Course: Mathematical Economics, a course taken by economics majors in their third or fourth year. They will have had principles of economics (both micro and macro) and at least one calculus class. In most cases, this course will be the student's first exposure to integrating sophisticated mathematical models with economic theory. The text can also be used as a first course for students about to enter graduate studies. The market is small but the potential is great. Watch comps. Everyone will want a copy.
Overview: It has been 20 years since the last edition of this classic text. Kevin Wainwright, a long time user of the text (British Columbia University and Simon Fraser University), has executed the perfect revision?he has updated examples, applications and theory without changing the elegant, precise presentation style of Alpha Chiang. Readers will find the wait was worthwhile.
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 Good refreshment bookEasy to follow, and step by step explanation. I would like to have more answers to the questions, and more real life aplication examples.
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 Very good.The material in the text is very intricate and relies heavily on calculus and linear algebra. The text can be difficult to follow, but the examples are realistic in nature. Overall, the textbook covers any type of math you would need in dealing with economics.
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Table Of Contents
PART ONE INTRODUCTION
The Nature of Mathematical Economics
Mathematical versus Nonmathematical Economics
Mathematical Economics versus Econometrics
Economic Models
Ingredients of a Mathematical Model
Variables, Constants, and Parameters
Equations and Identities
The Real-Number System
The Concept of Sets
Set Notation
Relationships between Sets
Operations on Sets
Laws of Set Operations
Exercise 2.3
Relations and Functions
Ordered Pairs
Relations and Functions
Exercise 2.4
Types of Function
Constant Functions
Polynomial Functions
Rational Functions
Nonalgebraic Functions
A Digression on Exponents
Exercise 2.5
Functions of Two or More Independent Variables
Levels of Generality
PART TWO STATIC (OR EQUILIBRIUM) ANALYSIS
Equilibrium Analysis in Economics
The Meaning of Equilibrium
Partial Market Equilibrium---A Linear Model
Constructing the Model
Solution by Elimination of Variables
Exercise 3.2
Partial Market Equilibrium---A Nonlinear Model
Quadratic Equation versus Quadratic Function
The Quadratic Formula
Another Graphical Solution
Higher-Degree Polynomial Equations
Exercise 3.3
General Market Equilibrium
Two-Commodity Market Model
Numerical Example
n-Commodity Case
Solution of a General-Equation System
Exercise 3.4
Equilibrium in National-Income Analysis
Exercise 3.5
Linear Models and Matrix Algebra
Matrices and Vectors
Matrices as Arrays
Vectors as Special Matrices
Exercise 4.1
Matrix Operations
Addition and Subtraction of Matrices
Scalar Multiplication
Multiplication of Matrices
The Question of Division
The Σ Notation
Exercise 4.2
Notes on Vector Operations
Multiplication of Vectors
Geometric Interpretation of Vector Operations
Linear Dependence
Vector Space
Exercise 4.3
Commutative, Associative, and Distributive Laws
Matrix Addition
Matrix Multiplication
Exercise 4.4
Identity Matrices and Null Matrices
Identity Matrices
Null Matrices
Idiosyncrasies of Matrix Algebra
Exercise 4.5
Transposes and Inverses
Properties of Transposes
Inverses and Their Properties
Inverse Matrix and Solution of Linear-Equation System
Exercise 4.6
Finite Markov Chains
Special Case: Absorbing Markov Chains
Exercise 4.7
Linear Models and Matrix Algebra (Continued)
Conditions for Nonsingularity of a Matrix
Necessary versus Sufficient Conditions
Conditions for Nonsingularity
Rank of a Matrix
Exercise 5.1
Test of Nonsingularity by Use of Determinant
Determinants and Nonsingularity
Evaluating a Third-Order Determinant
Evaluating an nth-Order Determinant by Laplace Expansion
Exercise 5.2
Basic Properties of Determinants
Determinantal Criterion for Nonsingularity
Rank of a Matrix Redefined
Exercise 5.3
Finding the Inverse Matrix
Expansion of a Determinant by Alien Cofactors
Matrix Inversion
Exercise 5.4
Cramer's Rule
Derivation of the Rule
Note on Homogeneous-Equation Systems
Solution Outcomes for a Linear-Equation System
Exercise 5.5
Application to Market and National-Income Models
Market Model
National-Income Model
IS-LM Model: Closed Economy
Matrix Algebra versus Elimination of Variables
Exercise 5.6
Leontief Input-Output Models
Structure of an Input-Output Model
The Open Model
A Numerical Example
The Existence of Nonnegative Solutions
Economic Meaning of the Hawkins-Simon Condition
The Closed Model
Exercise 5.7
Limitations of Static Analysis
PART THREE COMPARATIVE-STATIC ANALYSIS
Comparative Statics and the Concept of Derivative
The Nature of Comparative Statics
Rate of Change and the Derivative
The Difference Quotient
The Derivative
Exercise 6.2
The Derivative and the Slope of a Curve
The Concept of Limit
Left-Side Limit and Right-Side Limit
Graphical Illustrations
Evaluation of a Limit
Formal View of the Limit Concept
Exercise 6.4
Digression on Inequalities and Absolute Values
Rules of Inequalities
Absolute Values and Inequalities
Solution of an Inequality
Exercise 6.5
Limit Theorems
Theorems Involving a Single Function
Theorems Involving Two Functions
Limit of a Polynomial Function
Exercise 6.6
Continuity and Differentiability of a Function
