Learning in a double-phase cobweb model

Abstract

In this paper, we study a class of markets, among which we can mention agricultural and energy markets, characterized by seasonality, i.e., in which demand and/or supply conditions cyclically alternate with a precise and known periodicity. We propose a new theoretical framework based on a cobweb model with adaptive expectations, accordingly modified to be consistent with market’s seasonality. The model, consisting in a second-order non-autonomous difference equation, is investigated with the aim of understanding how the periodical nature of the market together with the agents’ expectation formation mechanism affects the resulting dynamics. We analytically prove the emergence of dynamical scenarios that are missing in the classic cobweb model for non-seasonal markets, such as quasi-periodic dynamics and an ambiguous role on stability of the expectation weight. Finally, we discuss their economic rationale with the help of numerical simulations. In such a peculiar economic framework, agents’ learning plays a key role to explain the dynamical properties of economic observables.

Production delays, supply distortions and endogenous price dynamics

“…In this way, he obtains a higher-order dynamical system that is capable of producing endogenous cyclical price dynamics. Cavalli et al (2021) develop a cobweb model in which a firm's supply depends on the season in which it is manufactured. For instance, a firm's supply may be high in the summer and low in the winter, resulting, for a time-independent demand schedule, in low summer prices and high winter prices.…”