Entropy, Environment and Resources

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2 M. Faber H. Niemes G. Stephan With the Cooperation of L. Freytag Entropy, Environment and Resources An Essay in Physico-Economics Translated from the German:by I. Pellengahr With 33 Figures Springer-Verlag Berlin Heidelberg New York London Paris Tokyo

3 Authors Prof. Dr. Malte Faber Dr. Gunter Stephan Alfred Weber-Institut fur Sozial- und Staatswissenschaften Universitat Heidelberg, Grabengasse 14, D-6900 Heidelberg 1 Dr. Horst Niemes GKW-Consult Gottlieb-Daimler-StraBe 12a, D-6800 Mannheim With the Cooperation of Dipl.-Phys. Dr. Lutz Freytag Physikalisches Institut, Universitat Tiibingen Auf der Morgenstelle 14, D-7400 Tiibingen 1 Translator Dipl.-Volksw. Ingo Pellengahr Alfred Weber-Institut fur Sozial- und Staatswissenschaften Universitat Heidelberg, Grabengasse 14, D-6900 Heidelberg 1 Title of the original German edition: Lecture Notes in Economics and Mathematical Systems, Vol. 214 Entropie, Umweltschutz und Rohstoffverbrauch: Eine naturwissenschaftlich okonomische Untersuchung Springer-Verlag Berlin Heidelberg 1983 ISBN-13: ISBN-13: e-isbn-13: DOl: / Library of Congress Cataloging-in-Publication Data. Faber, Malte Michael. Entropy, environment, and resources. Translated from German. Bibliography: p. Includes index. I. Environmental policy-mathematical models. 2. Environmental protection-mathematical models. 3. Natural resources-mathematical models. 4. Austrian school of economists. L Niemes, Horst. II. Stephan, Gunter. III. Title. HC79.E5F ' This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9,1965, in its version of June 24,1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. Springer-Verlag Berlin Heidelberg 1987 Softcover reprint of the hardcover 1st edition 1987 The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. 2142/

4 Preface This book is one of the products of a three-year research project. Our objectives were: - to apply neo-austrian capital theory to long-run problems of environmental protection and resource use; - to develop an approach that takes physical relationships into consideration; - to narrow the gap between theory and practice in environmental economics. For this purpose, we established three interrelated research programs. In the first of these we supplemented and generalized neo Austrian capital theory (STEPHAN 1980, REISS 1981, FABER 1986). In the second which is presented in this volume we developed an interdisciplinary approach to natural resources, Using concepts and methods from thermodynamics we investigated environmental and resource problems and their interrelationships. Finally, in the third research program we authored the monograph "Umweltschutz und Input-Output-Analyse. Mit zwei Fallstudien aus der Wassergiitewirtschaft" (Environmental Protection and Input-Output-Analysis. With Two Case Studies in Water-Quality Management) (FABER, NIEMES, and STEPHAN 1983). Here we first gave an extensive description of the development of the management, in particular of the water-quality management, of the waste treatment sector of the BASF AG., Ludwigshafen/FRGl, in the seventies. In this we could resort to prior work done by NIEMES (1978, 1981). With the help of the information from these plants, as well as from the chemical industry, we constructed a dynamic input-output model of the environment. This we then applied to the water quality management of the state of Baden-Wiirttemberg from 1971 to This is one of the three great chemical enterprises in the Federal Republic of Germany; 50,000 workers are employed.

5 VI Preface Whereas the monograph mentioned is a purely economic analysis with both theoretical and empirical content, the present work is the attempt to develop an interdisciplinary approach. An extensive overview of the content will be given in the second part of our Introduction. Thermodynamic methods are used to relate natural science to our economic considerations. An essential reason for this is that in this way the "directedness" of physical processes, which equally applies to every economic production process, could be explicitly taken into consideration. For instance, GEORGESCU-RoEGEN (1971:3) writes: "The significant fact for the economist is that the new science ofthermodynamics began as a physics of economic value and, basically, can still be regarded as such. The Entropy Law itself emerges as the most economic in nature of all natural laws." We use thermodynamics, in particular the notion of entropy, in order to establish relationships between the economic system and the environmental system.. It is well-known that interdisciplinary research is as urgently needed as it is difficult to put into practice (KOOPMANS 1979, FABER and PROOPS 1985). On the one hand, the time and the effort necessary to make ourselves familiar with physical relationships and to apply them to economic relationships often seemed insurmountable. On the other hand, more than once we were so violently criticized that we seriously considered abandoning our attempts. Finally, however, we were helped by the insight that an interdisciplinary procedure can entail mistakes, and that if one wants to undertake interdisciplinary work, one will need the courage to expose oneself to the critique not only of one's own, but also to that of other disciplines. At the last stage of our endeavor, Mr. Lutz FREYTAG, who holds a degree in physics from the University of Tiibingen, helped us in re-arranging and re-writing the physical Part II of our analysis. For this reason we have mentioned his collaboration in the title. We are aware of the fact that it is almost impossible to give an introduction to thermodynamics in a space as confined as that in this book. We have thus foregone completeness and confined ourselves to a relatively simple presentation of those physical ideas that we needed for the development of our theory. In this we have to accept that to the natural scientist some concepts or relationships may seem to be explained in an unduly simplified manner. We considered, however, this procedure to be advisable for our more social science oriented readership.

