Preface
Contents
Chapter 1: Introduction
1.1 Differential Rent
1.2 Resource Rents and Opportunity Costs
1.3 Commodity Prices
1.4 Resource Cartel
References
Part I: Resource Rents and Opportunity Costs
Chapter 2: The Economics of Exhaustible Resources
2.1 Introduction
2.2 Hotelling´s Model
2.2.1 Hotelling Rule
2.2.2 The Decentralized Solution
2.2.3 Remarks on the Discount Rate and the Real Interest Rate
2.3 Equilibrium Extraction Paths
2.3.1 A Numerical Example
2.3.2 Constant-Elasticity Demand
2.4 Resource Exhaustion and the Backstop Technology
2.4.1 Solution for Constant-Elasticity Demand
2.5 The Herfindahl Principle
2.5.1 Solution for Two Sites
2.5.2 A Modified Hotelling Rule
2.6 The Principle of Comparative Advantage
2.6.1 Two Cities, Two Sites
2.7 Concluding Remarks
Appendices
A.1 Equation (2.44)
A.2 Inequalities (2.45)
A.3 Equation (2.51)
References
Chapter 3: Prices and Rents of Economically Recoverable Resources
3.1 Introduction
3.2 The Model of Economically Recoverable Resources
3.2.1 The Equilibrium Extraction Path
3.2.2 Dynamics of Marginal Rents
3.2.3 Solution for the Linear Case
3.2.4 A Numerical Example
3.2.5 Incomplete Resource Exhaustion in Hotelling´s Model
3.3 The Reservoir Model and the Structure of Oil Rents
3.3.1 Equilibrium Conditions
3.3.2 Decision Rule for Reserves Addition
3.3.3 Equilibrium Dynamic in the Linear Case
3.3.4 The Depletion Rate and the Initial Reserve Stock
3.3.5 The Structure of Rents
3.4 Resource Development and Extraction Without Depletion
3.4.1 The Stationary Equilibrium
3.4.2 The Linear-quadratic Case
3.5 Measuring Resource Scarcity
3.6 Concluding Remarks
Appendices
A.1 Decreasing Marginal Resource Rent w(t) for σ 1
A.2 The Solution (3.16), (3.17)
A.3 System (3.40)-(3.41)
References
Chapter 4: Pricing Energy Resources Under Transition to Alternative Energy
4.1 Introduction
4.2 The Model
4.2.1 Energy Consumption
4.2.2 Resource Extraction
4.2.3 Alternative Energy
4.2.4 Equilibrium Conditions
4.3 Valuation of Energy Resource and Energy Capital
4.3.1 Valuation of Conventional Energy Resource
4.3.2 Valuation of Alternative Energy Capital
4.4 The Equilibrium Transition Path
4.4.1 The Structure of Demand
4.4.2 Dynamic of the Energy Price Index
4.4.3 Dynamic of Energy Capital
4.4.4 Dynamic of Resource Extraction
4.5 The Resource Price Determination
4.5.1 The Equilibrium Utility Level
4.5.2 An Example: σ = 2
4.6 Transition Paths of Energy Capital and Extraction
4.6.1 Variation of the Elasticity of Substitution
4.6.2 Variation of the Preference Weight
4.7 The Green Paradox
4.8 Concluding Remarks
Appendices
A.1 Hicksian Demand Functions (4.23)
A.2 Time Derivatives of the Energy Price Index
A.3 The Time Path of Capital (4.33)
A.4 The Case σ = 2
References
Chapter 5: Global Carbon Budgeting and the Social Cost of Carbon
5.1 Introduction
5.2 Modelling Climate-Economy Interactions
5.3 The Overlapping-Generations Model
5.3.1 The Damage Function and the Greenhouse Effect
5.4 The Laissez-Faire Dynamic Equilibrium
5.4.1 The Long-Term Equilibrium
5.4.2 Equilibrium Transition Paths
5.5 The Social Planner´s Problem
5.5.1 The Long-Term Optimum
5.6 Numerical Analysis
5.7 The Social Cost of Carbon
5.7.1 The Long-Term Carbon Tax
5.7.2 The Social Cost of Carbon and Excess Returns
5.8 Concluding Remarks
Appendices
A.1 Characteristic Eq. (5.16)
A.2 The First-Order Conditions (5.24)-(5.26)
A.3 The Steady-State Rule (5.30)
References
Part II: Commodity Prices
Chapter 6: Commodity Prices, Convenience Yield and Inventory Behaviour
6.1 Introduction
6.2 Consumption-Based Model of Commodity Storage
6.3 Convenience Yield
6.4 Deterministic Dynamic of Commodity Price and Storage
6.5 Stochastic Dynamic of Commodity Market
6.5.1 Current Availability of Commodity
6.5.2 Inventory Behaviour
6.6 Solution for the Convenience Yield and the Commodity Price
6.6.1 Two Limit Cases
6.6.2 The First-Order Autocorrelation for Commodity Price
6.6.3 The Vector Autoregression
