Comparative statics analysis in economics / Kevin M. Currier.

Format:

Book

Author/Creator:

Currier, Kevin M.

Language:

English

Subjects (All):

Statics and dynamics (Social sciences).

Physical Description:

xiii, 135 pages ; 23 cm

Place of Publication:

Singapore ; River Edge, NJ : World Scientific, [2000]

Summary:

As an empirical science, economics employs theoretical models to describe economic phenomena and processes. These models are then used to generate testable propositions. Comparative statics analysis facilitates the derivation of such propositions.

This book is a self-contained introduction to comparative statics analysis which is appropriate for a first year PhD course in mathematics for economists. The demands that modern economic analysis places upon the student renders an incremental approach to learning essential. This permits students' intuition to develop as mathematical tools are employed in problem solving. In this book, students learn comparative statics by doing comparative statics in progressively more sophisticated models. Repeated application of the basic technique allows the student to gain competence in comparative statics analysis with minimal distraction.

Contents:

1. Mathematical Preliminaries 1

1.1 Differentiable Functions 1

1.2 The Chain Rule 1

1.3 Determinants 3

1.4 Cramer's Rule 3

1.5 Optimization, f: R [right arrow] R 4

1.6 Optimization, f: R[superscript 2] [right arrow] R 5

1.7 Constrained Optimization, Two Variables, One Constraint 7

2. The Methodology of Comparative Statics 11

2.1 Comparative Statics and Empirical Testing 13

2.2 Implicit Differentiation 14

2.3 The Implicit Function Theorem (One Variable, One Parameter) 15

2.4 The Implicit Function Theorem (Two Variables, One Parameter) 19

2.5 Summary of the Technique of Comparative Statics 22

3. Comparative Statics with Explicit Solutions 27

3.1 Two Classes of Comparative Statics Problems 27

3.2 Equilibrium Comparative Statics 28

3.3 Comparative Statics with Unconstrained Optimization 30

3.4 Comparative Statics with Constrained Optimization 34

4. Comparative Statics in General Function Models 43

4.1 Introduction to General Function Models 43

4.2 Equilibrium Comparative Statics 43

4.3 Comparative Statics with Unconstrained Optimization 47

4.4 Comparative Statics with Constrained Optimization 54

4.5 Second-Order Conditions and the Implicit Function Theorem 68

5. Comparative Statics Theorems for Parameterized Optimization Problems 75

5.2 Conjugate Pairs Theorems 80

5.3 Envelope Theorems 83

5.4 Reciprocity Theorems 86

5.5 Applications 89

5.6 Profit Maximization and the Le Chatelier Principle 99

5.7 Two Approaches to Comparative Statics Analysis 104

6. Introduction to Primal-Dual Analysis 111

6.1 (Border-Preserving) Principal Minors 111

6.2 Comparative Statics with Unconstrained Optimization Using Primal-Dual Analysis 113

6.3 Comparative Statics with Constrained Optimization Using Primal-Dual Analysis 122.

Notes:

Includes bibliographical references (pages 131-132) and index.

ISBN:

9810243669

OCLC:

44632925