Monopoly models with time-varying demand function

Abstract

We study a family of monopoly models for markets characterized by timevarying demand functions, in which a boundedly rational agent chooses output levels on the basis of a gradient adjustment mechanism. After presenting the model for a generic framework, we analytically study the case of cyclically alternating demand functions. We show that both the perturbation size and the agent's reactivity to profitability variation signals can have counterintuitive roles on the resulting period-2 cycles and on their stability. In particular, increasing the perturbation size can have both a destabilizing and a stabilizing effect on the resulting dynamics. Moreover, in contrast with the case of timeconstant demand functions, the agent's reactivity is not just destabilizing, but can improve stability, too. This means that a less cautious behavior can provide better performance, both with respect to stability and to achieved profits. We show that, even if the decision mechanism is very simple and is not able to always provide the optimal production decisions, achieved profits are very close to those optimal. Finally, we show that in agreement with the existing empirical literature, the price series obtained simulating the proposed model exhibit a significant deviation from normality and large volatility, in particular when underlying deterministic dynamics become unstable and complex.

Learning in a double-phase cobweb model

“…Agricultural markets are the typical competitive market example provided in microeconomics courses, and energy markets have been liberalized in the last twenty years.4 For an introduction and survey on cobweb models we refer toHommes (2013). A first attempt to describe seasonal markets through a cobweb model is proposed in, while the effect of demand seasonality in a monopolistic market model is studied inCavalli and Naimzada (2018).5 It is well known that if agents takes into account in their expectation formation mechanism several previously realized prices, then the resulting difference equation is non-autonomousBischi et al 2015), and this has been already applied to cobweb models(Carlson 1968;Manning 1971;Bischi and Naimzada 1997;Gaffney and Pearce 2004), too. However, in such literature the non-autonomous nature of the resulting equation is due to a refinement of the expectation formation mechanism, while the economic framework under consideration is left unchanged.…”