The format of this monograph is three essays, which we arrived at after spending a year writing over one hundred pages of what we even tually realized was a tedious reworking of old material. So we started over determined to write something new. At first we thought this approach might not work as a coherent mono graph, which is why we chose the essay format rather than chapters. As it turns out, there is a common thread-namely the directional distance function, which also gave us our title. As you shall see, the directional distance function includes traditional distance functions and efficiency measures as special cases providing a unifying framework for existing productivity and efficiency measures. It is also flexible enough to open up new areas in productivity and efficiency analysis such as environmen tal and aggregation issues. That we did not see this earlier is humbling; a student at a recent conference raised his hand and asked 'Why didn't you start with the directional distance function in the first place? In deed. This manuscript is intended to make up for our earlier oversights. This monograph contains papers coauthored with Wen-Fu Lee and Osman Zaim and one paper written by two former students, Hiroyuki Fukuyama and Bill Weber. We thank them for their contributions. An other former student, Jim Logan (Logi) read and critiqued the manu script for which we are grateful."

Economists have long studied the efficiency of firms, industries, and entire economies. This volume brings together leading scholars to make connections between efficiency and a number of diverse areas of current interest to economists, including an examination of the efficiency of tax systems across generations that overlap, and the efficiency of firm mergers that highlights the tradeoff between the synergy of the merger and the problem of managerial oversight in the now larger firm. An empirical look at productivity growth of states uses a tripartite decomposition of labor productivity into technological innovation, improvement in efficiency, and the capital deepening brought about by new business investment, shedding light on important debates on their relative importance. The efficiency of patent laws is examined in a modern model of economic growth. These contributions are complemented by analyses of methodological problems involved in the measurement, estimation and aggregation of efficiency indices.

Professor Sten Malmquist constructed the Malmquist quantity index and in doing so developed a distance function defined on a consumption space. This function is the consumer analog to the Shephard input distance function of producers and is used in ratio form to define the quantity index. This volume contains new contributions based on Malmquist's work nearly 50 years ago and provides modern perspectives on the value of this research.

Our original reason for writing this book was the desire to write down in one place a complete summary of the major results in du ality theory pioneered by Ronald W. Shephard in three of his books, Cost and Production Functions (1953), Theory of Cost and Produc tion Functions (1970), and Indirect Production Functions (1974). In this way, newcomers to the field would have easy access to these important ideas. In adg, ition, we report a few new results of our own. In particular, we show the duality relationship between the profit function and the eight equivalent representations of technol ogy that were elucidated by Shephard. However, in planning the book and discussing it with colleagues it became evident that such a book would be more useful if it also provided a number of applications of Shephard's duality theory to economic problems. Thus, we have also attempted to present exam ples of the use of duality theory in areas such as efficiency measure ment, index number theory, shadow pricing, cost-benefit analysis, and econometric estimation. Much of our thinking about duality theory and its uses has been influenced by our present and former collaborators. They include Charles Blackorby, Shawna Grosskopf, Knox Lovell, Robert Russell, and, not surprisingly, Ronald W. Shephard. We have also benefit ted over the years from many discussions with W. Erwin Diewert."

Our intention with this book is to extend the efficiency literature to the case of intertemporal models. We do this in steps. First, we introduce static network models which will serve as building blocks for our intertemporal budgeting models and our dynamic models. Next, we devote two chapters to productivity measurements, which we think of as comparative static models. Intertemporal budgeting models and dynamic models are taken up after that. Each chapter, except Chapter One, contains an empirical applica- tion. These applications are coauthored with colleagues and stu- dents; thanks are due to Runar Brannlund, Yijan He, Julius Hor- vath, Pontus Roos, Jerry Whittaker and S. (Lek) Yaisawarng . . We would also like to thank Dale Boisso and Kathy Hayes for gra- ciously sharing their data on Illinois municipalities with us. Two of the applications are already published, namely: "Environmental Regulation and Profitability: Applications to Swedish Pulp and Pa- per Mills," Environmental and Resource Economics 6: 23-36, 1995, (Section 2. 5) and "Productivity and Quality Changes in Swedish Pharmacies," International Journal of Production Economics 39: 137-144, 1995, (Section 3. 5). We are grateful to Kluwer Academic Publishers and Elsevier Science for kindly allowing us to reproduce these publications here. During the summer 1995 we spent a very enjoyable two months at the Center for Economic Studies (CES) at the University of Munich.