6 Preface VII The first German edition of this book has been used three times as a graduate textbook in economics at the University of Heidelberg. However, this book is not easy to read, even though the mathematical requirements are not beyond the knowledge of a student of economics. Difficulties arise on the one hand because we analyze four- and five-sector models over many periods. In order to facilitate the understanding of production and consumption in multi-sector models for the student, we have chosen the following procedure in Heidelberg. We started the course with Chapter 4 and the first two Sections of Chapter 5 of the "Introduction to Modem Austrian Capital Theory" (FABER 1979). This, however, is only a helpful, but by no means a necessary condition for an understanding of the monograph at hand. For economic readers another difficulty stems from the fact that they are unacquainted with the physical relationships presented in Part II, Chapters 3 and 4. In order to reach these readers we chose a procedure which assumed practically no prior knowledge of physics.;. Moreover, one can understand the following Parts III and IV 'without having read Part ll. The case will be reversed for readers with a stronger background in physical science. These will find Parts I, III, and IV not easy reading. We hope, however, that the reader senses that we took much pain in presenting our material. Thus we use many examples from reality, draw many graphs, develop all derivations step by step, and summarize more extensive formal relationships in appendices to the chapters concerned. Wherever it was possible, we confined ourselves to a graphical presentation. This book is addressed primarily, but not exclusively, to social scientists; it is also addressed to physicists, engineers, students, and those dealing with interdisciplinary environmental problems. We thus hope that our book will be read also by natural scientists and technicians interested in economic relationships. We thank many friends and collegues who have read parts of the manuscript and have given us much advice and valuable criticism. Out of these we would like to especially mention the natural scientists Mr. Dipl.-Physiker Dietrich BRUNE (Kernforschungszentrum Karlsruhe (Nuclear Research Center Karlsruhe», Prof. Dr. Werner BOGE (Heidelberg), Prof. Dr. Ulrich FORSTNER (Hamburg), Prof. Dr. Reiner KUMMEL (Wiirzburg), MARTIN O'CONNOR, Msc, MA (Auckland, New Zealand), Prof. Dr. Udo SCHERZ (Berlin), Dr. Dieter SCHUMANN (Heidelberg), Prof. Dr. Upke-Walther SCHMINCKE (Aachen), and an unknown referee of the Springer Press. We also wish to mention the economists Prof. Dr. Friedrich BREYER (Hagen), Prof. Dr. Peter FLASCHEL (Bielefeld), Prof. Dr.

7 VIII Preface Klaus JAEGER (Berlin), Prof. Dr. Hans Jiirgen JAKSCH (Heidelberg), Gernot KLEPPER, Ph. D. (Kiel), Prof. Dr. Wilhelm KRELLE (Bonn), Gabriel LOZADA, Ph. D. (Stanford), and especially Dr. Gerhard MAmR (Heidelberg) who has read and discussed with us all versions of the manuscript. The first German edition appeared in 1983, as Lecture Notes in Economics and Mathematical Systems No. 214 of the Springer Press. It was revised and in parts enlarged for the English edition by Malte FABER and Gunter STEPHAN. Mr. Dipl.-Volkswirt Ingo PELLENGAHR has, although in contact with the autors, independently translated the text. John PROOPS, Ph. D. (Keele/U.K.) examined the entire manuscript and made numerous suggestions with regard to both style and content. Dipl.-Volkswirt Peter MI CHAELIS proofread the finished text and compiled the subject index. Mrs. Brigitte RUGER typed our manuscript. A subject as controversial as ours requires special emphasis of the fact that all responsibility for the way in which we have taken advice and criticism into consideration' remains with us. We finally thank the Deutsche Forschungsgemeinschaft for the considerable financial support of our endeavor over a two-year period, without which it could not have been realized. Heidelberg, September 1987 Malte FABER Horst NIEMES Gunter STEPHAN

