Cover image for Mathematical bioeconomics : the optimal management of renewable resources
Title:
Mathematical bioeconomics : the optimal management of renewable resources
Author:
Clark, Colin Whitcomb, 1931-
Publication Information:
New York : Wiley, [1976]

©1976
Physical Description:
xi, 352 pages ; 23 cm.
General Note:
"Wiley-Interscience publication."

Includes index.
Language:
English
ISBN:
9780471158561
Format :
Book

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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

Introductionp. 1
1 Elementary Dynamics of Exploited Populationsp. 9
1.1 The Logistic Growth Modelp. 10
1.2 Generalized Logistic Models: Depensationp. 16
1.3 Summary and Critiquep. 21
2 Economic Models of Renewable-Resource Harvestingp. 24
2.1 The Open-Access Fisheryp. 24
2.2 Economic Overfishingp. 28
2.3 Biological Overfishingp. 32
2.4 Optimal Fishery Managementp. 35
2.5 The Optimal Harvest Policyp. 39
2.6 Examples Based on the Schaefer Modelp. 45
2.7 Linear Variational Problemsp. 50
2.8 The Possibility of Extinctionp. 59
2.9 Summary and Critiquep. 62
3 Capital-Theoretic Aspects of Resource Managementp. 68
3.1 Interest and Discount Ratesp. 68
3.2 Capital Theory and Renewable Resourcesp. 72
3.3 Nonautonomous Modelsp. 74
3.4 Applications to Policy Problems: Labor Mobility in the Fisheryp. 76
4 Optimal Control Theoryp. 88
4.1 One-Dimensional Control Problemsp. 89
4.2 A Nonlinear Fishery Modelp. 97
4.3 Economic Interpretation of the Maximum Principlep. 102
4.4 Multidimensional Optimal Control Problemsp. 107
4.5 Optimal Investment in Renewable-Resource Harvestingp. 110
5 Supply and Demand: Nonlinear Modelsp. 122
5.1 The Elementary Theory of Supply and Demandp. 122
5.2 Supply and Demand in Fisheriesp. 131
5.3 Nonlinear Cost Effects: Pulse Fishingp. 144
5.4 Game-Theoretic Modelsp. 152
5.5 Transboundary Fishery Resources: A Further Application of the Theoryp. 158
5.6 Summary and Critiquep. 164
6 Dynamical Systemsp. 168
6.1 Basic Theoryp. 168
6.2 Dynamical Systems in the Plane: Linear Theoryp. 172
6.3 Isoclinesp. 179
6.4 Nonlinear Plane-Autonomous Systemsp. 181
6.5 Limit Cyclesp. 187
6.6 Gause's Model of Interspecific Competitionp. 192
7 Discrete-Time and Metered Modelsp. 197
7.1 A General Metered Stock-Recruitment Modelp. 198
7.2 The Beverton-Holt Stock-Recruitment Modelp. 204
7.3 Depensation Modelsp. 211
7.4 Overcompensationp. 215
7.5 A Simple Cohort Modelp. 217
7.6 The Production Function of a Fisheryp. 221
7.7 Optimal Harvest Policiesp. 228
7.8 The Discrete Maximum Principlep. 234
7.9 Dynamic Programmingp. 240
8 The Theory of Resource Regulationp. 245
8.1 A Behavioral Modelp. 246
8.2 Optimization Analysisp. 250
8.3 Limited Entryp. 254
8.4 Taxes and Allocated Transferable Quotasp. 255
8.5 Total Catch Quotasp. 260
8.6 Summary and Critiquep. 264
9 Growth and Agingp. 267
9.1 Forestry Management: The Faustmann Modelp. 268
9.2 The Beverton-Holt Fisheries Modelp. 275
9.3 Dynamic Optimization in the Beverton-Holt Modelp. 282
9.4 The Case of Bounded Fp. 287
9.5 Multiple Cohorts: Nonselective Gearp. 291
9.6 Pulse Fishingp. 298
9.7 Multiple Cohorts: Selective Gearp. 301
9.8 Regulationp. 303
9.9 Summary and Critiquep. 306
10 Multispecies Modelsp. 310
10.1 Differential Productivityp. 311
10.2 Harvesting Competing Populationsp. 319
10.3 Selective Harvestingp. 324
10.4 A Diffusion Model: The Inshore-Offshore Fisheryp. 331
10.5 Summary and Critiquep. 340
11 Stochastic Resource Modelsp. 343
11.1 Stochastic Dynamic Programmingp. 344
11.2 A Stochastic Forest Rotation Modelp. 349
11.3 Uncertainty and Learningp. 352
11.4 Searching for Fishp. 353
11.5 Summary and Critiquep. 363
Supplementary Readingp. 365