Complex Price Dynamics in Vertically Linked Cobweb Markets in Less Developed Countries

Advances in nonlinear dynamics have resuscitated interest in the theory of endogenous price fluctuations. In this paper, we enrich the traditional cobweb model by incorporating vertical linkages between agricultural markets, an important aspect of agricultural production in less developed countries that has been largely ignored by the existing literature on chaotic cobweb models. To this end, under sufficiently general cost and demand functions, we develop a parsimonious, dynamic model to capture mutual interdependencies between upstream and downstream markets arising from the vertically linked structure of agricultural values chains. The model is solved under the naïve expectations hypothesis to derive a system of coupled, timedelay difference equations characterizing price dynamics in vertically linked cobweb markets. Mathematical and numerical analyses reveal that vertical linkages between downstream and upstream cobweb markets have profound effects on local stability, global price dynamics and onset of chaos. We also add an empirical dimension to an otherwise theoretical literature by benchmarking moments of prices simulated by our model against actual poultry value chain price data from Pakistan. Simulated prices reproduce the stylized patterns observed in the actual price data, i.e., quasi-periodic behavior, positive first-order autocorrelation, relatively higher variation in upstream prices compared to downstream prices, low skewness and negative kurtosis. In doing so the paper addresses a major criticism of the theory of endogenous price fluctuations, most notably the failure of chaotic cobweb models to adequately replicate positively autocorrelated prices. From a policy perspective, our model predicts that the increasingly unpredictable behavior of agricultural commodity prices in less developed countries may be driven by improvements in technological efficiency at the downstream level, combined with declines in consumer’s sensitivity to agricultural commodity prices.