Asymptotic Dynamics in a Multi-market Delayed Cobweb Model

This study analyzes a two-market cobweb model involving production delays for agricultural products and information delays concerning cross-market prices. Our cobweb model has two markets because interdependency between agricultural markets is observed. It has multiple delays because each commodity good has a different length of production delay based on the nature of the product, and two-market dependency newly generates cross-market information delays. Under these circumstances, we construct a 2-D system of multi-delay differential equations and investigate cobweb dynamics in which the production and information delays are correlated. It represents the linear stability conditions in parameter spaces containing the two production delays and the sum of the information delays. First, it is confirmed that the two-market dynamics are similar to the one-market dynamics if the interdependency is one-way. Second, it is shown that the production delay has a destabilizing effect, and the information delay has a stabilizing effect. Depending on the relative degree between those opposite-signed effects, the unstable steady-state price bifurcates various dynamics from a simple cycle to chaotic fluctuations in the two-way cobweb model.