Entropy, Environment and Resources

0 Introduction: Starting Point, Objectives, and Content.- 0.1 Starting Point and Objectives.- 0.2 Content.- I. Environmental Protection.- 1 An Introduction to Dynamic Models of the Environment.- 1.1 The Relationships Between the Ecosystem and Its Economic Subsystem.- 1.2 Some Approaches to the Dynamic Analysis of the Use of the Environment.- 1.2.1 The Environment as a Source of Resources.- 1.2.1.1 The Optimal Use of a Non-Renewable Resource.- 1.2.1.2 The Optimal Use of a Renewable Resource.- 1.2.2 The Environment as a Recipient of Pollutants and as a Supplier of Public Goods.- 1.2.2.1 The Accumulation of Pollutants.- 1.2.2.2 An Optimization Model.- 1.2.3 Environmental Models with Capital Accumulation.- 1.2.3.1 Natural Purification.- 1.2.3.2 Recycling.- 2 A Disaggregated Environment-Capital Model.- 2.1 The Basic Model.- 2.1.1 The Technology.- 2.1.2 The Environmental Sector.- 2.1.2.1 The Transformation of Emissions into Pollutants: The Diffusion Function.- 2.1.2.2 The Effects of Pollutants on the Flow of Environmental Goods: The Damage Function.- 2.1.3 The Allocative Effects of Marginal Changes in the Production Program.- 2.2 Extending the Model.- 2.2.1 A Capital Good in the Waste Treatment Sector.- 2.2.1.1 The Technology.- 2.2.1.2 Optimality Conditions.- 2.2.2 Emissions in the Consumption Sector.- 2.2.3 The Case of Several Pollutants with Centralized Waste Treatment.- 2.2.3.1 The Assignment of Waste Treatment Costs.- 2.2.3.2 Private and Social Aspects of the Assignment of Waste Treatment Costs and of Environmental Damage.- 2.2.4 Local and Central Waste Treatment Measures.- Appendix: Constraints and Optimality Conditions for the Environmental Protection Model with Capital Formation in the Waste Treatment Sector.- II. Entropy and the Use of the Environment.- 3 The Notion of Entropy.- 3.1 Thermodynamics.- 3.2 Energy, GIBBS' Fundamental Equation, Intensive and Extensive Quantities.- 3.3 An Example of Entropy: The Diffusion of Gases.- 3.4 The Second Law of Thermodynamics.- 3.5 The Irreversibility of Economic Processes and the Impossibility of the Land of Cockaigne.- 3.6 Negative Flow of Entropy.- 3.7 Entropy, Order, and Information.- 3.8 Using the Entropy Approach to Characterize the Environment as a Recipient of Pollutants.- 3.8.1 Entropy and Equilibrium.- 3.8.2 The Entropy Approach as a Means of Determining Deviations from Equilibrium.- 3.9 A First Attempt to Employ Entropy as a Variable in a Pollution Function.- 4 Using the Entropy Approach to Characterize the Environment as a Supplier of Resources.- 4.1 Resource Concentration and Factor Requirements in the Extraction of Resources.- 4.1.1 The Separation Process as a Reversal of the Diffusion Process.- 4.1.2 The Change in Entropy as a Function of Resource Concentration.- 4.1.3 The Energy Requirements in the Extraction Process.- 4.1.4 Factor Input in Resource Extraction.- 4.2 The Change in Entropy in the Environmental Sector as a Result of Resource Extraction.- 4.3 The Limits of Our Approach.- Appendix: Value Charts for Section 4.1.2 (Numerical Tables for the Relationship Between the Mol-Specific Change in Entropy and Resource Concentration).- III. The Use of Scarce Resources with Decreasing Resource Concentration.- 5 The Integration of the Resource Problem into a Disaggregated Capital Model.- 5.1 The Structure of the Model.- 5.1.1 The Resource Sector.- 5.1.2 Resource Quantities and Concentrations in the Environmental Sector.- 5.2 The System of Constraint Equations.- 6 Replacement of Techniques over Time.- 6.1 The Transition from Technique T1 to Technique and Its Effects on the Economic System.- 6.1.1 A Schema of Replacement Processes in the Resource Model.- 6.1.2 The Effects of Replacement Processes in the Resource Model on the Major Economic Variables.- 6.2 Necessary Conditions for the Replacement of Techniques.- 6.3 Optimality Conditions.- 6.4 Interpreting the Optimality Conditions.- 6.4.1 Model Variant I.- 6.4.2 Model Variant II.- Appendix: Derivation of Shadow Prices of Model Variant.- IV. Environmental Protection and Resources.- 7 Interdependencies Between Environmental Protection and Resource Use Exemplified for Recycling and Deposition.- 7.1 Optimal Resource Use and Environmental Protection in an Environment-Resource Model.- 7.1.1 The Model.- 7.1.2 Optimality Conditions.- 7.2 Interdependencies Between Environmental Protection and Resource Use with Recycling and Deposition.- 7.2.1 Recycling in the Environment-Resource Model.- 7.2.2 Allocative Aspects of Recycling.- 7.2.3 Deposition as a Support for Recycling.- 7.3 How Can We Avoid Wasting Low Entropy?.- 7.4 Outlook.- 8 References.- 9 Subject Index.