Production Functions

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.

Electricity Economics: Production Functions with Electricity studies the production output from analyzing patterns of electricity consumption. Since electricity data can be used to measure scenarios of economic performance due to its accuracy and reliability, it could therefore also be used to help scholars explore new research frontiers that directly and indirectly benefits human society. Our research initially explores a similar pattern to substitute the Cobb–Douglas function with the production function with electricity to track and forecast economic activities. The book systematically introduces the theoretical frameworks and mathematical models of economics from the perspective of electricity consumption. The E-GDP functions are presented for case studies of more than 20 developed and developing countries. These functions also demonstrate substantial similarities between human DNA and production functions with electricity in terms of four major characteristics, namely replication, mutation, uniqueness, and evolution. Furthermore, the book includes extensive data and case studies on the U.S., China, Japan, etc. It is intended for scientists, engineers, financial professionals, policy makers, consultants, and anyone else with a desire to study electricity economics as well as related applications. Dr. Zhaoguang Hu is the vice president and chief energy specialist at the State Grid Energy Research Institute, China. Zheng Hu is a PhD candidate at the Center for Energy and Environmental Policy, University of Delaware, USA.

This study is the result of an interest in the economic theory of production intermittently pursued during the past three years. Over this period I have received substantial support from the Office of Naval Research, first from a personal service consulting contract directly with the Mathematics Division of the Office of Naval Research and secondly from Project N6 onr-27009 at Princeton Univer sity under the direction of Professor Oskar Morgenstern. Grateful acknowledgement is made to the ·Office of Naval Research for this support and to Professor Morgenstern, in particular, for his interest in the puolication of this research. The responsibility for errors and omissions, how ever, rests entirely upon the author. Professor G. C. Evans has given in terms of a simple total cost function, depending solely upon output rate, a treatment of certain aspects of the economic theory of production which has inherent generality and convenience of formulation. The classical approach of expressing the technology of production by means of a production function is potentially less restrictive than the use of a simple total cost function, but it has not been applied in a more general form other than to derive the familiar conditions between marginal productivities of the factors of produc tion and their market prices.

This monograph is intended as a contribution to applied work in production theory by treating: a) The measurement problems involved whenever several outputs are jointly produced, and b) The (possible) econometric framework for estimating production function parameters whenever (relative) prices vary sufficiently over the observations. Thus, the "pure" theory of production, and the theory of non-linear regression is not treated in sufficient detail: for these topics we refer to the available literature~ for a comprehensive list of references we refer to Uebe (1975). Some years ago, papers by L. J. Lau and W. E. Diewert initiated my interest in duality within production theory, and then I started to appreciate R. W. Shephard's fundamental contribution to this topic. This monograph is a (minor) revision of a Ph. D. dissertation submitted to the Department of Economics, The University of Wisconsin, Madison, in August 1973. The Graduate School and the Social Systems Research Institute provided funds for the reported computer work, Lawrence R. Klein and Laurits R. Christensen provided data, and as a Graduate Student I received financial support in form of an University Fellowship~ all this is very much appreciated. With some nostalgia I think back to the enjoyable period of learning during the preparation of my diFosertation~ I appreciate the spirit within the department, and the guidance of my committee Arthur S. Goldberger, Dennis J. Aigner, and Laurits R. Christensen.