A 'Gormanesque' Approach to the Solution of Intertemporal Consumption Models

In this paper we compare the standard dynamic programming method for the derivation of closed form solutions to stochastic control problems with three alternatives. Our first alternative is a minor variant of dynamic programming which requires solution of an alternative partial differential equation. In the context of a ba.sic, stochastic intertemporal utility maximizing model, this alternative solution procedure is particularly useful when preferences are represented by an instantaneous profit function. Our second alternative is based on intertemporal duality theory, and is most useful when preferences are represented by an indirect intertemporal expected utility (or value) function. Our third alternative is based on matching restrictions across inverse marginal instantaneous and indirect intertemporal expected utility functions - Gorman "expenditure" and "wealth" functions. Each of the approaches is suitable to particular model specifications and preference representations. As a collection of methods based to varying degrees on the exploitation of separability and duality, the methodology of this paper may be termed 'Gormanesque' (in the. spirit of Gorman (1976)). Taken together, these methods expand considerably the range of models for which closed form analytical solutions may be obtained.