Additive habit formation: Consumption in incomplete markets with random endowments

TL;DR

This paper characterizes optimal consumption in incomplete markets with habit formation, showing how consumption depends on wealth and supporting classical economic conjectures.

Contribution

It provides a detailed theoretical framework for optimal consumption with habit formation in general incomplete markets, extending classical economic theories.

Findings

Optimal consumption is monotonic in wealth.

Optimal consumption is concave in wealth.

Results support Keynes's classical conjectures.

Abstract

We provide a detailed characterization of the optimal consumption stream for the additive habit-forming utility maximization problem, in a framework of general discrete-time incomplete markets and random endowments. This characterization allows us to derive the monotonicity and concavity of the optimal consumption as a function of wealth, for several important classes of incomplete markets and preferences. These results yield a deeper understanding of the fine structure of the optimal consumption and provide a further theoretical support for the classical conjectures of Keynes (1936).