Technical Note—Minimizing Cost to Maintain a Steady-State Growth Rate in a Population

Abstract

An approach for estimating the minimum cost of holding a specified steady-state growth rate for a population is given. The behavior of the population is described by a constant “population matrix.” The components of the state vector are the number of women in various age intervals. All age intervals are of equal length and equal to the length of the fundamental time period. Within each age bracket we assume that the fraction of women using birth-control devices is the controllable variable and that the cost depends linearly on the number of women using the devices.