Mathematical Bioeconomics: The Mathematics of Conservation / Edition 3

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Overall, this is an appealing work for students and professionals, and is certain to remain as one of the key works in natural resource analysis.
—Mathematical Reviews

Biological renewable resources, essential to the survival of mankind, are increasingly overexploited by individuals and corporations that often sacrifice long-term economic health and sustainability for short-term gains. Mathematical Bioeconomics: The Mathematics of Conservation, Third Edition analyzes the economic forces underlying these misuses of renewable resources and discusses more effective methods of resource management. Promoting a complete understanding of general principles, the book allows readers to discover how rigorous mathematical models that incorporate both economic and biological factors should replace intuitive arguments for conservation and sustainability.

This Third Edition continues to combine methodologies from the fields of economics, biology, and mathematics to explain how analytic models are essential for developing a complete understanding of complex resource systems. The book has been updated to address the need for incorporating individual economic incentives, the value of diversity, and the overriding importance of uncertainty in mathematical models. Coverage of game theory, overcapacity, uncertainty, and risk analysis has been added as well a expanded treatment of topics such as:

  • Models of individual harvest behavior and economic incentives
  • Response of individual harvester to various types of harvesting regulations
  • Reasons underlying excess harvesting capacity
  • Externalities in resource harvesting industries
  • Decision analysis in biological resource management

Fundamental concepts of population dynamics and economics are utilized throughout the book while mathematical techniques are incorporated in an accessible manner. Relevant data from current research sheds light on the presented material, and exercises provide readers with an opportunity to test comprehension of discussed mathematical methods and techniques.

Continuing to provide a complete and modernized presentation of the fundamental principles of the topic, Mathematical Bioeconomics, Third Edition is an excellent book for courses on applied mathematics, resource management, and environmental studies at the upper-undergraduate and graduate levels. It also serves as an insightful reference for resource managers, ecologists, biologists, and other professionals who work to improve the management of renewable resources and develop sustainable practices in the environmental sciences.

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Product Details

Meet the Author

Colin W. Clark, PhD, is Professor Emeritus at the University if British Columbia (Canada). Throughout his career, he has collaborated with biologists and economists in model construction and application. A Fellow of the Royal Society of Canada and the Royal Society of London, Dr. Clark has published extensively in his areas of research interest, which include behavioral ecology and the economics of natural resources with an emphasis on commercial fisheries.

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Table of Contents

Preface ix

Acknowledgments xv

1 A Generic Bioeconomic Model 1

1.1 What is Conservation? 1

1.2 What is a Model? 3

Exercises 4

1.3 A Dynamic Resource-Harvesting Model 4

Exercises 13

1.4 A Bioeconomic Model 14

Exercises 22

1.5 A Dynamic Optimization Model 23

Exercises 31

1.6 A Model of Individual Behavior 32

Exercises 39

1.7 Individual Vessel Quotas 40

Exercises 49

1.8 The Veil of Uncertainty 49

Exercises 50

1.9 Other Resources 50

2 Dynamic Optimization 55

2 1 Constrained Optimization 55

Exercises 61

2.2 Optimal Control Theory in One Dimension 62

Exercises 75

2.3 Nonlinear Control Problems 76

Exercises 82

2.4 Discrete-time Optimal Control 83

Exercises 94

2.5 Appendix 95

Exercises 98

3 Basic Economic Concepts 101

3.1 Interest and Discounting 101

Exercises 106

3.2 Supply and Demand 106

Exercises 116

3.3 Demand-limited Bionomic Equilibrium 116

Exercises 125

3.4 Optimal Harvesting Strategies 125

3.5 External Costs 127

Exercises 137

3.6 Competition, Cooperation, and the Theory of Games 137

Exercises 142

3.7 The Economics of Uncertainty 142

Exercises 150

4 Investing in Harvesting Capacity 153

4.1 Optimal Harvesting Capacity 154

Exercises 162

4.2 Investment Decisions under Competition 163

Exercises 167

4.3 Eliminating Excess Capacity 167

Exercises 173

4.4 Appendix: Optimal Investment 174

5 Regulation of Renewable Resource Harvesting 179

5.1 The Consequences of Unregulated Resource Harvesting 179

Exercises 185

5.2 Methods of Regulating Resource Harvesting 185

Exercises 189

5.3 Shadow Prices, Taxes and Tradeable Quotas 189

Exercises 211

5.4 Regulation without Taxes or Tradeable Quotas 212

Exercises 221

6 Growth and Aging 223

6.1 Forestry Models 224

Exercises 232

6.2 Fisheries: The Cohort Model 233

Exercises 243

6.3 Multicohort Fisheries 244

Exercises 250

7 Resource Management under Uncertainty 253

7.1 Process and Observational Uncertainly 255

Exercises 260

7.2 Understanding Uncertainty 261

Exercises 272

7.3 Process Uncertainty 273

Exercises 276

Exercises 279

7.4 An Introduction Decision Analysis 279

Exercises 283

7.5 Economic Uncertainties 284

Exercises 287

7.6 Appendix: Bayesian Updating 287

Exercises 300

8 Disaggregated Resource Models 303

8.1 Source-sink Models 304

Exercises 304

Exercises 309

8.2 Predator-prey Models 309

Exercises 316

8.3 Mixed-species Harvesting 317

Exercises 321

9 Synopsis 323

Problem Solutions 329

References 355

Index 365

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