The asymptotic behavior of dynamic producer-consumer systems

• Published in: Mathematical and computer modelling 2004-06, Vol.39 (11), p.1297-1312
• Main Authors: Szidarovszky, F., Chiarella, C.
• Format: Article
• Language: English
• Subjects: Bifurcation; Delayed information; Dynamic systems; Exact sciences and technology; Global analysis, analysis on manifolds; Mathematical analysis; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); Numerical analysis. Scientific computation; Ordinary differential equations; Producer-consumer systems; Sciences and techniques of general use; Stability; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
• ISSN: 0895-7177; 1872-9479
• DOI: 10.1016/j.mcm.2004.06.009

Dynamic Arrow-type price dynamics are investigated in a continuous time framework. The existence of a unique equilibrium is first proved under realistic conditions. Then, the local asymptotic stability of the equilibrium in the presence of instantaneous price and output information is shown. Continuously distributed time lags are then assumed in obtaining and implementing price and output information, or equivalently, it may be assumed that the firms and/or the market wants to react to long term effects rather than to follow sudden changes in price or outputs. If a time lag is assumed only in estimating the demand in the market, then the local asymptotic stability of the equilibrium is preserved. If the producers also use delayed information, then instability may occur. Stability conditions are derived and in the case of bifurcation the possibility of the birth of limit cycles is explored.