Theory of Cost and Production Functions

Ronald William Shephard

Published by Princeton University Press 1971

Theory of Cost and Production Functions

Ronald William Shephard

Volume 1605 in the series Princeton Studies in Mathematical Economics

In the series Princeton Legacy Library

https://doi.org/10.1515/9781400871087

Overview
Contents

About this book

A sequel to his frequently cited Cost and Production Functions (1953), this book offers a unified, comprehensive treatment of these functions which underlie the economic theory of production.

The approach is axiomatic for a definition of technology, by mappings of input vectors into subsets of output vectors that represent the unconstrained technical possibilities of production. To provide a completely general means of characterizing a technology, an alternative to the production function, called the Distance Function, is introduced.

The duality between cost function and production function is developed by introducing a cost correspondence, showing that these two functions are given in terms of each other by dual minimum problems.

The special class of production structures called Homothetic is given more general definition and extended to technologies with multiple outputs.

Originally published in 1971.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Topics

Frontmatter Publicly Available Download PDF	i
Preface Requires Authentication Unlicensed Licensed Download PDF	vii
Table of Contents Publicly Available Download PDF	ix
Chapter 1. Introduction Requires Authentication Unlicensed Licensed Download PDF	1
Chapter 2. The Producton Functon Requires Authentication Unlicensed Licensed Download PDF	13
Chapter 3. The Distance Function of a Production Structure Requires Authentication Unlicensed Licensed Download PDF	64
Chapter 4. The Factor Minimal Cost Function Requires Authentication Unlicensed Licensed Download PDF	79
Chapter 5. The Cost Structure Requires Authentication Unlicensed Licensed Download PDF	96
Chapter 6. The Aggregation Problem for Cost and Production Functions Requires Authentication Unlicensed Licensed Download PDF	114
Chapter 7. The Price Minimal Cost Function Requires Authentication Unlicensed Licensed Download PDF	147
Chapter 8. Duality of Cost and Production Structures and Related Functions Requires Authentication Unlicensed Licensed Download PDF	159
Chapter 9. Production Correspondences Requires Authentication Unlicensed Licensed Download PDF	178
Chapter 10. Cost and Benefit (Revenue) Functions for Production Correspondences, and the Related Cost, Benefit (Revenue), Cost-Limited-Output and Benefit (Revenue)-Afforded-Input Correspondences Requires Authentication Unlicensed Licensed Download PDF	223
Chapter 11. Dualities for Production Correspondences Requires Authentication Unlicensed Licensed Download PDF	261
Appendix 1. Mathematical Concepts and Theorems for Semi-Continuity and Quasi-Concavity (Convexity) Requires Authentication Unlicensed Licensed Download PDF	295
Appendix 2. Mathematical Concepts and Propositions for Correspondences Requires Authentication Unlicensed Licensed Download PDF	298
Appendix 3. Utility Functions Requires Authentication Unlicensed Licensed Download PDF	301
Index Requires Authentication Unlicensed Licensed Download PDF	306