6.7 Price-Stabilizing and -Destabilizing Inventory Behaviour
6.7.1 The Adjustment of Storage
6.7.2 The Shock Effects on the Convenience Yield
6.8 Concluding Remarks
Appendices
A.1 Proposition 6.1
A.2 Proposition 6.2
A.3 Equation (6.31)
A.4 Proposition 6.3
A.5 Equation (6.40)
References
Chapter 7: Commodity Prices and Competitive Storage
7.1 Introduction
7.2 The Base Model
7.3 Two Regimes of Inventory Management
7.4 Stationary Rational Expectations Equilibrium
7.5 Autocorrelation of Supply
7.5.1 The Equilibrium Price Function
7.5.2 Contribution of Storage to Autocorrelation of Prices
7.6 Stochastic Demand: Persistence of Shocks and Volatility of the Oil Price
7.6.1 The Trader´s Problem
7.6.2 Equilibrium Prices
7.6.3 Income Processes
7.6.4 Price-Stabilizing and -Destabilizing Inventory Behaviour
7.6.5 The Three Epochs of Oil
7.7 Concluding Remarks
References
Chapter 8: Commodity Trade in Continuous Time, Long-Term Availability and Storage Capacity
8.1 Introduction
8.2 The Model
8.2.1 Commodity Market
8.2.2 Traders and Storage
8.3 The Value Function
8.4 Stationary Rational Expectations Equilibrium
8.4.1 The Equilibrium Price Function
8.4.2 Free-Boundary Conditions
8.5 The Saddle-Path Solution
8.5.1 Existence and Uniqueness of Equilibrium
8.6 The Storage Capacity Constraint
8.6.1 Storage Capacity and Trading Zones
8.7 Concluding Remarks
Appendices
A.1 Smooth-Pasting Condition (8.22)
A.2 System (8.23), (8.24)
A.3 Inequalities (8.32)
References
Part III: Resource Cartel
Chapter 9: Cartel Behaviour in an Exhaustible Resource Industry
9.1 Introduction
9.2 The Base Competitive Model
9.3 The Pure Monopoly Model
9.3.1 Dynamic of Marginal Revenue
9.3.2 Solution for Linear Demand
9.3.3 Conservationism of Resource Monopoly
9.3.4 The Case of Low-Elasticity Demand
9.4 Perfect Competition of Two Regions
9.5 The Cartel-Fringe Model
9.5.1 Dynamics of Outputs
9.5.2 The Bounds of the Cost Differential
9.6 Cartel and Fringe in the Presence of a Backstop Technology
9.6.1 The Cartel´s Strategic Choice
9.6.2 Cournot-Nash Equilibrium
9.6.3 The Equilibrium Resource Allocation
9.6.4 The Cartel´s Distorting Effects
9.7 Concluding Remarks
Appendices
A.1 Formula (9.11)
A.2 Condition (9.15)
A.3 Equation (9.24)
A.4 The Objective Function (9.39)
References
Chapter 10: The Oil Cartel and Misallocation of Production
10.1 Introduction
10.2 A Model of the Competitive Global Oil Industry
10.3 The Competitive Oil Price and the Allocation of Production
10.3.1 The Stationary Competitive Equilibrium
10.3.2 Competitive Production
10.3.3 The Firm´s Value and the Social Benefit of Extraction
10.4 Equilibrium in the Global Oil Industry with a Cartel
10.4.1 Resource Reallocation
10.4.2 The Pure Monopoly Case
10.4.3 A Numerical Example
10.5 Production Shifting and Welfare Losses
10.5.1 Cartel´s Value Gain
10.5.2 Welfare Losses
10.5.3 The Graphical Illustration
10.5.4 Continuation of the Numerical Example
10.6 The Effects of Technological Change
10.7 Concluding Remarks
Appendices
A.1 Condition (10.20)
A.2 Equations (10.27), (10.28)
A.3 Proposition 10.2
A.4 The Pure Monopoly Case
A.5 Proposition 10.3
A.6 Equations (10.41), (10.42)
A.7 Equation (10.44)
A.8 Equations (10.47)-(10.49)
References
Chapter 11: Anti-Conservationist Effects of the Conservationist Oil Cartel
11.1 Introduction
11.2 The Base Model of a Competitive Market
11.3 The Pure Monopoly Model
11.3.1 A Numerical Example
11.3.2 Comparison of Transition Paths
11.4 The Two-Region Model with Competitive Market
11.4.1 The Marginal Costs Equalization
11.4.2 The Equilibrium Extraction Path
11.5 The Two-Region Model with a Cartel
11.5.1 The Dynamic System
11.5.2 The Solution
11.5.3 Time Profiles of Extraction Rates and the Cartel´s Market Share
11.5.4 Production Shifting Over Time
11.6 Concluding Remarks
Appendices
A.1 Solution (11.19), (11.20)
A.2 Solution (11.29), (11.30)
A.3 Equation (11.36)
A.4 Characteristic Equation (11.41)
A.5 Formulae (11.45), (11.46)
References
