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

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