- ホーム
- > 洋書
- > 英文書
- > Business / Economics
基本説明
Using state of the art mathematical techniques this book proides a complete characterization of the Uzawa-Lucas growth model.
Full Description
The Uzawa-Lucas model is a two-sector capital accumulation growth model where human capital plays the role of the key variable through which ongoing growth can be generated. Although it has gained a fair amount of popularity in the literature, Mattana (U. of Cagliari, Italy) believes there are gaps in its treatment, particularly the use of the op
Contents
List of Figures ix; List of Tables xi; Preface xiii; Introduction and Outline of the Book xv; 1 The Model and the Existence of Non-Degenerate Balanced Solutions 1; 1.1 Introduction and Plan of the Chapter 1; 1.2 The Formal Structure of the Model 3; 1.2.1 The Environment and the Technology 3; 1.2.2 Preferences 4; 1.3 The Optimization Problems 4; 1.3.1 The Optimization Problem from the Planner's Viewpoint 4; 1.3.2 The Optimization Problem in the Decentralized Economy 6; 1.3.3 The Properties Shared by Optimal and Equilibrium Paths 9; 1.4 Sufficiency of the Admissible Candidates 11; 1.5 The Possibility for Non-Degenerate Balanced Dynamics 12; 1.5.1 Some Preliminary Properties of the Balanced Evolution of the Economy 13; 2 The General Properties of the Uzawa-Lucas Economy 17; 2.1 Introduction and Plan of the Chapter 17; 2.2 Some General Features of Balanced Growth 20; 2.2.1 Some BGP-Stationary Useful Variables: the Great Ratios 20; 2.2.2 The Adjoint Variables along the BGP 21; 2.3 The Transition along Optimal and Equilibrium Paths 25; 2.3.1 Some Principles for Mathematical Analysis 25; 2.3.2 A Dimensional-Reducing Transformation of the Variables 26; 2.3.3 The Jacobian and the Characteristic Equation 27; 2.3.4 The Potential for non Saddle-Path Behavior in the ULM 28; 2.3.5 The Functions Linking the State of the Economy to its Control Part 29; 2.3.6 The Mechanisms Driving the Adjustment of the Economy 30; 2.3.7 Growth Cases 31; 2.4 The Possibility of a Further Dimensional Reduction 32; 2.5 Appendix 34; 3 The Centralized Economy 39; 3.1 Introduction and Plan of the Chapter 39; 3.2 The Optimal BGP Evolution of the Variables 42; 3.2.1 The Relevant System of Differential Equations 42; 3.2.2 The Optimal Allocation of Time along the BGP 42; 3.2.3 The BGP Growth Rate of the Centralized Economy 44; 3.2.4 The BGP Values of the Great Ratios 45; 3.2.5 The Adjoint Variables Along the BGP 46; 3.3 Transitional Dynamics. The Local Point of View 49; 3.3.1 A First Stationarizing Transformation of the Variables 49; 3.3.2 The Local Stability Properties 50; 3.3.3 Some Local Characteristics of the Transition 51; 3.4 Transitional Dynamics. The Global Point of View 54; 3.4.1 The Dynamics in R2 54; 3.4.2 The Logistic Path of The Average Goods Production 55; 3.4.3 The Global Behavior of the Average Consumption 56; 3.4.4 Time Paths in the Original Dimension 58; 3.4.5 The explicit transition simulated 60; 3.5 Global Welfare Analysis 67; 3.6 Appendix 70; 4 The Properties of the Competitive Equilibrium 75; 4.1 Introduction and Plan of the Chapter 75; 4.2 Equilibrium Dynamics Along the BGP 79; 4.2.1 The Relevant System of Differential Equations 79; 4.2.2 The Equilibrium Allocation of Time along the BGP 79; 4.2.3 The BGP Growth Rates of the Primitive Variables 82; 4.2.4 The Stationary Values of the Great Ratios 83; 4.2.5 The BGP Behavior of the Adjoint Variables 85; 4.3 The Transitional Dynamics from the Local Point of View 87; 4.3.1 A Stationarizing Transformation of the Dynamic Laws 87; 4.3.2 The Local Stability Properties of the Fixed Point in R3 88; 4.3.3 A Numerical Investigation of the Characteristics of the Eigenvalues 90; 4.3.4 The Economic Forces Governing Transition in the Market Economy 94; 4.3.5 The Emergence of Deterministic Cycles 100; 4.3.6 The Stability Properties of the Orbits 101; 4.4 Transitional Dynamics from the Global Point of View 103; 4.4.1 Restricted Parameter Space and the Laws of Motion 103; 4.4.2 The Solution of the Simplified Differential Equations 103; 4.4.3 Indeterminacy Versus Exogenous Growth 106; 4.4.4 The Properties of a Market Economy Belonging to the Exogenous Growth Case 110; 4.4.5 A Numerical Analysis of Equilibrium Paths when Indeterminacy is Present 114; 4.4.6 Welfare Considerations in the Exogenous Growth Case 119; 5 The Inefficiency of the Market Economy and the Design of Optimal Fiscal Policies 121; 5.1 Introduction and Plan of the Chapter 121; 5.2 Centralization Vs Decentralization. The Parameter Space 123; 5.3 The Inefficiency and the BGP 125; 5.3.1 The Inefficiency in Terms of the BGP Growth Rate of the Economy 125; 5.3.2 The Inefficiency and the Great Ratios 127; 5.3.3 Inefficiency and the Adjoint Variables 127; 5.4 Comparing the Transitional Dynamics from the Local Point of View 128; 5.4.1 The Inefficiency and the Stability Properties in R3 128; 5.4.2 The Speeds of Adjustment 129; 5.4.3 The Slopes of the Functions Linking Control and State Variables 130; 5.5 Optimal and Equilibrium Off-balanced Paths from the Global Point of View 131; 5.5.1 Optimal and Equilibrium Exogenous Growth 131; 5.5.2 Welfare when the Economy Belongs to the Exogenous Growth Case 137; 5.6 The Desirability of Public Policies 138; 5.6.1 The Optimization Problem in Presence of Government Interventions 139; 5.6.2 Some General Characteristics of Optimal Fiscal Policy 141; 5.6.3 The Optimal Fiscal Policy Along the BGP 142; 5.6.4 Fiscal Policy in Transition. The Case of a Small Coefficient of Risk Aversion 144; 5.6.5 The Fiscal Policy in Transition. The Case of a Large Coefficient of Risk Aversion 148; Bibliography 151
