Heterogeneous Adaptive Expectations and Cobweb Phenomena

We study a cobweb-type commodity market characterised by a strictly monotone demand and supply, in which n firms operate. The firms are assumed to differ in a key parameter governing price expectations which we suppose to be adaptive. We characterise the unique steady state of the resulting economic dynamics in terms of stability and we study the impact of the number and diversity of firms: to this end we introduce the notions of structural and behavioural degree of instability which prove to be crucial in determining whether stability or instability prevail. We also consider the case of market integration and establish conditions to have stability (or instability) in the aggregated market in terms of the original (structural and behavioural) degrees of instability. We take up the issue of transitional dynamics and speed of convergence when the system is stable and characterise parametric configurations that maximise the speed of convergence. Finally, we assume that the firms - via the parameter which defines their expectations - are sampled independently from a population described by a given probability distribution. In this case the structural degree of instability determines how the number of potentially different firms affects the probability of ending up with a stable outcome