ACTIVITY ANALYSIS OF
PRODUCTION AND ALLOCATION
Proceedings of a Conference

Edited by
TJALLING C. KOOPMANS
In Cooperation with
ARMEN ALCHIAN       GEORGE B. DANTIZG
NICHOLAS GEORGESCU-ROEGEN
PAUL A. SAMUELSON       ALBERT W. TUCKER
John Wiley & Sons, Inc., New York
Chapman & Hall, Limited, London
1951
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TABLE OF CONTENTS

Chapter  Page 
Preliminary Pages
Introduction, by Tjalling C. Koopmans

PART ONE: THEORY OF PROGRAMMING AND ALLOCATION

I.  The Programming of Interdependent Activities: General Discussion, by Marshall K. Wood and George B. Dantzig 15 
II.  The Programming of Interdependent Activities: Mathematical Model, by George B. Dantzig 19 
III.  Analysis of Production as an Efficient Combination of Activities, by Tjalling C. Koopmans 33 
IV.  The Aggregate Linear Production Function and Its Applications to von Neumann's Economic Model, by Nicholas Georgescu-Roegen 98 
V.  Relaxation Phenomena in Linear Dynamic Models, by Nicholas Georgescu-Roegen 116 
VI.  Uses of Leontief's Open Input-Output Models, by Harlan M. Smith 132 
VII.  Abstract of a Theorem Concerning Substitutability in Open Leontief Models, by Paul A. Samuelson 142 
VIII.  Alternative Proof of the Substitution Theorem of Leontief Models in the Case of Three Industries, by Tjalling C. Koopmans 147 
IX.  Alternative Proof of the Substitution Theorem of Leontief Models in the General Case, by Kenneth J. Arrow 155 
X.  Some Properties of a Generalized Leontief Model, by Nicholas Georgescu-Roegen 165 

PART TWO: APPLICATIONS OF ALLOCATION MODELS

XI.  On the Choice of a Crop Rotation Plan, by Clifford Hildreth and Stanley Reiter 177 
XII.  Development of Dynamic Models for Program Planning, by Marshall K. Wood and Murray A. Geisler 189 
XIII.  Representation in a Linear Model of Nonlinear Growth Curves in the Aircraft Industry, by Marshall K. Wood 216 
XIV.  A Model of Transportation, by Tjalling C. Koopmans and Stanley Reiter 222 
XV.  Effects of Technological Change in a Linear Model, by Herbert A. Simon
    With comments by Ansley Coale and Yale Brozen
260 
XVI.  The Accuracy of Economic Observations, by Oskar Morgenstern 282 

PART THREE: MATHEMATICAL PROPERTIES OF CONVEX SETS

XVII.  Convex Polyhedral Cones and Linear Inequalities, by David Gale 287 
XVIII.  Theory of Convex Polyhedral Cones, by Murray Gerstenhaber 298 
XIX.  Linear Programming and the Theory of Games, by David Gale, Harold W. Kuhn, and Albert W. Tucker 317 
XX.  A Proof of the Equivalence of the Programming Problem and the Game Problem, by George B. Dantzig 330 

PART FOUR: PROBLEMS OF COMPUTATION

XXI.  Maximization of a Linear Function of Variables Subject to Linear Inequalities, by George B. Dantzig 339 
XXII.  Application of the Simplex Method to a Game Theory Problem, by Robert Dorfman 348 
XXIII.  Application of the Simplex Method to a Transportation Problem, by George B. Dantzig 359 
XXIV.  Iterative Solution of Games by Fictitious Play, by George W. Brown 374 
XXV.  Computational Suggestions for Maximizing a Linear Function Subject to Linear Inequalities, by George W. Brown and Tjalling C. Koopmans 377 
References 381 
Index of Names 387 
Subject Index 389