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### Summary

### Summary

The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. Mathematical Bioeconomics: Optimal Management of Renewable Resources, Second Edition serves as an introduction to the theory of biological conservation, including a wealth of applications to the fishery and forestry industries. The mathematical modeling of the productive aspects of renewable-resource management is explained, featuring both economic and biological factors, with much attention paid to the optimal use of resource stocks over time. This Second Edition provides new chapters on the theory of resource regulation and on stochastic resource models, new sections on irreversible investment, game-theoretic models, dynamic programming, and an expanded bibliography. Book jacket.

### Author Notes

Colin W. Clark, PhD, is Emeritus Professor at the University of British Columbia in Vancouver, Canada

### Table of Contents

Introduction | p. 1 |

1 Elementary Dynamics of Exploited Populations | p. 9 |

1.1 The Logistic Growth Model | p. 10 |

1.2 Generalized Logistic Models: Depensation | p. 16 |

1.3 Summary and Critique | p. 21 |

2 Economic Models of Renewable-Resource Harvesting | p. 24 |

2.1 The Open-Access Fishery | p. 24 |

2.2 Economic Overfishing | p. 28 |

2.3 Biological Overfishing | p. 32 |

2.4 Optimal Fishery Management | p. 35 |

2.5 The Optimal Harvest Policy | p. 39 |

2.6 Examples Based on the Schaefer Model | p. 45 |

2.7 Linear Variational Problems | p. 50 |

2.8 The Possibility of Extinction | p. 59 |

2.9 Summary and Critique | p. 62 |

3 Capital-Theoretic Aspects of Resource Management | p. 68 |

3.1 Interest and Discount Rates | p. 68 |

3.2 Capital Theory and Renewable Resources | p. 72 |

3.3 Nonautonomous Models | p. 74 |

3.4 Applications to Policy Problems: Labor Mobility in the Fishery | p. 76 |

4 Optimal Control Theory | p. 88 |

4.1 One-Dimensional Control Problems | p. 89 |

4.2 A Nonlinear Fishery Model | p. 97 |

4.3 Economic Interpretation of the Maximum Principle | p. 102 |

4.4 Multidimensional Optimal Control Problems | p. 107 |

4.5 Optimal Investment in Renewable-Resource Harvesting | p. 110 |

5 Supply and Demand: Nonlinear Models | p. 122 |

5.1 The Elementary Theory of Supply and Demand | p. 122 |

5.2 Supply and Demand in Fisheries | p. 131 |

5.3 Nonlinear Cost Effects: Pulse Fishing | p. 144 |

5.4 Game-Theoretic Models | p. 152 |

5.5 Transboundary Fishery Resources: A Further Application of the Theory | p. 158 |

5.6 Summary and Critique | p. 164 |

6 Dynamical Systems | p. 168 |

6.1 Basic Theory | p. 168 |

6.2 Dynamical Systems in the Plane: Linear Theory | p. 172 |

6.3 Isoclines | p. 179 |

6.4 Nonlinear Plane-Autonomous Systems | p. 181 |

6.5 Limit Cycles | p. 187 |

6.6 Gause's Model of Interspecific Competition | p. 192 |

7 Discrete-Time and Metered Models | p. 197 |

7.1 A General Metered Stock-Recruitment Model | p. 198 |

7.2 The Beverton-Holt Stock-Recruitment Model | p. 204 |

7.3 Depensation Models | p. 211 |

7.4 Overcompensation | p. 215 |

7.5 A Simple Cohort Model | p. 217 |

7.6 The Production Function of a Fishery | p. 221 |

7.7 Optimal Harvest Policies | p. 228 |

7.8 The Discrete Maximum Principle | p. 234 |

7.9 Dynamic Programming | p. 240 |

8 The Theory of Resource Regulation | p. 245 |

8.1 A Behavioral Model | p. 246 |

8.2 Optimization Analysis | p. 250 |

8.3 Limited Entry | p. 254 |

8.4 Taxes and Allocated Transferable Quotas | p. 255 |

8.5 Total Catch Quotas | p. 260 |

8.6 Summary and Critique | p. 264 |

9 Growth and Aging | p. 267 |

9.1 Forestry Management: The Faustmann Model | p. 268 |

9.2 The Beverton-Holt Fisheries Model | p. 275 |

9.3 Dynamic Optimization in the Beverton-Holt Model | p. 282 |

9.4 The Case of Bounded F | p. 287 |

9.5 Multiple Cohorts: Nonselective Gear | p. 291 |

9.6 Pulse Fishing | p. 298 |

9.7 Multiple Cohorts: Selective Gear | p. 301 |

9.8 Regulation | p. 303 |

9.9 Summary and Critique | p. 306 |

10 Multispecies Models | p. 310 |

10.1 Differential Productivity | p. 311 |

10.2 Harvesting Competing Populations | p. 319 |

10.3 Selective Harvesting | p. 324 |

10.4 A Diffusion Model: The Inshore-Offshore Fishery | p. 331 |

10.5 Summary and Critique | p. 340 |

11 Stochastic Resource Models | p. 343 |

11.1 Stochastic Dynamic Programming | p. 344 |

11.2 A Stochastic Forest Rotation Model | p. 349 |

11.3 Uncertainty and Learning | p. 352 |

11.4 Searching for Fish | p. 353 |

11.5 Summary and Critique | p. 363 |

Supplementary Reading | p. 365 |