The purpose of this note is to show that the so-called Principle of Minimum Differentiation, as based on Hotelling’s 1929 paper “Stability in Competition” is invalid. The purpose of this note is to show that the so-called Principle of Minimum Differentiation, as based on Hotelling’s 1929 celebrated paper (Hotelling [3]), is invalid. Firstly, we assert that, contrary to the statement formulated by Hotelling in his model, nothing can be said about the tendency of both sellers to agglomerate at the center of the market. The reason is that no equilibrium price solution will exist when both sellers are not far enough from each other. Secondly, we consider a slightly modified version of Hotelling’s example, for which there exists a price equilibrium solution everywhere. We show however that, for this version, there is a tendency for both sellers to maximize their differentiation. This example thus constitutes a counterexample to Hotelling’s conclusions. We shall first recall Hotelling’s model and notations. On a line of length `, two sellers A and B of a homogeneous product, with zero production cost, are located at respective distances a and b from the ends of this line (a+ b ≤ `; a ≥ 0, b ≥ 0). Customers are evenly distributed along the line, and each customer consumes exactly a single unit of this commodity per unit of time, irrespective of its price. Since the product is homogeneous, a customer will buy from the seller Econometrica, 47(5), 1145–1150, September 1979. Center for Operations Research and Econometrics

The paper deals with a measure theoretic model of a pure exchange economy. There are two kinds of traders: big traders, represented by atoms of the measure space, and small traders, represented by the atomless part of the measure space. The restriction of an allocation to the atomless sector is called competitive if there exists a price vector such that the consumption of every small trader is a maximal element (in terms of his preference) in the budget set defined by that price vector and by his initial endowment. We consider the set of allocations that are not blocked by any atomless coalition, or by the complement of any atomless coalition, and call it the 6~T2-core. The main results of the paper consist in defining sufficient conditions under which allocations in the Y'-core have a competitive restriction to the atomless sector, and vice versa. The economic implications and significance of the results are briefly discussed.