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.     

Dynamic effects of externalities,optimal saving and economic growth

Conclusion Recognizing the fact that provision of mixed public goods can result in both consumption externalities of the Samuelsonian variety as well as production externalities we set out to extend the earlier results of Rao and Kalpagam (1977) on the effect of public goods on economic growth. In so doing, we considered three standard specifications of production externalities and enlarged the concept of consumption displacement. Our basic conclusion is that the results of our earlier paper remain valid under the more general conditions set out in this paper.     

On the theory of macroeconomic quasi-equilibria

Conclusion It has been shown that for the Classical System a quasi-equilibrium cannot exist, unless we make the ad hoc assumption of inflexible nominal wages⁸. The equilibrium in the classical regime corresponds to the general competitive equilibrium, and of course the validity of Walras' Law cannot be questioned. At the same time, however, it has been shown that to extend these conclusions to the Keynesian system as well is not justified. The Keynesian system has, in general, a quasi-equilibrium. The model constructed in this paper and the resulting conclusions are significant because the model: (a) Incorporates the Keynesian notion of effective demand, which includes the demand for capital goods (investment) as being performed by a group of people distinct from the consumers (and so, answering Negishi's point, there is a prince in Hamlet!), (b) Unlike other models (like the recent paper by Glustoff), it does not rely on nominal wage rigidity to explain unemployment, but instead, again answering Negishi's remark, it explains rather than postulates why real wages do not adjust in the presence of unemployment so as to eliminate it. (c) It verifies the validity of Clower's proposition that in the Keynesian System Walras' Law holds only in equilibrium. (d) It reconsiles Bent Hansen's original quasi-equilibrium model with the Keynesian proposition of an unemployment equilibrium, against the apparent view of Hansen that to do that would require the assumption of a Phillips curve, a view also shared by Arrow and Hahn, and many others.An earlier version of this paper was presented in the December 1974 meeting of the Econometric Society in San Francisco. The author wishes to thank Prof. R. Clower, Prof. B. Hansen, Prof. S. Black, and Dr. G. Winckler for their valuable comments, but he obviously claims any errors for himself.     

Gold,liquidity and secured loans in a multistage economy Part I: Gold as money

This work relates to Department of the Navy Contract N00014-86-K0220 issued by the Office of Naval Research under Contract Authority NR 047-006. However, the content does not necessarily reflect the position or the policy of the Department of the Navy or the Government, and no official endorsement should be inferred. Revised with support of NSF contract SES-8812051.The United States Government has at least a royalty-free, non-exclusive and irrevocable license throughout the world for Government purposes to publish, translate, reproduce, deliver, perform, dispose of, and to authorize others so to do, all or any portion of this work.     

Versicherungsvertragliche Anzeigepflicht und Garantiehaftung für culpa in contrahendo

To sanction the insurant’s obligation to disclose the risk-relevant circumstances by the insurer’s exemption from performance does not comply with the ordinary pattern of pre-contractual liability. Instead of making the insurant responsible for the consequences of his breach of duty, the German Insurance Act subjects him to a guarantee which is comparable to the one imposed by the German Civil Code in the case of initial impossibility. The insurant has to guarantee that the facts which he did not, or at least not entirely, disclose do not cause any obligation of the insurer. The structure of this sanction is equivalent to the insurer’s so-called liability of performance. But contrary to the latter it can be justified by the specific importance of the insurant’s pre-contractual obligation of disclosure.