Bounded Rationality and Animal Spirits: A Fluctuation-Response Approach to Slutsky Matrices

TL;DR

This paper introduces a statistical physics approach to consumer choice, relaxing traditional assumptions and revealing how bounded rationality and social influence can lead to asymmetries in the Slutsky matrix, especially near phase transitions.

Contribution

It develops a fluctuation-response framework linking the Slutsky matrix to consumption fluctuations and explores effects of social influence on consumer behavior, including symmetry breaking.

Findings

Slutsky matrix symmetry holds under bounded rationality without interactions.

Social influence can cause asymmetry in the Slutsky matrix.

Near phase transitions, asymmetry peaks indicating herding effects.

Abstract

The Slutsky equation, central in consumer choice theory, is derived from the usual hypotheses underlying most standard models in Economics, such as full rationality, homogeneity, and absence of interactions. We present a statistical physics framework that allows us to relax such assumptions. We first derive a general fluctuation-response formula that relates the Slutsky matrix to spontaneous fluctuations of consumption rather than to response to changing prices and budget. We then show that, within our hypotheses, the symmetry of the Slutsky matrix remains valid even when agents are only boundedly rational but non-interacting. We then propose a model where agents are influenced by the choice of others, leading to a phase transition beyond which consumption is dominated by herding (or `"fashion") effects. In this case, the individual Slutsky matrix is no longer symmetric, even for fully rational agents. The vicinity of the transition features a peak in asymmetry.