Mathematical Economics

Mathematical Economics

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Graduate-level text provides complete and rigorous expositions of economic models analyzed primarily from the point of view of their mathematical properties, followed by relevant mathematical reviews. Part I covers optimizing theory; Parts II and III survey static and dynamic economic models; and Part IV contains the mathematical reviews, which range fromn linear algebra to point-to-set mappings.
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Product details

  • Paperback | 448 pages
  • 137 x 216 x 22.86mm | 462.66g
  • New York, United States
  • English
  • New edition
  • New edition
  • black & white illustrations
  • 0486653919
  • 9780486653914
  • 956,402

Table of contents

1. Introduction
1.1 Mathematical Economics
1.2 Outline of the Book
1.3 Notes on the Literature
Part I: Optimizing Theory
2. The General Optimizing Problem
2.1 Introduction
2.2 The General Structure
2.3 Constraints and the Feasible Set
2.4 The General Optimizing Problem
2.5 The General Solution Principle
2.6 Conditions for a Global Optimum
2.7 Important Special Cases
2.8 Direct Solutions or Optimal Condtions?
3. The Theory of Linear Programming
3.1 Introduction
3.2 The Feasible Set
3.3 Duality
3.4 The Optimum Conditions
3.5 Basic Solutions
3.6 The Basis Theorem
3.7 Interpretation of the Dual Variables
Further Reading
4. Classical Calculus Methods
4.1 Introduction
4.2 The Lagrangean Function
4.3 Interpretation of the Lagrange Multipliers
4.4 A Geometrical Note
4.5 Second Order Conditions for the Classical Case
4.6 The Substitution Effect of Neoclassical Demand Theory
4.7 Global Optimum Condtions in the Classical Problem
5. Advanced Optimizing Theory
5.1 Introduction
5.2 Nonnegative Variables
5.3 Inequality Constraints
5.4 Saddle Points and Duality
5.5 The Dual Variables
5.6 The Minimax Theorem
5.7 Exercises of Optimal Solutions
Further Reading
Part II: Static Economic Models
6. Input-Output and Related Models
6.1 Input-Output Models
6.2 The Closed Model
6.3 The Leontief Open Model
6.4 Direct and Indirect Input Requirements
6.5 Factor Intensity in the Leontief Model
6.6 A Labor Theory of Value
6.7 The Substitution Theorem
6.8 Matrix Multipliers
Further Reading
7. Linear Optimizing Models
7.1 Activity Analysis of Production
7.2 The Production Set
7.3 Efficient Production
7.4 Constrained Production
7.5 Consumption as an Activity
Further Reading
8. Nonlinear Optimizing Models
8.1 Introduction
8.2 Neoclassical Demand Theory
8.3 Convexity Proof of the Substitution Theorem
8.4 The Neoclassical Transformation Surface
8.5 Returns to Scale
8.6 Relative Factor Intensity
8.7 Generalized Production Theory
Further Reading
9. General Equilibrium
9.1 Equilibrium in a Market Economy
9.2 Walras' Law and the Budget Constraint
9.3 The Excess Demand Theorem
9.4 The Walras-Wald Model
9.5 The Arrow-Debreu-McKenzie Model
Further Reading
Part III: Dynamic Economic Models
10. Balanced Growth
10.1 Introduction
10.2 A Leontief-Type Model
10.3 The Von Neumann Growth Model
10.4 The Von Neumann-Leontief Model
10.5 General Balanced Growth Models
Further Reading
11. Efficient and Optimal Growth
11.1 Efficiency and Optimality in Dynamic Models
11.2 The Principle of Optimality
11.3 Efficient Growth
11.4 Properties of Efficient Paths
11.5 A Turnpike Theorem
11.6 An Explicit Turnpike Example
Further Reading
12. Stability
12.1 The Concept of Stability
12.2 Stability Analysis
12.3 Market Stability
12.4 Stability of Decentralized Economic Policy
RI. Fundamental Ideas
R1.1 Sets
R1.2 Ordered and Quasi-Ordered Sets
R1.3 Cartesian Products and Spaces
R1.4 "Functions, Transformations, Mappings, Correspondences"
R1.5 Closedness and Boundedness
R1.6 Complex Numbers
R2. Linear Algebra
R2.1 Vectors
R2.2 Fundamental Theorem of Vector Spaces
R2.3 Basis and Rank
R2.4 Sums and Direct Sums
R2.5 Scalar Products
R2.6 Complex Vectors
R2.7 Matrices
R2.8 Matrix Algebra
R2.9 Matrix-Vector Products and Linear Transformations
R2.10 Partitioned Matrices
R2.11 Vector Sets
R3. Linear Equations and Inequalities
R3.1 Introduction
R3.2 The Rank of Matrix
R3.3 Homogeneous Equations
R3.4 Nonhomogeneous Equations
R3.5 Nonnegative Vectors and Vector Inequalities
R3.6 Fundamental Theorem on Linear Inequalities
R3.7 Results on Linear Equations and Inequalities
R4. Convex Sets and Cones
R4.1 Geometric Ideas
R4.2 Convex Sets
R4.3 Separating and Supporting Hyperplanes
R4.4 Extreme Points
R4.5 Convex Cones
R4.6 Finite Cones and Homogeneous Inequalities
R4.7 The Dual Cone
R5. Square Matrices and Characteristic Roots
R5.1 Introduction
R5.2 Determinants and Cramer's Rule
R5.3 The Inverse of a Square Matrix
R5.4 Charateristic Roots and Vectors
R5.5 Diagonalization
R5.6 Convergence of Matrix Series
R5.7 Charateristic Row Vectors
R5.8 Numerical Examples
R6. Symmetric Matrices and Quadratic Forms
R6.1 Symmetric Matrices
R6.2 Quadratic Forms
R6.3 Constrained Quadratic Forms
R7. Semipositive and Dominant Diagonal Matrices
R7.1 Introduction
R7.2 Indecomposability
R7.3 Properties of Semipositive Square Matrices
R7.4 Properties of Dominant Diagonal Matrices
R7.5 Proofs
R8. Continuous Functions
R8.1 Introduction
R8.2 Derivatives and Differentials
R8.3 Some Mapping Relationships
R8.4 Maxima and Minima
R8.5 Convex and Concave Functions
R8.6 Homogeneous and Homothetic Functions
R8.7 The Brouwer Fixed Point Theorem
R8.8 Linear Homogeneous Vector-Valued Functions
R9. Point-to-Set Mappings
R9.1 Introduction
R9.2 The Graph of a Mapping
R9.3 Continuity
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