Growth Dynamics and Returns to Scale : Bifurcation Analysis

We investigate the dependence of the dynamic behavior of an endogenous growth model on the degree of returns to scale. We focus on a simple (but representative) growth model with publicly funded inventive activity. We show that constant returns to reproducible factors (the leading case in the endogenous growth literature) is a bifurcation point, and that it has the characteristics of a transcritical bifurcation. The bifurcation involves the boundary of the state space, making it difficult to formally verify this classification. For a special case, we provide a transformation that allows formal classification by existing methods. We discuss the new methods that would be needed for formal verification of transcriticality in a broader class of models