Quasi-models of price evolution and their qualitative properties

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.