CONTENTS Preface to the Second Edition: What Stayed, What Went, What's New? page xi Acknowledgments xiii 1Basic Concepts 1 1.0 Renewable, Nonrenewable, and Environmental Resources 1 1.1Population Dynamics: Simulation, Steady State, and Local Stability 5 1.2Extraction of a Nonrenewable Resource10 1.3Discounting11 1.4 A Discrete-Time Extension of the Method of Lagrange Multipliers 17 1.5Asymptotic Depletion of a Nonrenewable Resource 25 1.6The Maximum Principle and Dynamic Programming in Discrete Time 26 1.7Dynamic Programming in a Two-Period, Two-State Model 30 1.8A Markov Decision Model and Stochastic Dynamic Programming32 1.9Exercises34 2Solving Numerical Allocation Problems Using Excel's Solver 41 2.0Introduction and Overview41 2.1Optimal Rotation for an Even-Aged Forest 42 2.2Solving an Implicit Equation for the .Optimal Steady-State Fish Stock 45 2.3Solving an Implicit Equation for the Optimal Date of Exhaustion 47 2.4Optimal First-Period Harvest in a Two-Period, Two-State Model 47 2.5The Optimal Linear Harvest Policy 50 2.6Optimal Escapement in a Finite-Horizon Deterministic Model 52 2.7Optimal Escapement for One Realization (Seedl)ofZ,+1 53 2.8An Optimal Depletion Problem: The Mine Manager's Problem 55 2.9Approximating 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 3The Economics of Fisheries 75 3.0Introduction and Overview 75 3.1Net Growth 76 3.2Fishery Production Functions 79 3.3The Yield-Effort Function 82 3.4The Static Model of Open Access 84 3.5The Dynamic Model of Open Access 85 3.6Regulated Open Access 90 3.7Maximization of Static Rent 95 3.8Present-Value Maximization 97 3.9Traditional Management Policies 102 3.10 Bioeconomic or Incentive-Based Management Policies 105 3.11 Marine Reserves 120 3.12 Exercises 126 4The 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 5The 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 6Stock Pollutants 200 6.0 Introduction and Overview 200 6.1 The Commodity-Residual Transformation Frontier202 6.2 Damage Functions and Welfare204 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 Change223 6.7 Emission Taxes and Marketable Pollution Permits 229 6.8 Exercises 238 7Maximin 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 Complications261 7.6 An Exercise 262 Annotated Bibliography 263 Index 283