8 Contents o Introduction: Starting Point, Objectives, and Content.... Starting Point and Objectives Content Part I. Environmental Protection 1 An Introduction to Dynamic Models of the Environment 1.1 The Relationships Between the Ecosystem and Its Economic Subsystem l.2 Some Approaches to the Dynamic Analysis of the Use of the Environment The Environment as a Source of Resources The Optimal Use of a Non-Renewable Resource l.2.l.2 The Optimal Use of a Renewable Resource The Environment as a Recipient of Pollutants and as a Supplier of Public Goods l The Accumulation of Poll utants An Optimization Model Environmental Models with Capital Accumulation Natural Purification l Recycling A Disaggregated Environment-Capital Model 2.1 The Basic Model The Technology The Environmental Sector

9 X Contents The Transformation of Emissions into Pollutants: The Diffusion Function.... The Effects of Pollutants on the Flow of Environmental Goods: The Damage Function The Allocative Effects of Marginal Changes in the Production Program.... Extending the Model.... A Capital Good in the Waste Treatment Sector The Technology.... Optimality Conditions Emissions in the Consumption Sector The Case of Several Pollutants with Centralized Waste Treatment.... The Assignment of Waste Treatment Costs Private and Social Aspects of the Assignment of Waste Treatment Costs and of Environmental Damage Local and Central Waste Tre3tment Measures Appendix: Constraints and Optimality Conditions for the Environmental Protection Model with Capital Formation in the Waste Treatment Sector Part II. Entropy and the Use of the Environment The Notion of Entropy Thermodynamics Energy, GIBBS' Fundamental Equation, Intensive and Extensive Quantities An Example of Entropy: The Diffusion of Gases The Second Law of Thermodynamics... The Irreversibility of Economic Processes and the Impossibility of the Land of Cockaigne Negative Flow of Entropy.... Entropy, Order, and Information.... Using the Entropy Approach to Characterize the Environment as a Recipient of Pollutants Entropy and Equilibrium.... The Entropy Approach as a Means of Determining Deviations from Equilibrium A First Attempt to Employ Entropy as a Variable in a Pollution Function

10 Contents XI Using the Entropy Approach to Characterize the Environment as a Supplier of Resources 104 Resource Concentration and Factor Requirements in the Extraction of Resources 105 The Separation Process as a Reversal of the Diffusion Process 105 The Change in Entropy as a Function of Resource Concentration 107 The Energy Requirements in the Extraction Process 112 Factor Input in Resource Extraction 115 The Change in Entropy in the Environmental Sector as a Result of Resource Extraction 119 The Limits of Our Approach 124 Appendix: Value Charts for Section (Numerical Tables for the Relationship Between the Mol-Specific Change in Entropy and Resource Concentration)...: Part m. The Use of Scarce Resources with Decreasing Resource Concentration The Integration of the Resource Prob/?m into a Disaggregated Capital Model The Structure of the Model The Resource Sector Resource Quantities and Concentrations in the Environmental Sector.... The System of Constraint Equations Replacement of Techniques over Time The Transition from Technique Tl to Technique T2 and Its Effects on the Economic System A Schema of Replacement Processes in the Resource Model The Effects of Replacement Processes in the Resource Model on the Major Economic Variables

11 X Contents Necessary Conditions for the Replacement of Techniques.... Optimality Conditions Interpreting the Optimality Conditions Model Variantl.... Model Variant II Appendix: Derivation of Shadow Prices of Model Variant II Part IV. Environmental Protection and Resources Interdependencies Between Environmental Protection and Resource Use Exemplifiedfor Recycling and Deposition Optimal Resource Use and Environmental Protection in an Environment-Resource Model The Model Optimality Conditions Interdependencies Between Environmental Protection and Resource Use with Recycling and Deposition Recycling in the Environment-Resource Model Allocative Aspects of Recycling Deposition as a Support for Recycling How Can We Avoid Wasting Low Entropy? Outlook References Subject Index 203