I Dynamic Models of Resource Extraction in Markets of Monopoly or Pure Competition with Full Information.- 1. Hotelling´s Model.- 2. Optimal Extraction Rates and Exploration.- 2.1 Pure Competition.- 2.2 Monopoly.- 3. Optimal Extraction Rates and Constant Elasticity of Demand.- 4. Market Structure and Optimal Depletion Rates.- 4.1 Pure Competition.- 4.2 Monopoly.- 5. Extraction of an Exhaustible Resource and Production of a Substitute.- 5.1 Social Optimum.- 5.2 Extraction of the Resource and Production of the Substitute by the same Monopoly.- 5.3 Many Owners of the Resource and Production of the Substitute by Monopoly.- 5.4 Many Owners of the Resource and Production of the Substitute by all.- 6. Extraction of Durable Exhaustible Resources.- 6.1 Discrete Time.- 6.2 Continuous Time.- 6.2.1 Pure Competition.- 6.2.2 Monopoly.- 7. Conclusions.- II Dynamic Models with Uncertainty and Monopolistic Markets or Pure Competition.- 1. Optimal Extraction Rates and Uncertainty with Respect to R&D towards Future Technologies.- 1.1 Exogenous Technical Progress.- 1.1.1 Basic Model.- 1.1.2 First Extension: Production.- 1.1.3 Second Extension: Exhaustible Resources.- 1.1.4 Third Extension: Uncertainty about the Future Technological Development.- 1.2 Endogenous Technical Progress.- 1.2.1 Basic Model.- 1.2.2 Modification of the Basic Model.- 1.2.3 Example with Exponentially Distributed Z.- 2. Optimal Extraction Rates and Unknown Reserves.- 2.1 Monopolistic Extraction Rates Depending on Time only.- 2.2 Monopolistic Extraction Rates Depending on Time and Quantities already Extracted.- 2.3 Optimal Extraction Rates and Pure Competition.- 2.3.1 Basic Model.- 2.3.2 Example with Two Suppliers.- 2.4 Optimal Extraction Rates from Consumer´s View.- 2.4.1 Basic Model.- 2.4.2 Example with Exponentially Distributed Z.- 2.5 Pure Competition and Optimal Extraction.- 3. Optimal Extraction Rates and Unknown Costs of the Development of a Substitute.- 3.1 One-period Analysis and Monopoly.- 3.2 One-period Analysis and Pure Competition.- 3.3 Two-period Analysis.- 3.3.1 Optimal Extraction and One Decision Maker.- 3.3.1.1 Basic Model.- 3.3.1.2 Example with Linear Demand.- 3.3.2 Optimal Extraction and Pure Competition.- 3.3.3 Extraction of the Resource and Production of the Substitute by Exactly One Monopoly.- 4. Conclusions.- III Short Introduction to the Theory of Differential Games.- IV Dynamic Models of Resource Extraction and Duopolistic Markets.- 1. An Introductory Duopoly Model with Production Strategies.- 2. Duopoly with Price Strategies and Exploration.- 2.1 Open-loop Controls.- 2.2 Closed-loop Controls.- 3. A Duopoly Model with Quantity Strategies.- 3.1 Introduction of the Model.- 3.2 Specialization of the Model: Linear-Quadratic Differential Game.- 4. Cartelization and Optimal Extraction of Exhaustible Resources.- 4.1 Pure Competition.- 4.2 Monopolistic Behaviour of the Cartel.- 4.3 Implications of Cartelization to the Profits of the Non-Cartel.- 5. Oligopoly with Discrete Time Parameter.- 6. Conclusions.- V Oligopolistic Extraction with Continuous Time.- 1. Basic Model with Quantity Strategies.- 1.1 Introduction of the Model.- 1.2 Algorithm for the Determination of a Nash Equilibrium.- 2. Specializations of the Basic Model.- 2.1 Fixed Resource Stock.- 2.2 Deterministic Expandable Resource Stocks.- 3. Oligopoly and Price Strategies.- 4. Conclusions.
