Spatial Price Equilibrium with Information Asymmetry in Quality and Minimum Quality Standards

Abstract

In this paper, a spatial price equilibrium model with information asymmetry in quality is developed. Producers at the supply markets are aware of the quality of their products, whereas consumers, located at the demand markets, are aware only of the average quality of the products that are shipped to their demand markets. We derive the governing equilibrium conditions, along with the variational inequality formulation. We then extend the model to include policy interventions in the form of minimum quality standards and provide an integrated variational inequality formulation of both models. We introduce a dynamic adjustment process for the evolution of the product shipments and quality levels over time and formulate it as a projected dynamical system. We establish qualitative results, in the form of existence, uniqueness, and stability analysis. An algorithm is proposed, along with a convergence proof. The algorithm tracks the evolution of the product shipment and quality level pattern until an equilibrium is achieved and, at each iteration, yields closed form expressions for the computation of the product shipments and quality levels. It is then utilized to compute solutions to a spectrum of spatial price equilibrium numerical examples in order to explore the impacts of information asymmetry under different scenarios.

This work adds to the growing research on spatial competition and product quality but is the first to incorporate information asymmetry of this specific form in both equilibrium and dynamic model versions.

Keywords: spatial price equilibrium, quality competition, information asymmetry, average quality, minimal quality standards, variational inequalities, projected dynamical systems