IN recent years, there has been a very marked rise in the interest economists have shown in the process of invention, and in industrial Research and Development the institutionalization of inventive activities by business enterprises. developing interest in invention has stemmed from several roots. One important one is the growing body of research findings on productivity,' which turned the attention of economists interested in economic growth toward the process of technological change. These studies showed that only a small fraction of the total increase in output per worker which had occurred in the American economy since the late igth century could be explained by capital per worker. lion's share had to be attributed to something else, to or efficiency. term increased productivity covers a wide number of different elements and the operation by which is defined and measured obscures a variety of economic phenomena. Better allocation of existing factor supplies (the process of dynamic adjustment) and capital formation in humans (education, health, etc.) are two of the most important. But it seems obvious that technological change also has been an important ingredient. A second source of the interest in invention is the changing way that economists are coming to look at the competitive process. Increasingly the focus is on competition through new products, rather than on direct price competition. And concurrently, normative considerations are shifting toward conditions of long run growth rather than fixing on short term Pareto optimality. In a sense these developments represent a renaissance of Schumpeter. A third source of the heightened interest in inventive activity has been the cold war, and the growing awareness that our national security may depend on the output of our military research and development effort organized inventive effort for the purpose of creating more effective weapons. Closely related to the interest in military R and D 2 is the growing concern with the technological race to which the Soviets have challenged us. interest in inventive activity which stems from interest in defense and the space program has tended to be more micro-oriented than the interest stemming from concern with problems of economic growth. studies generated have tended to be normative analyses of conditions of efficiency (how resources should be allocated), rather than analyses of factors determining the actual allocation of inventive effort. This paper is focused on one aspect of R and D efficiency: the problem of achieving a given objective at minimum cost. Thus the paper is directly concerned with the third area of interest discussed above. However, some of the implications of the model seem to have relevance to more macro issues of policy, and to a positive analysis of the allocation of inventive effort. In Section I, the basic efficiency problem is discussed and the concept of a parallel path strategy is introduced. Section II presents a model. Lest the reader expect too much, let me state at the outset that the model is much too crude to provide reliable quantitative answers. Rather, the purpose of the model is to provide a framework for analysis and to explore some implications of two aspects of the R and D nrocess. the uncertaintv which exists * This paper is one product of a continuing RAND study of Research and Development management. idea of a parallel development strategy has a long history at RAND. Burton Klein, William Meckling, Emmanuel Mesthene, Leland Johnson, Thomas Marschak, Armen Alchian, William Capron, and others all have contributed to its evolution. ' See, for example: J. Schmookler, The Changing Efficiency of the American Economy, I869--I934, this REVIEW, XXXIV (Aug. I952); M. Abramowitz, Resource and Output Trends in the United States since I870, American Economic Review, XLVI (May I956); Robert Solow, Technical Change and the Associate Production Function, this REVIEW, XXXIX (Aug. I957); B. F. Massell, Capital Formation and Technological Change in United States' Manufacturing, this REVIEW, XLII (May I960). 2 Research and Development will henceforth be abbreviated as R and D.

ONE of the more conceptually mysterious aspects of linear programming is the problem of degeneracy the breaking down of the simplex calculation method under certain circumstances. Although a set of rules for dealing with degeneracy is well known, in the absence of an understanding of the nature of the problem the rules must be followed by rote. This note presents a simple geometrical explanation of the problem, the solution, and explains why certain types of programming problems frequently lead to degeneracy. It is hoped that the presentation will be of use both to students and teachers of linear programming. Before presenting the geometry of degeneracy, it is necessary to review briefly the geometry of linear programming and the simplex method of computing optimum linear programs.