I Dynamic Models of Resource Extraction in Markets of Monopoly or Pure Competition with Full Information.- 1. Hotelling's Model.- 2. Optimal Extraction Rates and Exploration.- 2.1 Pure Competition.- 2.2 Monopoly.- 3. Optimal Extraction Rates and Constant Elasticity of Demand.- 4. Market Structure and Optimal Depletion Rates.- 4.1 Pure Competition.- 4.2 Monopoly.- 5. Extraction of an Exhaustible Resource and Production of a Substitute.- 5.1 Social Optimum.- 5.2 Extraction of the Resource and Production of the Substitute by the same Monopoly.- 5.3 Many Owners of the Resource and Production of the Substitute by Monopoly.- 5.4 Many Owners of the Resource and Production of the Substitute by all.- 6. Extraction of Durable Exhaustible Resources.- 6.1 Discrete Time.- 6.2 Continuous Time.- 6.2.1 Pure Competition.- 6.2.2 Monopoly.- 7. Conclusions.- II Dynamic Models with Uncertainty and Monopolistic Markets or Pure Competition.- 1. Optimal Extraction Rates and Uncertainty with Respect to R&D towards Future Technologies.- 1.1 Exogenous Technical Progress.- 1.1.1 Basic Model.- 1.1.2 First Extension: Production.- 1.1.3 Second Extension: Exhaustible Resources.- 1.1.4 Third Extension: Uncertainty about the Future Technological Development.- 1.2 Endogenous Technical Progress.- 1.2.1 Basic Model.- 1.2.2 Modification of the Basic Model.- 1.2.3 Example with Exponentially Distributed Z.- 2. Optimal Extraction Rates and Unknown Reserves.- 2.1 Monopolistic Extraction Rates Depending on Time only.- 2.2 Monopolistic Extraction Rates Depending on Time and Quantities already Extracted.- 2.3 Optimal Extraction Rates and Pure Competition.- 2.3.1 Basic Model.- 2.3.2 Example with Two Suppliers.- 2.4 Optimal Extraction Rates from Consumer's View.- 2.4.1 Basic Model.- 2.4.2 Example withExponentially Distributed Z.- 2.5 Pure Competition and Optimal Extraction.- 3. Optimal Extraction Rates and Unknown Costs of the Development of a Substitute.- 3.1 One-period Analysis and Monopoly.- 3.2 One-period Analysis and Pure Competition.- 3.3 Two-period Analysis.- 3.3.1 Optimal Extraction and One Decision Maker.- 3.3.1.1 Basic Model.- 3.3.1.2 Example with Linear Demand.- 3.3.2 Optimal Extraction and Pure Competition.- 3.3.3 Extraction of the Resource and Production of the Substitute by Exactly One Monopoly.- 4. Conclusions.- III Short Introduction to the Theory of Differential Games.- IV Dynamic Models of Resource Extraction and Duopolistic Markets.- 1. An Introductory Duopoly Model with Production Strategies.- 2. Duopoly with Price Strategies and Exploration.- 2.1 Open-loop Controls.- 2.2 Closed-loop Controls.- 3. A Duopoly Model with Quantity Strategies.- 3.1 Introduction of the Model.- 3.2 Specialization of the Model: Linear-Quadratic Differential Game.- 4. Cartelization and Optimal Extraction of Exhaustible Resources.- 4.1 Pure Competition.- 4.2 Monopolistic Behaviour of the Cartel.- 4.3 Implications of Cartelization to the Profits of the Non-Cartel.- 5. Oligopoly with Discrete Time Parameter.- 6. Conclusions.- V Oligopolistic Extraction with Continuous Time.- 1. Basic Model with Quantity Strategies.- 1.1 Introduction of the Model.- 1.2 Algorithm for the Determination of a Nash Equilibrium.- 2. Specializations of the Basic Model.- 2.1 Fixed Resource Stock.- 2.2 Deterministic Expandable Resource Stocks.- 3. Oligopoly and Price Strategies.- 4. Conclusions.
