Production delays, technology choice and cyclical cobweb dynamics

Abstract

We develop a cobweb model in which firms, facing a two-period production delay, have access to a flexible (costly) and an inflexible (cheap) production technology.Moreover, firms select between production technologies depending on their evolutionary fitness, measured in terms of past realized profits. The dynamics of our cobweb model is driven by a four-dimensional nonlinear map. We analytically show that its unique steady state may become unstable due to a Neimark-Sacker bifurcation, a scenario that gives rise to cyclical price dynamics, as observed in actual commodity markets. Simulations furthermore reveal that our cobweb model may also produce chaotic motion.

Production delays, supply distortions and endogenous price dynamics

“…Third, it may also be interesting to assume that manufacturing firms may be able to adjust their production quantity when they observe new information about the commodity price. See Dieci et al (2022) for a starter in this direction. Fourth, we assume that firms have naïve expectations.…”

“…Note that a major difference between our paper and the work by Ezekiel (1938) and Dieci et al (2022) is that we consider that firms may switch between different production technologies that take different lengths of time. 1 There are only a few other cobweb models that may produce endogenous cyclical price dynamics.…”

“…One exception is the recent contribution by Dieci et al (2022), who develop a cobweb model in which firms, facing a fixed production delay of two periods, have access to two different production technologies. In particular, they can select between an inflexible production technology, requiring them to start the production process immediately, and a flexible production technology, allowing them to delay the production process by one period.…”