Sweden has a long history of ambitious environmental, energy and climate policy. Due to the large amount of data available it is possible to perform statistically sound analysis and assess long term changes in productivity, efficiency, and technological development. The data at hand together with Sweden's ambitious energy and climate policy provides a unique opportunity to shed light on pertinent policy issues. The Impact of Climate Policy on Environmental and Economic Performance answers several key questions: What is the effect of the CO2 tax on environmental performance and profitability of firms? Does including emissions in productivity measurement of the industrial firm matter? Did the introduction of the EU ETS spur technological development in the Swedish industrial firm? What air pollutant is most inhibiting production when regulated? Being aware and learning from the Swedish case can be very relevant for countries that are in the process of shaping their climate policy. This book is of great importance to researchers and policy makers who are interested in environmental economics, industrial economics and climate change.

Data Envelopment Analysis (DEA) is often overlooked in empirical work such as diagnostic tests to determine whether the data conform with technology which, in turn, is important in identifying technical change, or finding which types of DEA models allow data transformations, including dealing with ordinal data.Advances in Data Envelopment Analysis focuses on both theoretical developments and their applications into the measurement of productive efficiency and productivity growth, such as its application to the modelling of time substitution, i.e. the problem of how to allocate resources over time, and estimating the 'value' of a Decision Making Unit (DMU).

Sweden has a long history of ambitious environmental, energy and climate policy. Due to the large amount of data available it is possible to perform statistically sound analysis and assess long term changes in productivity, efficiency, and technological development. The data at hand together with Sweden's ambitious energy and climate policy provides a unique opportunity to shed light on pertinent policy issues. The Impact of Climate Policy on Environmental and Economic Performance answers several key questions: What is the effect of the CO2 tax on environmental performance and profitability of firms? Does including emissions in productivity measurement of the industrial firm matter? Did the introduction of the EU ETS spur technological development in the Swedish industrial firm? What air pollutant is most inhibiting production when regulated? Being aware and learning from the Swedish case can be very relevant for countries that are in the process of shaping their climate policy. This book is of great importance to researchers and policy makers who are interested in environmental economics, industrial economics and climate change.

This book presents a mathematical programming approach to the analysis of production frontiers and efficiency measurement. The authors construct a variety of production frontiers, and by measuring distances to them are able to develop a model of efficient producer behaviour and a taxonomy of possible types of departure from efficiency in various environments. Linear programming is used as an analytical and computational technique in order to accomplish this. The approach developed is then applied to modelling producer behaviour. By focusing on the empirical relevance of production frontiers and distances to them, and applying linear programming techniques to artificial data to illustrate the type of information they can generate, this book provides a unique study in applied production analysis. It will be of interest to scholars and students of economics and operations research, and analysts in business and government.

Professor Sten Malmquist constructed the Malmquist quantity index and in doing so developed a distance function defined on a consumption space. This function is the consumer analog to the Shephard input distance function of producers and is used in ratio form to define the quantity index. This volume contains new contributions based on Malmquist's work nearly 50 years ago and provides modern perspectives on the value of this research.

Our original reason for writing this book was the desire to write down in one place a complete summary of the major results in du ality theory pioneered by Ronald W. Shephard in three of his books, Cost and Production Functions (1953), Theory of Cost and Produc tion Functions (1970), and Indirect Production Functions (1974). In this way, newcomers to the field would have easy access to these important ideas. In adg, ition, we report a few new results of our own. In particular, we show the duality relationship between the profit function and the eight equivalent representations of technol ogy that were elucidated by Shephard. However, in planning the book and discussing it with colleagues it became evident that such a book would be more useful if it also provided a number of applications of Shephard's duality theory to economic problems. Thus, we have also attempted to present exam ples of the use of duality theory in areas such as efficiency measure ment, index number theory, shadow pricing, cost-benefit analysis, and econometric estimation. Much of our thinking about duality theory and its uses has been influenced by our present and former collaborators. They include Charles Blackorby, Shawna Grosskopf, Knox Lovell, Robert Russell, and, not surprisingly, Ronald W. Shephard. We have also benefit ted over the years from many discussions with W. Erwin Diewert."

This book presents a mathematical programming approach to the analysis of production frontiers and efficiency measurement. The authors construct a variety of production frontiers, and by measuring distances to them are able to develop a model of efficient producer behaviour and a taxonomy of possible types of departure from efficiency in various environments. Linear programming is used as an analytical and computational technique in order to accomplish this. The approach developed is then applied to modelling producer behaviour. By focusing on the empirical relevance of production frontiers and distances to them, and applying linear programming techniques to artificial data to illustrate the type of information they can generate, this book provides a unique study in applied production analysis. It will be of interest to scholars and students of economics and operations research, and analysts in business and government.

