Second-Order, Dissipative Tâtonnement: Economic Interpretation and 2-Point Limit Cycles

Economy – Quantitative Finance – General Finance

Scientific paper

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11 pages, 1 figure: First revision included a simple motivating model that gives rise to a second-order dynamic, and fixed som

Scientific paper

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.

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