Fundamental Methods of Mathematical Economics

ISBN-10: 0070109109
ISBN-13: 9780070109100
Edition: 4th 2005 (Revised)
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Book details

List price: $299.33
Edition: 4th
Copyright year: 2005
Publisher: McGraw-Hill Education
Publication date: 2/2/2005
Binding: Hardcover
Pages: 704
Size: 7.50" wide x 9.30" long x 1.30" tall
Weight: 2.178
Language: English

Jeffrey S. Taube is Professor in the Department of Psychological and Brain Sciences and in the Center for Cognitive Neuroscience at Dartmouth College.

Kevin Wainwright is a professor at the British Columbia Institute of Technology (Burnaby, BC,Canada).

Preface
Introduction
The Nature of Mathematical Economics
Mathematical versus Nonmathematical Economics
Mathematical Economics versus Econometrics
Economic Models
Ingredients of a Mathematical Model
The Real-Number System
The Concept of Sets
Relations and Functions
Types of Function
Functions of Two or More Independent Variables
Levels of Generality
Static (or Equilibrium) Analysis
Equilibrium Analysis in Economics
The Meaning of Equilibrium
Partial Market Equilibrium--A Linear Model
Partial Market Equilibrium--A Nonlinear Model
General Market Equilibrium
Equilibrium in National-Income Analysis
Linear Models and Matrix Algebra
Matrices and Vectors
Matrix Operations
Notes on Vector Operations
Commutative, Associative, and Distributive Laws
Identity Matrices and Null Matrices
Transposes and Inverses
Linear Models and Matrix Algebra (Continued)
Conditions for Nonsingularity of a Matrix
Test of Nonsingularity by Use of Determinant
Basic Properties of Determinants
Finding the Inverse Matrix
Cramer's Rule
Application to Market and National-Income Models
Leontief Input-Output Models
Limitations of Static Analysis
Comparative-Static Analysis
Comparative Statics and the Concept of Derivative
The Nature of Comparative Statics
Rate of Change and the Derivative
The Derivative and the Slope of a Curve
The Concept of Limit
Digression on Inequalities and Absolute Values
Limit Theorems
Continuity and Differentiability of a Function
Rules of Differentiation and Their Use in Comparative Statics
Rules of Differentiation for a Function of One Variable
Rules of Differentiation Involving Two or More Functions of the Same Variable
Rules of Differentiation Involving Functions of Different Variables
Partial Differentiation
Applications to Comparative-Static Analysis
Note on Jacobian Determinants
Comparative-Static Analysis of General-Function Models
Differentials
Total Differentials
Rules of Differentials
Total Derivatives
Derivatives of Implicit Functions
Comparative Statics of General-Function Models
Limitations of Comparative Statics
Optimization Problems
Optimization: A Special Variety of Equilibrium Analysis
Optimum Values and Extreme Values
Relative Maximum and Minimum: First-Derivative Test
Second and Higher Derivatives
Second-Derivative Test
Digression on Maclaurin and Taylor Series
Nth-Derivative Test for Relative Extremum of a Function of One Variable
Exponential and Logarithmic Functions
The Nature of Exponential Functions
Natural Exponential Functions and the Problem of Growth
Logarithms
Logarithmic Functions
Derivatives of Exponential and Logarithmic Functions
Optimal Timing
Further Applications of Exponential and Logarithmic Derivatives
The Case of More than One Choice Variable
The Differential Version of Optimization Conditions
Extreme Values of a Function of Two Variables
Quadratic Forms--An Excursion
Objective Functions with More than Two Variables
Second-Order Conditions in Relation to Concavity and Convexity
Economic Applications
Comparative-Static Aspects of Optimization
Optimization with Equality Constraints
Effects of a Constraint
Finding the Stationary Values
Second-Order Conditions
Quasiconcavity and Quasiconvexity
Utility Maximization and Consumer Demand
Homogeneous Functions
Least-Cost Combination of Inputs
Some Concluding Remarks
Dynamic Analysis
Economic Dynamics and Integral Calculus
Dynamics and Integration
Indefinite Integrals
Definite Integrals
Improper Integrals
Some Economic Applications of Integrals
Domar Growth Model
Continuous Time: First-Order Differential Equations
First-Order Linear Differential Equations with Constant Coefficient and Constant Term
Dynamics of Market Price
Variable Coefficient and Variable Term
Exact Differential Equations
Nonlinear Differential Equations of the First Order and First Degree
The Qualitative-Graphic Approach
Solow Growth Model
Higher-Order Differential Equations
Second-Order Linear Differential Equations with Constant Coefficients and Constant Term
Complex Numbers and Circular Functions
Analysis of the Complex-Root Case
A Market Model with Price Expectations
The Interaction of Inflation and Unemployment
Differential Equations with a Variable Term
Higher-Order Linear Differential Equations
Discrete Time: First-Order Difference Equations
Discrete Time, Differences, and Difference Equations
Solving a First-Order Difference Equation
The Dynamic Stability of Equilibrium
The Cobweb Model
A Market Model with Inventory
Nonlinear Difference Equations--The Qualitative-Graphic Approach
Higher-Order Difference Equations
Second-Order Linear Difference Equations with Constant Coefficients and Constant Term
Samuelson Multiplier-Acceleration Interaction Model
Inflation and Unemployment in Discrete Time
Generalizations to Variable-Term and Higher-Order Equations
Simultaneous Differential Equations and Difference Equations
The Genesis of Dynamic Systems
Solving Simultaneous Dynamic Equations
Dynamic Input-Output Models
The Inflation-Unemployment Model Once More
Two-Variable Phase Diagrams
Linearization of a Nonlinear Differential-Equation System
Limitations of Dynamic Analysis
Mathematical Programming
Linear Programming
Simple Examples of Linear Programming
General Formulation of Linear Programs
Convex Sets and Linear Programming
Simplex Method: Finding the Extreme Points
Simplex Method: Finding the Optimal Extreme Point
Further Notes on the Simplex Method
Linear Programming (Continued)
Duality
Economic Interpretation of a Dual
Activity Analysis: Micro Level
Activity Analysis: Macro Level
Nonlinear Programming
The Nature of Nonlinear Programming
Kuhn-Tucker Conditions
The Constraint Qualification
Kuhn-Tucker Sufficiency Theorem: Concave Programming
Arrow-Enthoven Sufficiency Theorem: Quasiconcave Programming
Economic Applications
Limitations of Mathematical Programming
The Greek Alphabet
Mathematical Symbols
A Short Reading List
Answers to Selected Exercise Problems
Index

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