A probability inequality for ranges and its application to maximum range test procedures

Summary It is proved that for any fixed argument the sequence (P _k) of the distribution functions of the ranges ofk i.i.d. univariate random variables is log-concave if the random variables have a log-concave density. If the support of the distribution is an infinite interval and the density is monotonous then the theorem holds also with “log-convex” instead of “log-concave”. The resulting inequalities can be used by a quick algorithm for closed maximum range test procedures for all pairwise comparisons (Royen 1988, 1989a, 1989b). Under the above assumptions the application of this algorithm can be extended e.g. to pairwise comparisons of variances.     

Firm Growth and Survival: Does Ownership Structure Matter?

The publication of the passive learning model of Jovanovic and subsequently the active exploration model of Ericson and Pakes led to a resurgence in research on firm growth and survival. Empirical work measuring the relationship of growth and survival relative to size and age uncovered a number of strong regularities, consistent with the new theoretical models and also with a rather broad class of models of which the above represent special cases. But recent theoretical work has shown that when the learning models are applied to the special case of the labor managed firm, most of the sharp empirical predictions derived for profit maximization are rendered indeterminate. Given the impact of ownership structure on the theoretical results of the learning models, we use a dataset of French producer cooperatives to determine whether firms of different ownership structures actually have substantially different growth and survival patterns. We find that French cooperatives survive and grow in very much the same way as has been found for U.S. firms, suggesting that the empirical regularities previously uncovered hold for a much broader class of firms. We are left to conclude that the underlying empirical growth and survival relationships continue to hold for firms with sharply differing ownership structures, and the theoretical models are attempting to explain these broad-based relationships by means of overly specific modeling.     

Über die Existenz einer stetigen,reellenNutzenfunktion

Ohne ZusammenfassungHerrn Prof. J. Nitsche (Freiburg) danke ich für die kritische Durchsicht einer ersten Fassung des Manuskriptes, ebenso danke ich Prof. Robert Reichardt (Wien) für einige kritische Anmerkungen. Für mögliche Fehler bleibe ich jedoch allein verantwortlich.     

Rising marginal cost and concavity of the production function

Suppose a production function, f, is continuous, quasi-concave and weakly monotone on the non-negative orthant of Euclidean n-space. Let c(·, ·) be the associated cost function. Then it is shown that f is concave if and only if for each w, c(w, ·) is convex.