A Cobweb Model with Alternating Demand and Supply Functions

Abstract

In this work I present a cobweb model for markets characterized by two couples of demand and supply functions which cyclically alternate with period two, in a succession of peak and off-peak market phases. Starting from classical adaptive expectations, a new expectation formation mechanism is presented, to take into account such markets' peculiarity. In particular, to adapt the previous in-phase expected price, agents use both in-phase and out-of-phase expectation errors, suitably weighted through a phase weight. It is shown that the resulting model is described by a nonautonomous difference equation. The local asymptotic stability of the steady state equilibrium is studied, showing that it depends on the expectation weight, the phase weight and on both the relative slopes, at the equilibrium, of the supply functions with respect to the demand functions. Several crucial differences with respect to the classical cobweb model are highlighted, showing the potentially ambiguous role of expectation weight and of relative slopes. It is shown that destabilization can occur both through a flip and a Neimark-Sacker bifurcation, which can occur for the same market conditions and different expectation weights.

The Development of Housing Market in Ukraine: Modelling and Prospects

“…The analysis of the dependence of the market equilibrium on time was based on the method of comparative statics, in which several times-equal equilibrium conditions are compared without considering the process of transition from one equilibrium to another. The description of processes occurring in time is carried out by means of dynamic analysis, in which price and volume are functions of time [6]. In the cobweb model, we take into account that when planning the volumes of a market transaction, consumers and producers often find themselves in a different position.…”