On feedback and stable price adjustment mechanisms

Guillermo Fernandez-Anaya, Jose Alvarez-Ramirez and Carlos Ibarra-Valdez

Physica A: Statistical Mechanics and its Applications, 2007, vol. 377, issue 1, 211-226

Abstract: Given an excess demand function of an economy, say Z(p), a stable price adjustment mechanism (SPAM) guarantees convergence of solution path p(t,p0) to an equilibrium peq solution of Z(p)=0. Besides, all equilibrium points of Z(p) are asymptotically stable. Some SPAMs have been proposed, including Newton and transpose Jacobian methods. Despite this powerful stability property of SPAMs, their acceptation in the economics community has been limited by a lack of interpretation. This paper focuses on this issue. Specifically, feedback control theory is used to link SPAMs and price dynamics models with control inputs, which match the economically intuitive Walrasian Hypothesis (i.e., prices change with excess demand sign). Under mild conditions, it is shown the existence of a feedback function that transforms the price dynamics into a desired SPAM. Hence, a SPAM is interpreted as a fundamental (e.g., Walrasian) price dynamics under the action of a feedback function aimed to stabilize the equilibrium set of the excess demand function.

Keywords: Econophysics; Price adjustment mechanism; Stable price adjustment mechanism; Feedback (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:377:y:2007:i:1:p:211-226

DOI: 10.1016/j.physa.2006.10.088

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