rate

OPTIMAL CONTROL OF AGE-STRUCTURED POPULATIONS IN ECONOMY, DEMOGRAPHY, AND THE ENVIRONMENT, R. Boucekkine, pp. 20-44, N. Hritonenko, Y. Yatsenko, eds., Taylor & Francis, UK, 2011

26 Pages Posted: 9 Feb 2008 Last revised: 30 Mar 2014

See all articles by Kenneth J. Arrow

Kenneth J. Arrow

Stanford University - Department of Economics

Alain Bensoussan

University of Texas at Dallas - Naveen Jindal School of Management

Qi Feng

Mitchell E. Daniels, Jr School of Business, Purdue University

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Date Written: October 27, 2009

Abstract

We study an economy in which the rate of change of population depends on population policy decisions. This requires population as well as capital as state variables. By showing the algebraic relationship between the shadow price of the population and the shadow price of the per capita capital stock, we are still able to depict the optimal path and its convergence to the long-run equilibrium on a two-dimensional phase diagram. Moreover, we derive explicitly the expression of genuine savings in our model to evaluate the sustainability of the system.

Keywords: savings, genuine savings, green gross national product, population policy, value of the population, economic growth, optimal control, phase diagram, dynamic programming, Maximum principle

JEL Classification: O4, C61, A13, I12, I18,I28, J13, O10, O21

Suggested Citation

Arrow, Kenneth J. and Bensoussan, Alain and Feng, Qi and Sethi, Suresh, The Genuine Savings Criterion and the Value of Population in an Economy with Endogenous Fertility Rate (October 27, 2009). OPTIMAL CONTROL OF AGE-STRUCTURED POPULATIONS IN ECONOMY, DEMOGRAPHY, AND THE ENVIRONMENT, R. Boucekkine, pp. 20-44, N. Hritonenko, Y. Yatsenko, eds., Taylor & Francis, UK, 2011 , Available at SSRN: https://ssrn.com/abstract=1091628

Kenneth J. Arrow

Stanford University - Department of Economics ( email )

Landau Economics Building
579 Serra Mall
Stanford, CA 94305-6072
United States

Alain Bensoussan

University of Texas at Dallas - Naveen Jindal School of Management ( email )

800 West Campbell Rd
SM 30
Richardson, TX 75080-3021
United States
9728836117 (Phone)

HOME PAGE: http://www.utdallas.edu/~axb046100/

Qi Feng

Mitchell E. Daniels, Jr School of Business, Purdue University ( email )

403 Mitch Daniels Blvd.
West Lafayette, IN 47907
United States

Suresh Sethi (Contact Author)

University of Texas at Dallas - Naveen Jindal School of Management ( email )

800 W. Campbell Road, SM30
Richardson, TX 75080-3021
United States

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