作者:
G Fernandez-Anaya，J Alvarez-Ramirez，C Ibarra-Valdez
关键词:
Econophysics ； Price adjustment mechanism ； Stable price adjustment mechanism ； Feedback
摘要:
Given an excess demand function of an economy, say Z(p) Z ( p ) mathContainer Loading Mathjax , a stable price adjustment mechanism (SPAM) guarantees convergence of solution path p(t, p 0 ) p ( t , p 0 ) mathContainer Loading Mathjax to an equilibrium p eq p eq mathContainer Loading Mathjax solution of Z(p)=0 Z ( p ) = 0 mathContainer Loading Mathjax . Besides, all equilibrium points of Z(p) Z ( p ) mathContainer Loading Mathjax 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.
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