Interacting Cobweb Demands

This paper proposes a simple, stylized two-good, two-market dynamical cobweb model. Consumers and producers are located in two countries, where they can choose to consume either locally produced or imported goods. We introduce a heuristic rule for consumers, which considers a convex combination of purchasing the cheapest good and the expected intrinsic quality of the two goods. Numerical simulations demonstrate that the interconnection between markets is a primary driver of instability, manifesting through either a flip or a Hopf bifurcation. Additionally, the dynamics depend closely on the price-quality trade-off. We identify three scenarios: when only price matters, a stable period-2 cycle arises; when only quality matters, the system converges; and in intermediate cases, complex dynamics emerge. Notably, we discovered a boundary crisis region, where there is a sudden shift from a chaotic attractor to stability. Finally, as a brief extension, we analyze the system when tariffs are considered for policy purposes.