Lecture notes in economics and mathematical systems, 263.
CONTENTS NOTE
Text of Note
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.