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Diminishing Returns is a concept deeply rooted in economic thought. After being introduced by Turgot in 1767 it has become accepted as one of the cornerstones of contemporary economic theory. My interest in this area started in the fall semester of 1971 at U.C. Berkeley where I was enrolled in Professor Ronald W. Shephard's class on the theory of production. Shephard introduced me to his work on the Law of Diminishing Returns, and encouraged me to continue that work. This monograph is a result of my inspiring experience with Professor Shephard; and I am sincerely grateful to him for everything he has taught me. In developing some of the materials in this monograph I have collabo rated with my Swedish friends Leif Jansson and Leif Svensson. It has been a pleasure to work with such capable individuals. For reading and making suggestions on a preliminary version of the monograph, thanks are due to W. Eichhorn, R. Kirk and R. Sato, and of course to my SIu friends Shawna Grosskopf and Dan Primont. I would also like to gratefully acknowledge the support received from a Stiftelsen Siamon grant. Lastbut not least, special thanks are given to Claudia Striegel for her care and patience in typing this manuscript. Rolf Fare October, 1979 Carbondale, Illinois TABLE OF CONTENTS Page CHAPTER 1. DIMINISHING RETURNS 1 1.1 Introduction .. 1.2 Restrictions of the Study 3 1.3 Outline of the Monograph. 4 CHAPTER 2. THE PRODUCTION TECHNOLOGY 5 2.1 Introduction ...... .

Laws of Diminishing Returns

1. Diminishing Returns.- 1.1 Introduction.- 1.2 Restrictions of the Study.- 1.3 Outline of the Monograph.- 2. The Production Technology.- 2.1 Introduction.- 2.2 The Input Correspondence.- 2.3 The Production Function.- 2.4 Properties of the Production Technology.- 2.5 Special Production Structures.- 3. Laws of Bounded Output and Diminishing Average Returns.- 3.1 Introduction.- 3.2 Essential and Weak Limitational Subsets of Factors of Production.- 3.3 Essential and Strong Limitational Subsets of Factors of Production.- 3.4 The Production Axioms and Bounded Output.- 3.5 Law of Bounded Average Returns.- 4. Congestion, Null Jointness and Laws of Variable Proportions.- 4.1 Introduction.- 4.2 Congestion of Production Factors.- 4.3 Properties of OL-, MOL- and OP- Congestion..- 4.4 Null Joint Factors of Production.- 4.5 OP- Congestion and Null Joint Factors of Production.- 4.6 Laws of Variable Proportions.- 4.7 An Empirical Example of Congested and Null Joint Factors of Production ..- 5. The Law of Diminishing Returns at the Extensive Margin.- 5.1 Introduction.- 5.2 Diminishing Returns to Extensive Use of a Production Factor.- 5.3 Holothetic Production Structure and Diminishing Returns to Extensive Use of a Production Factor ..- 6. Standard Notations and Mathematical Appendix.- 6.A Some Standard Notations.- 6.B Mathematical Appendix.- 7. Bibliography.- 8. Subject Index.