Knowledge that Transforms

A procedure is presented for the efficient computational solution of linear programs having a certain structural property characteristic of a large class of problems of practical interest. The property makes possible the decomposition of the problem into a sequence of small linear programs whose iterated solutions solve the given problem through a generalization of the simplex method for linear programming. 1. THE DECOMPOSED LINEAR PROGRAM MANY LINEAR programming problems of practical interest have the property that they may be described, in part, as composed of separate linear programming problems tied together by a number of constraints considerably smaller than the total number imposed on the problem. When the matrix of coefficients of such a problem, suitably ordered, is displayed in the usual way, a pattern emerges like that shown in Figure 1. In this figure the constraint matrix has been partitioned into nonzero blocks A1 and By, the right-hand side column of constants correspondingly into b, bl,..., bn; and the costs,

This paper investigates the factors determining how rapidly the use of a new technique spreads from one firm to another. A simple model is presented to help explain differences among innovations in the rate of imitation. Deterministic and stochastic versions of this model are tested against data showing how rapidly firms in four industries came to use twelve important innovations. The empirical results seem quite consistent with both versions of the model.

In order to explain fairly simply how expectations are formed, we advance the hypothesis that they are essentially the same as the predictions of the relevant economic theory. In particular, the hypothesis asserts that the economy generally does not waste information, and that expectations depend specifically on the structure of the entire system. Methods of analysis, which are appropriate under special conditions, are described in the context of an isolated market with a fixed production lag. The interpretative value of the hypothesis is illustrated by introducing commodity speculation into the system. 1. INTRODUCTION THAT EXPECTATIONS of economic variables may be subject to error has, for some time, been recognized as an important part of most explanations of changes in the level of business activity. The ex ante analysis of the Stockholm School-although it has created its fair share of confusion-is a highly suggestive approach to short-run problems. It has undoubtedly been a