Our intention with this book is to extend the efficiency literature to the case of intertemporal models. We do this in steps. First, we introduce static network models which will serve as building blocks for our intertemporal budgeting models and our dynamic models. Next, we devote two chapters to productivity measurements, which we think of as comparative static models. Intertemporal budgeting models and dynamic models are taken up after that. Each chapter, except Chapter One, contains an empirical applica- tion. These applications are coauthored with colleagues and stu- dents; thanks are due to Runar Brannlund, Yijan He, Julius Hor- vath, Pontus Roos, Jerry Whittaker and S. (Lek) Yaisawarng . . We would also like to thank Dale Boisso and Kathy Hayes for gra- ciously sharing their data on Illinois municipalities with us. Two of the applications are already published, namely: "Environmental Regulation and Profitability: Applications to Swedish Pulp and Pa- per Mills," Environmental and Resource Economics 6: 23-36, 1995, (Section 2. 5) and "Productivity and Quality Changes in Swedish Pharmacies," International Journal of Production Economics 39: 137-144, 1995, (Section 3. 5). We are grateful to Kluwer Academic Publishers and Elsevier Science for kindly allowing us to reproduce these publications here. During the summer 1995 we spent a very enjoyable two months at the Center for Economic Studies (CES) at the University of Munich.

The basic notion underlying this monograph - budget or revenue constrained models of production - we owe to Ronald W. Shephard, who recognized its fundamental importance in modeling behavior in a wide variety of settings including the service and public sector. Our endeavor here is to extend Shephard's earlier work in several directions while maintaining his axiomatic approach. Our contributions include an expanded set of duality results and a general bent toward empirical implementation: including various parameterizations, applications to efficiency and productivity measurement, and shadow pricing. We hope to provide those engaged in empirical work with some powerful and useful tools which have received relatively little attention. The nature of the material in this monograph is somewhat technical, however, the level of mathematical difficulty is standard. Although we have tried to keep the monograph fairly self-contained, we have also kept technical detail to a minimum in the body of the text. Many technical extensions appear as problems at the ends of Chapters. The reader is also referred to the notes at the end of each chapter for references to additional literature. A prepublication draft of this manuscript was used as lecture notes in a graduate course in production theory at the Department of Economics at Bilkent University. We thank our students as well as faculty members for their patience and interest. Special thanks go to Dean Togan, Zeynap Koksal and Ali Dogramaci for making our stay in Ankara not only productive, but also enjoyable.

This volume brings together leading scholars to make connections between efficiency and a number of diverse areas of current interest to economists. Included are new results concerning aggregation of technical efficiency, sources of productivity growth in U.S. manufacturing, intellectual property rights, and the determinants of successful mergers.

The format of this monograph is three essays, which we arrived at after spending a year writing over one hundred pages of what we even tually realized was a tedious reworking of old material. So we started over determined to write something new. At first we thought this approach might not work as a coherent mono graph, which is why we chose the essay format rather than chapters. As it turns out, there is a common thread-namely the directional distance function, which also gave us our title. As you shall see, the directional distance function includes traditional distance functions and efficiency measures as special cases providing a unifying framework for existing productivity and efficiency measures. It is also flexible enough to open up new areas in productivity and efficiency analysis such as environmen tal and aggregation issues. That we did not see this earlier is humbling; a student at a recent conference raised his hand and asked 'Why didn't you start with the directional distance function in the first place? In deed. This manuscript is intended to make up for our earlier oversights. This monograph contains papers coauthored with Wen-Fu Lee and Osman Zaim and one paper written by two former students, Hiroyuki Fukuyama and Bill Weber. We thank them for their contributions. An other former student, Jim Logan (Logi) read and critiqued the manu script for which we are grateful."

Written by production economics and finance specialists Rolf Fare and Shawna Grosskopf of Oregon State University and Dimitris Margaritis of the University of Auckland, Pricing Non-marketed Goods Using Distance Functions, is an inspiring new contribution highlighting the importance of duality theory for valuation purposes, especially for hard to price inputs or resources, intended or unintended goods and assets. The theoretical pricing models are supplemented by self-standing empirical applications covering real estate pricing, environmental preservation, transfer pricing, shadow prices of university knowledge outputs and spillovers, and the pricing of bank equity capital and non-performing loans.

This graduate text develops production theory from a set of reasonable axioms. The theory is presented both in a primal and dual as well as in an indirect (constrained) framework. The basic model leads to a set of efficiency measures which can be readily employed in empirical work. A first draft of the text was used to teach students at Vanderbilt University. The text includes a variety of exercise problems.

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 ...... .