Some characterization theorems for generalized measures of uncertainty and information

Summary Some characterization theorems are given for the various generalized measures of information and uncertainty by using two types of functional inequalities. This paper unifies several existing results on the various measures of information and some special cases of interest are mentioned at appropriate places.The work of this paper was done while the author was a visiting postdoctoral fellow with the University of Waterloo. This paper was presented at the Meeting on Information Measures held at the University of Waterloo, Waterloo, Ontario, Canada from April 10–14, 1970.     

An essay on the “New” Kaldorian macrodynamics

Conclusion Considering that employment and output are positively related, and that productivity growth and inflation are inversely related, we see that Kaldor, through the hypothesis of embodied technical progress and induced investment, has presented us with the elements of a general theory of stagflation. As such, this Kaldorian theory constitutes the only serious opposition to the various monetarist explanations (most notably Milton Friedman's 1977 Nobel Lecture) of a positively sloped Phillips curve, based on the inflationary expectations mechanism and the notion of a changing natural rate of unemployment. Not so long ago, people were talking about the so-called locomotive theory of export-led growth, with such surplus countries as Germany and Japan, or large economies as the U. S., playing the role of the engine, given that the equally surplus oil-producing countries will also maintain a strong import-demand for industrial output. Fears (perhaps legitimate ones) about inherent inflationary tendencies have caused the abandonment of this approach to pull the world economy from its vicious stagflationary circle. Contrary to the monetarists' view that a recession is needed in order to combat inflation, Kaldor's own theory can serve as a guide to those who, more optimistically, believe or simply hope that investment and output growth is the only longterm weapon against both inflation and unemployment.The importance of the writings of Professor Kaldor, influential as they have proved to be well beyond his immediate Cambridge milieu, cannot be overestimated. He is a truly great economist, one of the few who make economic theory rather than simply repeat established dogmas. All economists will be educated by reading and re-reading his collected essays.     

Nederlands Overgang Van Onderon twikkeld Gebied Tot Industrieland

Summary The author, emeritus professor in the Univeristy of Amsterdam, describes the transition from the pre-industrial period in the Netherlands to the stage of sustained economic growth; the take-off has taken place after the middle of the 19th century. He then compares the economic development of the Netherlands with the problems of the underdeveloped countries at the present time.During the pre-industrial period the Netherlands were underdeveloped in some respects only. The country was not purely agrarian, commercial activities playing an important part. There was no lack of capital, but the capitalists were more interested in foreign bonds than in industrial concerns. Agriculture was at a high level, the peasantry producing for the national and even international market. There was no over-population, and the growth of the population remained rather small.Under these circumstances the industrialisation of the Netherlands did not involve many difficulties. In the beginning, many industrial and banking investments come from abroad. The Dutch government placed no obstacles in the foreigners' way. The wageworkers were quite willing to be employed in modern factories. Trade-unions and campaigns for higher wages were unknown. The government interfered little in economic affairs and confined its activities to improvement of the infrastructure (construction of canals and railways). The civil servants were capable and free from corruption.In the underdeveloped countries of to-day these favourable circumstances are mostly absent. Yet there are factors which justify some optimism. The capitalist countries are willing to supply capital to the poor areas. Demographic measures, unknown in the 19th century, will sooner or later result in a slackening of the population growth. The greatest difficulties are to be found in the mental sphere. The will to economize is often absent, and it will take many years before traditional attitudes and conceptions have been replaced. The underdeveloped countries cannot expect to reach the economic level of the rich nations within a short time.     

The problem of optimum stratification and allocation withq=n/N>0

Summary Dalenius/Gurney [1951] published necessary conditions for the stratum boundaries, so that with Neyman's optimal allocation of the sample sizen the variance of the sample mean will become a minimum. They introduced in the variance of the sample mean for the sample sizesn _h the opti mal values according to Neyman and differentiated this variance with respect to the stratum boundaries. Because Neyman's allocation formula yields only feasible solutions forn _h N _h , the conditions ofDalenius result in wrong, i.e. nonfeasible solutions, if one of the restrictionsn _h N _h (h=1 (1) L) is violated.By the example of a logarithmic normal distribution with =0, =1,5 forL=2 the behaviour of the Dalenius-Neyman-minimum and that of the feasible minimum will be shown in dependence on the sampling fractionq=n/N and a critical valueq _c will be given. For valuesq>q _c the Dalenius-Neyman-minimum is no longer feasible.For the same logarithmic normal distribution andL=2 (1) 10 this critical sampling fractionq _c will be given (section 5).For different values of andq the optimal stratum boundaries and sampling fractions are listed in section 6 forL=2;3;4.