Closed-Form Solutions of General Intertemporal Consumption-Maximization Models*

TLDR: In this paper, explicit representations for very general (discrete and continuous-time) intertemporal consumption-maximization models which allow the instantaneous preferences of the consumer and the time-preference factors to vary over time and for the non-existence of utility functions, many commodities, and a wide class of preferences which do not necessarily satisfy the so-called "regularity conditions" (such as differentiability, strict convexity, boundedness, or continuity) were considered.

Abstract: This paper considers explicit representations for very general (discrete and continuous-time) intertemporal consumption-maximization models which allow the instantaneous preferences of the consumer and the time-preference factors to vary over time and for the the non-existence of utility functions, more than one generation of consumers with a given probability of death, many commodities, and, further, a wide class of preferences which do not necessarily satisfy the so-called “regularity conditions” (such as differentiability, strict convexity, boundedness, or continuity) and include most of the well-known preferences in the literature.