An Analysis of the Cobweb Model with Boundedly Rational Heterogeneous Producers

ABSTRACT. This paper studies the dynamics of the traditional cobweb model with risk averse heterogeneous producers who seek to learn the distribution of asset prices using geometric decay processes (GDP)—the expected mean and variance are estimated as a geometric weighted average of past observations—with either finite or infinite fading memory. With constant absolute risk aversion, the dynamics of the nonlinear model can be characterized with respect to the length of memory window and the memory decay rate of the learning GDP. The dynamics of such heterogeneous learning processes and the capacity of the producers to learn are discussed. It is found that the interaction of heterogeneity, risk aversion, memory decay rate and window length of the GDP play a complicated role on the price dynamics of the nonlinear cobweb model. In general, an increase of the memory decay rate plays a stabilizing role on the local stability of the steady state price when the memory length is infinite, but this role becomes ambiguous when the memory is finite.