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25 Remote Warehouse Economics- General

Mathematical Economics

by

Mathematical Economics Cover

 

Synopses & Reviews

Publisher Comments:

"An excellent book which should find wide use." — Mathematics Reviews.

In this classic volume, a noted economist and teacher has combined a modern text for graduate courses in mathematical economics with a valuable reference book of analytical economics for professional economists.

Unique in its unified and careful presentation of a variety of techniques of economic analysis, the book is divided into two parts: chapters on mathematical economics (i.e. economic models analyzed primarily from the point of view of their mathematical properties) and appropriate mathematical reviews. To keep the exposition as smooth as possible, the economic analysis has been separated from the purely mathematical material — permitting flexible use of the book as a text. Moreover, the chapters and reviews are designed as a self- contained system, wherein the reviews contain all the mathematics required for the chapters and the chapters illustrate the use of almost all the techniques set out in the reviews. An extensive mathematical background is not required; however, it is assumed the reader has some acquaintance with elementary calculus.

The economic analysis covers linear and nonlinear optimizing techniques, input-output, activity analysis, neoclassical and set- theoretic static economic models, modern general equilibrium theory, the Von Neumann and other models of balanced growth, efficient growth and turnpike theorems, and modern stability analysis.

The mathematical reviews include discussions of set theory, linear algebra, matrices, linear equations and inequalities, convex sets and functions, continuous functions and mappings (including neoclassical calculus methods), topological ideas, differential and difference equations, calculus of variations, and related topics.

Every attempt has been made to give a complete and rigorous exposition (except in topological methods where the approach is descriptive and heuristic) which omits no essential proofs or steps in the argument.

Synopsis:

Complete, rigorous expositions of economic models analyzed primarily according to their mathematical properties. Optimizing theory, static and dynamic models, mathematical reviews, more.

Synopsis:

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.

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?

    Exercises

  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

    Exercises

  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

    Exercises

  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

    Exercises

  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

    Exercises

  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

    Exercises

  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

  Part IV: MATHEMATICAL REVIEWS

  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

    Exercises

  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

    Exercises

  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

    Exercises

  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

    Exercises

  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

    Exercises

  R6. Symmetric Matrices and Quadratic Forms

    R6.1 Symmetric Matrices

    R6.2 Quadratic Forms

    R6.3 Constrained Quadratic Forms

    Exercises

  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

    Exercises

  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

    Exercises

  R9. Point-to-Set Mappings

    R9.1 Introduction

    R9.2 The Graph of a Mapping

    R9.3 Continuity

&

Product Details

ISBN:
9780486653914
Author:
Lancaster, Kelvin
Publisher:
Dover Publications
Location:
New York :
Subject:
General
Subject:
Mathematics
Subject:
Economics
Subject:
Economics, mathematical
Subject:
Economics - General
Subject:
General Mathematics
Subject:
Mathematical Economics
Subject:
Optimizing Theory
Subject:
Linear Programming
Subject:
Research
Copyright:
Edition Description:
Trade Paper
Series:
Dover Books on Computer Science
Publication Date:
19870731
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
448
Dimensions:
8.5 x 5.38 in 1 lb

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Related Subjects

History and Social Science » Economics » General
Science and Mathematics » Mathematics » Applied
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Science and Mathematics » Mathematics » General

Mathematical Economics New Trade Paper
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Product details 448 pages Dover Publications - English 9780486653914 Reviews:
"Synopsis" by ,
Complete, rigorous expositions of economic models analyzed primarily according to their mathematical properties. Optimizing theory, static and dynamic models, mathematical reviews, more.
"Synopsis" by ,
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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