Preface to the Second Edition: What Stayed, What Went,
What's New? .................................................... xi
Acknowledgments .............................................. xiii
1 Basic Concepts ............................................... 1
1.0 Renewable, Nonrenewable, and Environmental Resources .... 1
1.1 Population Dynamics: Simulation, Steady State, and
Local Stability ......................................... 5
1.2 Extraction of a Nonrenewable Resource .................. 10
1.3 Discounting ............................................ 11
1.4 A Discrete-Time Extension of the Method of Lagrange
Multipliers ............................................ 17
1.5 Asymptotic Depletion of a Nonrenewable Resource ........ 25
1.6 The Maximum Principle and Dynamic Programming in
Discrete Time .......................................... 26
1.7 Dynamic Programming in a Two-Period, Two-State Model ... 30
1.8 A Markov Decision Model and Stochastic Dynamic
Programming ............................................ 32
1.9 Exercises .............................................. 34
2 Solving Numerical Allocation Problems Using Excel's
Solver ...................................................... 41
2.0 Introduction and Overview .............................. 41
2.1 Optimal Rotation for an Even-Aged Forest ............... 42
2.2 Solving an Implicit Equation for the Optimal Steady-
State Fish Stock ....................................... 45
2.3 Solving an Implicit Equation for the Optimal Date
of Exhaustion .......................................... 47
2.4 Optimal First-Period Harvest in a Two-Period, Two-
State Model ............................................ 47
2.5 The Optimal Linear Harvest Policy ...................... 50
2.6 Optimal Escapement in a Finite-Horizon Deterministic
Model .................................................. 52
2.7 Optimal Escapement for One Realization (Seed 1) of
Zt+1 ................................................... 53
2.8 An Optimal Depletion Problem: The Mine Manager's
Problem ................................................ 55
2.9 Approximating the Asymptotic Approach to
a Bioeconomic Optimum .................................. 58
2.10 The Most Rapid Approach Path to an Optimal Pollution
Stock .................................................. 63
2.11 Optimal Escapement with Stochastic Growth .............. 67
2.12 Exercises .............................................. 69
3 The Economics of Fisheries .................................. 75
3.0 Introduction and Overview .............................. 75
3.1 Net Growth ............................................. 76
3.2 Fishery Production Functions ........................... 79
3.3 The Yield-Effort Function .............................. 82
3.4 The Static Model of Open Access ........................ 84
3.5 The Dynamic Model of Open Access ....................... 85
3.6 Regulated Open Access .................................. 90
3.7 Maximization of Static Rent ............................ 95
3.8 Present-Value Maximization ............................. 97
3.9 Traditional Management Policies ....................... 102
3.10 Bioeconomic or Incentive-Based Management Policies .... 105
3.11 Marine Reserves ....................................... 120
3.12 Exercises ............................................. 126
4 The Economics of Forestry .................................. 132
4.0 Introduction and Overview ............................. 132
4.1 The Volume Function and Mean Annual Increment ......... 133
4.2 The Optimal Single Rotation ........................... 135
4.3 The Faustmann Rotation ................................ 136
4.4 An Example ............................................ 139
4.5 Timber Supply ......................................... 143
4.6 The Optimal Stock of Old-Growth Forest ................ 146
4.7 Exercises ............................................. 149
5 The Economics of Nonrenewable Resources .................... 153
5.0 Introduction and Overview ............................. 153
5.1 A Simple Model ........................................ 154
5.2 Hotelling's Rule ...................................... 156
5.3 The Inverse Demand Curve .............................. 157
5.4 Extraction and Price Paths in the Competitive
Industry .............................................. 159
5.5 Extraction and Price Paths under Monopoly ............. 164
5.6 Reserve-Dependent Costs ............................... 167
5.7 Exploration ........................................... 171
5.8 The Economic Measure of Scarcity ...................... 176
5.9 A Postscript to "Betting the Planet" .................. 195
5.10 Exercises ............................................. 196
6 Stock Pollutants ........................................... 200
6.0 Introduction and Overview ............................. 200
6.1 The Commodity-Residual Transformation Frontier ........ 202
6.2 Damage Functions and Welfare .......................... 204
6.3 A Degradable Stock Pollutant .......................... 207
6.4 Diffusion and a Nondegradable Stock Pollutant ......... 212
6.5 Optimal Extraction with a Nondegradable Waste ......... 220
6.6 Climate Change ........................................ 223
6.7 Emission Taxes and Marketable Pollution Permits ....... 229
6.8 Exercises ............................................. 238
7 Maximin Utility with Renewable and Nonrenewable
Resources .................................................. 242
7.0 Introduction and Overview ............................. 242
7.1 The Maximin Criterion ................................. 244
7.2 The Gini Coefficient .................................. 246
7.3 Growth with Resources, Intergenerational Utility,
and the Maximin Criterion ............................. 248
7.4 Overlapping Generations ............................... 255
7.5 Complications ......................................... 261
7.6 An Exercise ........................................... 262
Annotated Bibliography ........................................ 263
Index ......................................................... 283
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