Complex price dynamics in vertically linked cobweb markets

Abstract

We enrich the traditional cobweb model by explicitly modelling interdependencies between upstream and downstream farmers in a vertically linked agricultural supply chain. Analysis of the system of nonlinear difference equations characterizing price dynamics in the underlying model reveal complex, quasi-cyclical price fluctuations around the unique equilibrium state. We show that time-delays arising from the unequal lengths of upstream and downstream production cycles have profound effects on price dynamics. From a policy perspective, we find that improvements in downstream production technology and declines in consumers’ sensitivity to prices lead to chaotic price fluctuations. Simulations under reasonable model calibrations reproduce the stylized features of actual prices, including quasi-cyclical fluctuations, positive first-order autocorrelation and fat-tailed distributions. In doing so, we address a major criticism of the theory of endogenous price fluctuations: the failure of chaotic cobweb models to replicate positively autocorrelated prices.