Linear programming and economic analysis

Linear programming has been one of the most important postwar developments in economic theory. Its growth has been particularly rapid, thanks to the joint efforts of mathematicians, business and defense administrators, statisticians, and economists. Yet the economist who wants to learn how linear programming is related to traditional economic theory can nowhere find a comprehensive treatment its many facets The present book hopes to give the economist, who knows existing economic theory but who does not pretend to be an accomplished mathe matician, a broad introduction to the theory of linear programming, or, as it is sometimes called, activity analysis. It hopes also to be useful to the practitioner of managerial economics, and possibly to provide the growing body of mathematicians interested in programming problems with insights into the vast body of modern economic theory.

When asked by The RAND Corporation to undertake the book, we agreed to avoid higher mathematics. We planned to stress the economic aspects of the problem, paying attention to practical problems of compu tation and giving important concrete applications but laying no stress on them. So vast has the theory become that we have had to be selective, reluctantly deciding to omit many interesting topics and applications Thus, we have not dealt with the important role of linear-programming concepts in statistical decision theory. On the other hand, we have gone into the extensive interrelations

between the celebrated von Neumann theory of games and linear pro

gramming, particularly since every economist will want to know the interrelations between game theory and traditional economic theories of duopoly and bilateral monopoly. And modern economists will be interested in the interrelations between linear programming and modern welfare economics and the insights that linear programming gives into the determinateness of Walrasian equilibrium-as perfected by the recent works of K. Arrow, G. Debreu, L. W. McKenzie, and others. This book can also serve as an expository introduction to the student interested in the Leontief theory of input-output, which has played so important a role in the last twenty years. Similarly, we have treated extensively problems of dynamic linear programming, not only beca of their intrinsic interest but also because of their vital connections with the economist's theory of capital that most difficult field of moders economic theory. Had we more space and time at our disposal we might have added some material summarizing the related "dynamic program ming" methods of Richard Bellman, also developed at RAND. This new theory is of considerable interest to economists but mathematically more difficult than what we have attempted here.