Recursive Utility and Turnpike Theory for GMM Thompson Aggregators

Abstract

The existence of a unique optimum, a unique optimal stationary program, and a turnpike theorem are demonstrated for a neoclassical one sector optimal growth model. The planner's allocation problem is formulated as a discrete time deterministic, infinite horizon programming model. The production sector is subject to diminishing marginal returns to capital. The planner's objective function is derived from a Generalized Marinacci and Montrucchio (GMM) Thompson aggregator preference. A given Thompson aggregator may be associated with many intertemporal utility functions (which may not be ordinally equivalent). The choice of one of these representations over another is shown to be a matter of mathematical tractability. There is an observational equivalence between those alternative objective functions: the qualitative features of the optimal solution do not depend on the particular utility function representation of the underlying Thompson aggregator preference structure.