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

We are delighted that Nicholas Rau has attempted to generalize our result that: the of rate of return regulation is highly sensitive to the nature of the uncertainty. His paper has stimulated us to reflect further on generalizing and simplifying our joint results. Originally, we stated the following results: a) If uncertainty affects the maximal quasi-rents function R(K, u) in a multiplicative way, R(K,u) = R(K)(1 + u), then a sufficiently large gap must exist between the regulated rate of return (s) and the cost of capital (i) to induce the firm to select ex ante a scale of plant greater than the scale chosen by the unregulated monopolist. The closer is the regulated rate to the cost of capital, the more likely is it that the regulated firm will select ex ante a smaller scale of plant than is chosen by the unregulated firm. Were that to occur, regulation would definitely be worse than no regulation. b) If the uncertainty enters the maximal quasi-rents function in an additive way, R(K,u) = R(K) + u, then the conventional Harvey Averch and Leland Johnson (A-J) occurs (unless the regulation drives it out of business). Rau's main conclusion is that: .... if the state of nature affects both the average and marginal return on capital, then whether an A-J or anti A-J prevails depends on the amount of randomness in the environment. The more 'noise,' the more likely is an anti A-J effect (p. 190). A general and simple statement of the regulation theorems is derived below which contains points a) and b) and Rau's conclusion as special cases. 1. A General Formulation of the Problem

A. Holly, P. C. B. Phillips, A Saddlepoint Approximation to the Distribution of the k-Class Estimator of a Coefficient in a Simultaneous System, Econometrica, Vol. 47, No. 6 (Nov., 1979), pp. 1527-1547

Reviews the book "Foozles and Frauds," by Harold F. Russel.

Reviews the book "Anatomy of Depreciation," by G.D. Roy.