The Principle of Minimum Differentiation Reconsidered: Some New Developments in the Theory of Spatial Competition

The paper is divided into two parts: one-dimensional markets and two-dimensional markets. Also, we develop both one and two-dimensional models. Within each, we distinguish (a) bounded, (b) unbounded but finite, and (c) unbounded, infinite spaces. Among other things, we show: in one dimension, the nature of the space is not, as many investigators have thought, critical; in two dimensions, however, the very existence of equilibrium is seen to depend upon the nature of the space; the commonly-used rectangular customer density function yields results that do not generalize to any other density function; the existence of multiple equilibria in both one and two dimensions is a pervasive phenomenon in any of the spaces studied, and MD occurs only when the number of firms is restricted to two. Although the analysis and discussion are in terms of location theory and are concerned with the relationship between equilibrium configuration of firms and the transport-cost minimizing configuration, many of the results generalize to other forms of differenciation. The conditions under which the results generalize are considered in the concluding section of the paper.