The Neoclassical Optimal Growth Model Revisited : An Explicit Equation for the Saddle Path

The goal of the paper is to present an alternative version of the Ramsey-Cass-Koopmans model (1965), starting from the idea of a time preference rate deduced from relative preferences for consumption and savings, which are represented by a Cobb Douglas Utility function. Such a maximising criterion including the flow of saving makes the model similar to the one of Heng-Fu Zou (1994), except that his specification, motivated as one that formalizes Max Weber's idea of the "Spirit of Capitalism" (1958), includes the capital stock instead. If the presented model preserves (differently) the long run implications on levels and growth rates of consumption and capital stock, the main feature coming from the use of this Cobb Douglas Utility function, is an intersting application of the Pontryagin's Maximum Principle with results of excellent quality : the model presents an extremly simple analytic expression for the saddle path, and becomes both qualitative and quantitative with strong analogies to the exogenous one of R.Solow (1956). The analysis comes after a generated numerical example, and the two models are put in relationship through a discussion of the golden rule (E.Phelps, 1961). Effects of structural changes in parameters are also explored.