Knowledge that Transforms

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

This paper proposes the Gini coefficient of the censored income distribution truncated from above by the poverty line as an index of poverty. An ordinalist axiomatic approach, which was introduced by Professor Sen, is used to justify this measure. In comparison with Sen's index, our alternative measure is simpler and more concerned with relative deprivation; it can be regarded as a more natural translation of the Gini coefficient from the measurement of inequality into that of poverty.

Ever since Antonelli noted ([ 2], [3]) the "integrability" (symmetry) conditions necessarily obeyed by an indirect demand function derived from maximizing a utility function, and ever since Volterra emphasized ([37], [38]) their importance to Pareto's attempt [23] to construct utility from consumer purchase data these conditions have retained a technical character eluding intuitive motivation.It is our purpose here to show that an axiom of Ville ([35], [36]) provides an intuitively appealing equivalent of these symmetry conditions.In doing this, with the help of our integrability theorem of [16], we will extend Ville's result and, we hope, clarify his very important contribution to axiomatic consumer theory.lFrom the dual versions ([27], Theorems 16 and 18) of an extension of Hurwicz and Uzawa's Theorems 1 and 2 [17], we know, roughly speaking, that the following two conditions together are equivalent to utility-rationality2 of a given C 1 competitive inverse demand function satisfying the budget identity: negative semi-definiteness of the Antonelli matrix 11.5) below), and symmetry of the Antonelli matrix.From duality theorems ([27], Theorems 20 and l2(b) applied to a recent result of Kihlstrom, Mas-Colell, and Sonnenschein ([19], Theorems 1 and 2), we know that the first (negative semi-definiteness) condition is equivalent to a weak version of the intuitively appealing Weak Axiom of Revealed Demand Preference. 3 What about the second condition, the

A class of statistical models which generate simultaneous equation models with both discrete and continuous endogenous variables is introduced. This class of models can also be regarded as a new class of switching simultaneous equation models which are of general interest. Identification and estimation problems are investigated. Several simple consistent two stage methods are proposed. The consistency of those estimators is proved. Two step maximum likelihood procedures are then developed. -Author

Malcolm R. Gray, Stephen J. Turnovsky, Expectational Consistency, Informational Lags, and the Formulation of Expectations in Continuous Time Models, Econometrica, Vol. 47, No. 6 (Nov., 1979), pp. 1457-1474

[This paper studies the existence, uniqueness, and stability of equilibrium for a class of random dynamical systems that arise frequently in the study of Markovtemporary equilibrium models and in models arising from maximization behavior over time. It is seen that equilibria in these models have very nice properties.]

Previous estimates of the magnitude of highway congestion costs have employed equations relating the external cost imposed on motorists by an additional vehicle to the speed of traffic flow or the ratio of traffic flow to the maximum capacity of the road. While those equations may be accurate for rural roads and expressways, they may be less accurate on city streets where delays at intersections are a dominant factor in congestion costs. This study replaces single speed-volume equations with a traffic simulation model that replicates the queuing of vehicles at traffic lights, the dispersion of platoons of vehicles as they move from one intersection to another, and the interaction of intersecting traffic flows on an urban street network. The model is used with actual Toronto road and traffic data to produce new estimates of congestion costs on specific streets during the morning rush hour. The model produces a surprisingly high average congestion cost during the morning rush hour and a poor correlation of the results with those that would be estimated for the same traffic flows by the single equation models. The simulation technique allows the calculation of congestion costs on a street-by-street basis, generating the detailed information that would be necessary for a complex congestion pricing scheme. TRAFFIC CONGESTION IN URBAN AREAS has long been recognized as a technological external diseconomy causing serious urban problems. Highway engineering studies show that over a range of traffic flow levels observed on city streets an increase in the volume of traffic flow will reduce the speed of that flow for all motorists. While the additional driver perceives the impact of this lower speed upon himself, he is not faced with the social costs of the time lost to all other motorists as a result of his entering the road. The private cost of using the road, as perceived by the added motorist is thus below the social cost, often by a large amount. It has been shown that if the marginal external social cost of an additional vehicle-mile can be calculated and a toll is charged to all motorists equal to this marginal external cost, a Pareto improvement in the efficiency of using the road can be achieved.2 Mohring [10] has estimated the magnitude of such tolls as a function of the volume/capacity ratio of the highway, a measure of capacity utilization. Johnson [6] calculated a similar set of tolls as a function of the speed of movement of traffic on the road. Walters [15] estimated the elasticity of costs with respect to speed or time of travel. Smeed [13] calculated congestion costs as a function of speed and of the volume/capacity ratio.

A method is proposed for the estimation of a general class of scalar linear time series models. The model takes the form of a stochastic difference equation for the dependent variable with exogenous variable inputs, and the disturbances are autocorrelated through an autoregressive moving average process. In the present paper an asymptotically efficient yet computationally simple estimation procedure (in the time domain) is derived for this model. The resulting estimator is shown to be asymptotically equivalent to the maximum likelihood estimator and to possess a limiting multivariate normal distribution. (Author)