Monopoly models with time-varying demand function

Abstract

We study a family of monopoly models for markets characterized by time-varying 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 time-constant 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.