Adaptively Adjusted Beliefs About Prices in an Evolutive Muthian Cobweb Model

In the present work, starting from the 1D evolutionary Muthian cobweb model in [Hommes & Wagener, 2010], where the economy is populated by biased firms and unbiased fundamentalist firms, we investigate the effects generated by adaptively adjusted beliefs on the long-period price of the goods produced. As in [Hommes & Wagener, 2010], we focus on the case in which the Muthian model is globally stable in the sense of Guesnerie [2002], stable under naive expectations. Coupling into the details, we first assume that just biased producers, being aware of the systematic errors they make in their forecasts, partially rely on an adaptive adjustment of beliefs, obtaining a 3D model, which has a unique steady state. Although in [Hommes & Wagener, 2010] the fundamental steady state is always stable and at most it can coexist with a period-two cycle, we show that the complexity degree increases in our case, where on increasing the reactivity of the evolutionary mechanism, there may be up to two stability thresholds for the steady state, both corresponding to flip bifurcations, and the equilibrium can coexist with a quasiperiodic attractor. On checking the robustness of such outcomes, we contrast them with those we find for the 4D setting, obtained by assuming that unbiased fundamentalists update their belief about the fundamental value partially relying on the same adaptive adjustment mechanism used by biased producers. The outcomes are similar to those of the 3D framework. For instance, in both cases, there exists just the fundamental equilibrium, which can coexist with a quasiperiodic attractor.