The dynamics of fertility in C-K model with endogenous fertility

Based on the Cass-Koopmans Model with endogenous fertility given in the paper [1-4], the fertility dynamics is discussed in this paper. It is proved that the first quadrant of the k,c plane is separated into two parts by a increasingly differentiable curve. The fertility increases with time on the upper half and decreases with time on the lower half. The fertility decreases along one arm of the economic growth path on which the per capita capital and per consumption increase and increases along the other arm of the economic growth path on which the per capita capital and per person consumption decrease under the condition 0 < theta < alpha. This confirms the empirical finds that negative relationship between the economic growth and population growth.