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The asymptotic behavior of dynamic producer-consumer systems

✍ Scribed by F. Szidarovszky; C. Chiarella

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
1007 KB
Volume
39
Category
Article
ISSN
0895-7177

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✦ Synopsis

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.

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