Optimal Consumption for Recursive Preferences with Local Substitution -- the Case of Certainty

TL;DR

This paper characterizes optimal consumption policies within a recursive utility framework with local substitution, providing existence, uniqueness, and explicit solutions for certain utility functions, advancing understanding of decision-making under uncertainty.

Contribution

It introduces a novel characterization of optimal consumption with local substitution in recursive preferences, including explicit solutions for Epstein-Zin utility functions.

Findings

Existence and uniqueness of optimal consumption policies established.

Explicit solutions provided for Epstein-Zin type felicity functions.

A Kuhn-Tucker theorem version applied to recursive utility setting.

Abstract

We characterize optimal consumption policies in a recursive intertemporal utility framework with local substitution. We establish existence and uniqueness and a version of the Kuhn-Tucker theorem characterizing the optimal consumption plan. An explicit solution is provided for the case when the felicity function is of the Epstein-Zin's type.