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Quasi-models of price evolution and their qualitative properties

  • Vladimir B. Bajić
  • Bratislav J. Petrović
Conference paper
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 35)

Abstract

In this paper we considered a simple technique for modeling a large-scale market system. Quasi-model approach, used in the paper, may considerably reduce the order of models obtained.

Because of the aggregation applied, inaccuracies occur in the model. In order to reduce these inaccuracies, time-varying interactions of deterministic and stochastic types were introduced.

For the deterministic case, conditions are derived, which ensure that the market system producing unbounded quasi-prices in the case of strongest interactions, can be stabilized by excluding some composite goods from the market. Similar results are obtained for the stochastic case. Also, it was shown that under proper conditions the market system that produces unbounded quasi-prices cannot be stabilized by introducing new composite goods into the market system.

Models are also derived in the case when in the market system actions exist consisting of changing the quasi-prices and these actions were included in the model.

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References

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    O. Lange, "The Stability of Economic Equilibrium", in Reading In Mathematical Economics, part I, P. Newman, ed., Baltimore, Md: 1968.Google Scholar
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    D.D. Šiljak, "Competitive Economic System: Stability, Decomposition and Aggregation", IEEE, Trans. On. Aut. Control, Vol. AC-21, No. 2, April 1976.Google Scholar
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    D.D. Šiljak, "Large-Scale Dynamic Systems — Stability and Structure", North-Holland, New York, 1978.Google Scholar
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    W. Hahn, "Stability of Motion", Springer-Verlag, Berlin, 1967.Google Scholar
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    C. Bruno, et al., "Bilinear Systems: An Appealing Class of ‘Nearly Linear’ Systems in Theory and Applications", IEEE, Trans. On. Aut. Contr., Vol. AC-19, No., August 1974.Google Scholar
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    R.R. Mohler, "Bilinear Control Processes", Academic Press, New York, London, 1973.Google Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Vladimir B. Bajić
    • 1
  • Bratislav J. Petrović
    • 2
  1. 1.PTT Educational CenterBelgradeYugoslavia
  2. 2.Faculty of Organizational SciencesBelgradeYugoslavia

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