Knowledge that Transforms

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[Defining a choice as a function which picks a subset of every set of alternatives, we consider a list of over thirty conditions (expressed as functional inequalities) which a choice may satisfy, demonstrating &-semilattices formed by certain sublists, thus summarily presenting as "synopses" all the implications obtaining between logical conjunctions formed within these sublists. The list studied includes many well known conditions, such as Plott's [13] path independence, for which we offer over a dozen new characterizations of various types.]

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.

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