The (Interesting) Dynamic Properties of the Neoclassical Growth Model with CES Production

Despite being the standard growth model for several decades, little is actually known analytically about the dynamic properties of the neoclassical Ramsey-Cass-Koopmans growth model. This papers derives analytically the properties of the endogenous savings rate when technology takes the Constant Elesticity of Substitution (CES) form. For a factor substitution elasticity between capital and labor less than unity, the saving rate decreases along the transition path after the capital stock reaches a critical value identified analytically herein. But before reaching this critical value, the saving rate might increase and so, taken as a whole, the saving rate path might manifest 'overshooting.' Similarly, for a factor substitution elasticity greater than unity, the saving rate increases along the transistion path after the capital stock reaches a critical value. Before reaching this critical value, the saving rate might decrease and the saving rate path might manifest 'undershooting.' A simulation illustrating these interesting dynamics is presented. (Copyright: Elsevier)