Second-Order, Dissipative T\^atonnement: Economic Interpretation and 2-Point Limit Cycles

TL;DR

This paper introduces a second-order, dissipative t extsuperscript{a}tonnement model inspired by damped harmonic oscillators, offering a dynamic and local-information-based approach to economic price adjustments that can produce stable or cyclical behaviors.

Contribution

It presents a novel second-order t extsuperscript{a}tonnement mechanism with a physical analogy, explaining how local rules can generate realistic economic dynamics including limit cycles.

Findings

The model can produce two-step limit cycles.

Damping influences stability and cycle size.

The mechanism aligns with observed economic fluctuations.

Abstract

This paper proposes an alternative to the classical price-adjustment mechanism (called "t\^{a}tonnement" after Walras) that is second-order in time. The proposed mechanism, an analogue to the damped harmonic oscillator, provides a dynamic equilibration process that depends only on local information. We show how such a process can result from simple behavioural rules. The discrete-time form of the model can result in two-step limit cycles, but as the distance covered by the cycle depends on the size of the damping, the proposed mechanism can lead to both highly unstable and relatively stable behaviour, as observed in real economies.