An economic growth model with endogenous fertility: multiple growth paths, poverty trap and bifurcation

In this paper, an extended Ramsey model with endogenous fertility is present. The existence, uniqueness and multiplicity of the steady states of the model are given. When the multiple steady states exist, the steady state with low fertility has high per capita capital and per capital consumption, which can explain the persistent difference in consumption and fertility between poor and rich countries. The dynamical system undergoes a bifurcation when parameters satisfy some given conditions.