Inhaltsverzeichnis
I Dynamic Models of Resource Extraction in Markets of Monopoly or Pure Competition with Full Information.- 1. Hotelling¿s Model.- 2. Optimal Extraction Rates and Exploration.- 2.1 Pure Competition.- 2.2 Monopoly.- 3. Optimal Extraction Rates and Constant Elasticity of Demand.- 4. Market Structure and Optimal Depletion Rates.- 4.1 Pure Competition.- 4.2 Monopoly.- 5. Extraction of an Exhaustible Resource and Production of a Substitute.- 5.1 Social Optimum.- 5.2 Extraction of the Resource and Production of the Substitute by the same Monopoly.- 5.3 Many Owners of the Resource and Production of the Substitute by Monopoly.- 5.4 Many Owners of the Resource and Production of the Substitute by all.- 6. Extraction of Durable Exhaustible Resources.- 6.1 Discrete Time.- 6.2 Continuous Time.- 6.2.1 Pure Competition.- 6.2.2 Monopoly.- 7. Conclusions.- II Dynamic Models with Uncertainty and Monopolistic Markets or Pure Competition.- 1. Optimal Extraction Rates and Uncertainty with Respect to R&D towards Future Technologies.- 1.1 Exogenous Technical Progress.- 1.1.1 Basic Model.- 1.1.2 First Extension: Production.- 1.1.3 Second Extension: Exhaustible Resources.- 1.1.4 Third Extension: Uncertainty about the Future Technological Development.- 1.2 Endogenous Technical Progress.- 1.2.1 Basic Model.- 1.2.2 Modification of the Basic Model.- 1.2.3 Example with Exponentially Distributed Z.- 2. Optimal Extraction Rates and Unknown Reserves.- 2.1 Monopolistic Extraction Rates Depending on Time only.- 2.2 Monopolistic Extraction Rates Depending on Time and Quantities already Extracted.- 2.3 Optimal Extraction Rates and Pure Competition.- 2.3.1 Basic Model.- 2.3.2 Example with Two Suppliers.- 2.4 Optimal Extraction Rates from Consumer¿s View.- 2.4.1 Basic Model.- 2.4.2 Example with Exponentially Distributed Z.- 2.5 Pure Competition and Optimal Extraction.- 3. Optimal Extraction Rates and Unknown Costs of the Development of a Substitute.- 3.1 One-period Analysis and Monopoly.- 3.2 One-period Analysis and Pure Competition.- 3.3 Two-period Analysis.- 3.3.1 Optimal Extraction and One Decision Maker.- 3.3.1.1 Basic Model.- 3.3.1.2 Example with Linear Demand.- 3.3.2 Optimal Extraction and Pure Competition.- 3.3.3 Extraction of the Resource and Production of the Substitute by Exactly One Monopoly.- 4. Conclusions.- III Short Introduction to the Theory of Differential Games.- IV Dynamic Models of Resource Extraction and Duopolistic Markets.- 1. An Introductory Duopoly Model with Production Strategies.- 2. Duopoly with Price Strategies and Exploration.- 2.1 Open-loop Controls.- 2.2 Closed-loop Controls.- 3. A Duopoly Model with Quantity Strategies.- 3.1 Introduction of the Model.- 3.2 Specialization of the Model: Linear-Quadratic Differential Game.- 4. Cartelization and Optimal Extraction of Exhaustible Resources.- 4.1 Pure Competition.- 4.2 Monopolistic Behaviour of the Cartel.- 4.3 Implications of Cartelization to the Profits of the Non-Cartel.- 5. Oligopoly with Discrete Time Parameter.- 6. Conclusions.- V Oligopolistic Extraction with Continuous Time.- 1. Basic Model with Quantity Strategies.- 1.1 Introduction of the Model.- 1.2 Algorithm for the Determination of a Nash Equilibrium.- 2. Specializations of the Basic Model.- 2.1 Fixed Resource Stock.- 2.2 Deterministic Expandable Resource Stocks.- 3. Oligopoly and Price Strategies.- 4. Conclusions.
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