Capital Theory, Equilibrium Analysis and Recursive Utility

Capital Theory, Equilibrium Analysis, and Recursive Utility is addressed to growth theorists, macroeconomic dynamicists, resource economists, general equilibrium theorists, and graduate students in economic theory. As a thorough presentation of basic research on the foundations of intertemporal decision-making, it provides advanced students and experts alike with the techniques of equilibrium analysis and recursive utility needed in the rapidly evolving field of economic dynamics.

Contents
List of Examples
Preface
1 The Recursive Utility Approach
1.1 Introduction
1.2 What Is a Recursive Utility Function?
1.3 Why Study Recursive Utility?
1.3.1 The Long-Run Incidence of Capital Taxation
The Tax Model
Tax Incidence with TAS Utility
Tax Incidence with Epstein-Hynes Utility
1.3.2 The Impatience Problem
The Impatience Problem with Epstein-Hynes Utility
1.4 Recursive Utility and Commodity Spaces
1.4.1 Diminishing Returns and Bounded Growth
1.4.2 Non-Decreasing Returns and Sustained Growth
Growth and Exogenous Technical Progress
Endogenous Growth Models
1.4.3 Order Structures
Weak Separability of the Future from the Present
Partial Orders on the Commodity Space
1.5 Conclusion
2 Commodity and Price Spaces
2.1 Introduction
2.2 Commodity Spaces
2.2.1 Order Properties Free Disposal
2.2.2 Topological Properties
Metric Spaces
Continuity
Compactness and Product Spaces
Connectedness
2.2.3 Linear Topologies
Order Convergence
Semicontinuity
Contraction Mapping Theorems
2.3 Commodity Price Dualities
2.3.1 Duals and Hyperplanes
2.3.2 Hahn-Banach Theorems
2.3.3 Dual Pairs and Weak Topologies
2.3.4 Order Duals
2.3.5 The Dual of XXX
2.4 Conclusion
3 Representation of Recursive Preferences
3.1 Introduction
3.2 Preference Orders and Utility Theory
3.3 Recursive Utility: the Koopmans Axioms
3.3.1 The Axioms
3.3.2 Biconvergence
3.3.3 Recursive Preferences and Additivity
3.4 Impatience, Discounting, and Myopia
3.4.1 Impatience and Time Perspective
3.4.2 Myopia and the Continuity Axiom
3.4.3 The Norm of Marginal Impatience
Conditions
3.5 Recursive Utility: the Aggregator
3.5.1 Basic Properties of the Aggregator
3.5.2 The Existence of Recursive Utility
3.5.3 Aggregators Bounded from Below
3.5.4 Unbounded Aggregators
3.6 Conclusion
4 Existence and Characterization of Optimal Paths
4.1 Introduction
4.2 Fundamentals of Existence Theory
4.2.1 A Simple Capital Accumulation Model
4.2.2 The Weierstrass Theorem
4.2.3 One-Sector TAS Existence Theory
4.2.4 Extended Utilitarianism
4.3 Multisector Capital Accumulation Models
4.3.1 The von Neumann and Malinvaud
Models
4.3.2 The Feasible Correspondence
4.4 The Existence and Sensitivity of Optimal Paths
4.4.1 The Maximum Theorem
4.4.2 Optimal Paths
4.5 Recursive Dynamic Programming
4.5.1 Dynamic Programming with TAS Utility
4.5.2 Recursive Utility and Multisector
Models
4.5.3 Dynamic Programming and Extended Utilitarianism
4.6 Characterization of Optimal Paths
4.6.1 No-Arbitrage Conditions
4.6.2 Complete Characterization of Optimal Paths
4.7 Conclusion
5 Statics and Dynamics of Optimal Paths
5.1 Introduction
5.2 One-Sector Models
5.2.1 The Inada Conditions
5.2.2 Stationary States in One-Sector
Models
5.2.3 Monotonicity and Turnpikes in TAS
Models
Differential Approach
Nonclassical Models
5.2.4 Monotonicity and Turnpikes in
Recursive Models
5.2.5 Growing Economies
5.3 Steady States in Multisectoral Models
5.3.1 Stationary Optimal Programs for Additive Utility
5.3.2 Stationary Optimal Programs for Recursive Utility
5.4 Stability of Multisectoral Models
5.4.1 The Undiscounted Model
5.4.2 The Visit Lemma
5.4.3 Uniqueness of Steady States
5.4.4 Local Analysis of Steady States
5.4.5 Local and Global Stability
5.5 Cycles and Chaos in Optimal Growth
5.5.1 The Existence of Cycles
5.5.2 Chaotic Dynamics
5.6 Conclusion
6 Equivalence Principles and Dynamic Equilibria
6.1 Introduction
6.2 Equivalence Principles for One-Sector
Models
6.2.1 The Perfect Foresight Equivalence Theorem
Perfect Foresight Competitive Equilibrium
The PFCE Equivalence Principle
6.2.2 The Fisher Equivalence Theorem
6.2.3 The Equivalence Theorem and Transversality
6.2.4 Recursive Competitive Equilibrium and Equivalence
6.3 Multisector Equivalence Principles
6.3.1 The Portfolio Equilibrium Condition
6.3.2 The Two-Sector Equivalence Theorem
The Household Sector
The Production Sector
The Transformation Function
Perfect Foresight Equilibrium
The Optimal Growth Problem
The Equivalence Theorem
6.3.3 Dynamics and the Two-Sector Equivalence Theorem
6.4 Transversality and the Hahn problem
6.5 Transversality and Decentralization
7 Comparative Dynamics
7.1 Introduction
7.2 The Reduced-Form TAS Model
7.2.1 Comparative Dynamics for Monotonic Programs
7.2.2 Comparative Dynamics for Oscillating Programs
7.2.3 Comparative Dynamics and Capital
Income Tax Reform
7.3 A Primer of Lattice Programming
7.3.1 More about Lattices
7.3.2 An Introduction to Monotone
Comparative Statics
7.3.3 Topkis's Theorems
7.4 Lattice Programming and the TAS Model
7.4.1 Monotonicity of Optimal Capital Policy Functions
7.4.2 The Capital Deepening Theorem
7.5 Recursive Utility Models
7.5.1 Recursive Utility, Monotonicity,
and Lattice Programming
7.5.2 Increasing Impatience and Recursive Utility
7.5.3 Capital Deepening and Recursive Utility
7.6 Conclusion
8 Dynamic Competitive Equilibrium
8.1 Introduction
8.2 Dynamic Economies
8.2.1 Infinite Horizon Economies
8.2.2 Existence of Pareto Optima
8.3 The Core and Edgeworth Equilibria
8.3.1 Existence of Core Allocations
8.3.2 Replicas and Edgeworth Equilibria
8.4 The Core and Competitive Equilibrium
8.4.1 Core Equivalence
8.4.2 The Welfare Theorems
8.4.3 Representation of Equilibrium as
Welfare Maximum
8.5 Models with Very Heterogeneous
Discounting
8.6 Conclusion
References
Index

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