Unexpectedly, and as a result of intellectual curiosity, the resolution of the Ramsey growth problem with a Utility function underlying relative preferences for consumption and savings, happens to provide remarkable results and interpretations. An advanced microeconomic analysis of this particular assumption which follows consequently, and presumably the sole one of the literature, brings important new insights to the consumer theory, and leads reasonably to the question of the validity of the current version of the Ramsey model.
Two reasons for excluding savings from Utility are usually given quickly, and may sound a bit obvious to justify the necessity of an advanced investigation. The first one, which is to consider savings as having no intrinsic value to the individual, may arguably be contested on a pure microeconomic basis. Introducing the saving flow is indeed not only a way to capture the wealth effect motivated as necessary by authors like H.Zou (1994), C.Carroll (2000), or Bakshi & Chen (1996), but also a way to control for the intensity of a direct preference for thriftiness, which may be involved when considering an individual deciding about levels of consumption and savings over time. For example, an individual may wish to be thrifty, or may wish to save (say, for a precautionary motive), at particular periods that are not necessarily those (of higher incomes and interest rates) predicted by the traditional theory. It could therefore be judicious to formalize this way the desire to save each time in the Ramsey context, and to control for some degree of preference for thriftiness.
The second reason for excluding savings from Utility, which is a mathematical redundancy deduced from a budget constraint always binding, can be shown to be misleading once income becomes determined endogenously as in optimal control settings. Indeed, in basic optimization cases, once consumption level is chosen, savings level is decided accordingly at any given point of time, but when the current decision affects the next level of income (as in the Ramsey model), the question of considering or not an eventual saving effect in the Utility function becomes an important matter. Mathematically, the derivation of optimal conditions provides substantially different solutions, even after neutralizing (ex-post) the saving effect in results. Conclusions of an objective comparative analysis, that highlights the better quality of properties of the new results, are such that the presented alternative version seems actually to be the right one.
