On price stability and the nature of product differentiation

Abstract

In a spatial competition model, we analyze the stability of the Nash-price equilibrium under horizontal and vertical product differentiation, considering both homogenous and heterogeneous expectations. Regardless of the nature of product differentiation, assuming that firms behave according to an adaptive expectations rule, it is found that the Nash-price equilibrium is asymptotically stable. If at least one firm follows the gradient rule based on marginal profit, an increase in the adjustment speed turns out to be a source of complexity. Moreover, the influence of the locations on price stability depends on the nature of product differentiation and on the expectations scheme.