
TABLE OF CONTENTS


Chapter 

Page 

Preliminary Pages 
i 

Introduction, by
Tjalling C. Koopmans 
1 

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
GeorgescuRoegen 
98 
V. 
Relaxation Phenomena
in Linear Dynamic Models, by Nicholas GeorgescuRoegen 
116 
VI. 
Uses of Leontief's
Open InputOutput 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 GeorgescuRoegen 
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 