Abstract: In this paper, a Cass-Koopmans model with solvable endogenous fertility is given. We prove that the multiple growth paths and multiple steady states exist when the paramenters a and θ satisfies a>1+θ/2 and there is only one nonzero stead state and an unique growth path when a ≤ 1+θ/2. So the dynamical system undergoes a bifurcation when a=1+θ/2.We discuss the geometric properties of th multiple growth paths and explain the economic sence of the main results.

Key words: Cass-Koopmans model, Multlple growth paths, Multiple steady states, Dynapsical System, Bifurcation