The C-K model with solvable endogenous fertility

Abstract

In this paper, a C-K model with solvable endogenous fertility under the strongly additive utility function is presented. The discrimination conditions of the existence of the nonzero steady states are given. Under a kind of utility function and production function, we prove that these conditions are satisfied and the economy at least has an optimal growth path. The positional relationship of the multiple steady states on the plane is discussed when multiple steady states and multiple growth paths exist. By numerical analysis, the fertility decreases with the per capita capital and per capita consumption increasing and increases with the per capita capital and per capita consumption decreasing on the economic growth path are obtained.