Continuity of a Function
Polynomial and Rational Functions
Differentiability of a Function
Exercise 6.7
Rules of Differentiation and Their Use in Comparative Statics
Rules of Differentiation for a Function of One Variable
Constant-Function Rule
Power-Function Rule
Power-Function Rule Generalized
Exercise 7.1
Rules of Differentiation Involving Two or More Functions of the Same Variable
Sum-Difference Rule
Product Rule
Finding Marginal-Revenue Function from Average-Revenue Function
Quotient Rule
Relationship Between Marginal-Cost and Average-Cost Functions
Exercise 7.2
Rules of Differentiation Involving Functions of Different Variables
Chain Rule
Inverse-Function Rule
Exercise 7.3
Partial Differentiation
Partial Derivatives
Techniques of Partial Differentiation
Geometric Interpretation of Partial Derivatives
Gradient Vector
Exercise 7.4
Applications to Comparative-Static Analysis
Market Model
National-Income Model
Input-Output Model
Exercise 7.5
Note on Jacobian Determinants
Exercise 7.6
Comparative-Static Analysis of General-Function Models
Differentials
Differentials and Derivatives
Differentials and Point Elasticity
Exercise 8.1
Total Differentials
Exercise 8.2
Rules of Differentials
Exercise 8.3
Total Derivatives
Finding the Total Derivative
A Variation on the Theme
Another Variation on the Theme
Some General Remarks
Exercise 8.4
Derivatives of Implicit Functions
Implicit Functions
Derivatives of Implicit Functions
Extension to the Simultaneous-Equation Case
Exercise 8.5
Comparative Statics of General-Function Models
Market Model
Simultaneous-Equation Approach
Use of Total Derivatives
National-Income Model (IS-LM)
Extending the Model: An Open Economy
Summary of the Procedure
Exercise 8.6
Limitations of Comparative Statics
PART FOUR OPTIMIZATION PROBLEMS
Optimization: A Special Variety of Equilibrium Analysis
Optimum Values and Extreme Values
Relative Maximum and Minimum: First-Derivative Test
Relative versus Absolute Extremum
First-Derivative Test
Exercise 9.2
Second and Higher Derivatives
Derivative of a Derivative
Interpretation of the Second Derivative
An Application
Attitudes toward Risk
Exercise 9.3
Second-Derivative Test
Necessary versus Sufficient Conditions
Conditions for Profit Maximization
Coefficients of a Cubic Total-Cost Function
Upward-Sloping Marginal-Revenue Curve
Exercise 9.4
Maclaurin and Taylor Series
Maclaurin Series of a Polynomial Function
Taylor Series of a Polynomial Function
Expansion of an Arbitrary Function
Lagrange Form of the Remainder
Exercise 9.5
Nth-Derivative Test for Relative Extremum of a Function of One Variable
Taylor Expansion and Relative Extremum
Some Specific Cases
Nth-Derivative Test
Exercise 9.6
Exponential and Logarithmic Functions
The Nature of Exponential Functions
Simple Exponential Function
Graphical Form
Generalized Exponential Function
A Preferred Base
Exercise 10.1
Natural Exponential Functions and the Problem of Growth
The Number e
An Economic Interpretation of e
Interest Compounding and the Function Aert
Instantaneous Rate of Growth
Continuous versus Discrete Growth
Discounting and Negative Growth
Exercise 10.2
Logarithms
The Meaning of Logarithm
Common Log and Natural Log
Rules of Logarithms
An Application
Exercise 10.3
Logarithmic Functions
Log Functions and Exponential Functions
The Graphical Form
Base Conversion
Exercise 10.4
Derivatives of Exponential and Logarithmic Functions
Log-Function Rule
Exponential-Function Rule
The Rules Generalized
The Case of Base b
Higher Derivatives
An Application
Exercise 10.5
Optimal Timing
A Problem of Wine Storage
Maximization Conditions
A Problem of Timber Cutting
Exercise 10.6
Further Applications of Exponential and Logarithmic Derivatives
Finding the Rate of Growth
Rate of Growth of a Combination of Functions
Finding the Point Elasticity
Exercise 10.7
The Case of More than One Choice Variable
The Differential Version of Optimization Conditions
First-Order Condition
Second-Order Condition
Differential Conditions versus Derivative Conditions
Extreme Values of a Function of Two Variables
First-Order Condition
Second-Order Partial Derivatives
Second-Order Total Differential
Second-Order Condition
Exercise 11.2
Quadratic Forms---An Excursion
Second-Order Total Differential as a Quadratic Form
Positive and Negative Definiteness
Determinantal Test for Sign Definiteness
Three-Variable Quadratic Forms
n-Variable Quadratic Forms
Characteristic-Root Test for Sign Definiteness
Exercise 11.3
Objective Functions with More than Two Variables
First-Order Condition for Extremum
Second-Order Condition
n-Variable Case
Exercise 11.4
Second-Order Conditions in Relation to Concavity and Convexity
Checking Concavity and Convexity
Differentiable Functions
Convex Functions versus Convex Sets
Exercise 11.5
Economic Applications
Problem of a Multiproduct Firm
Price Discrimination
Input Decisions of a Firm
Exercise 11.6
Comparative-Static Aspects of Optimization
Reduced-Form Solutions
General-Function Models
Exercise 11.7
Optimization with Equality Constraints
Effects of a Constraint
Finding the Stationary Values
Lagrange-Multiplier Method
Total-Differential Approach
An Interpretation of the Lagrange Multiplier
n-Variable and Multiconstraint Cases
Exercise 12.2
Second-Order Conditions
Second-Order Total Differential
Second-Order Conditions
The Bordered Hessian
n-Variable Case
Multiconstraint Case
Exercise 12.3
Quasiconcavity and Quasiconvexity
Geometric Characterization
Algebraic Definition
Differentiable Functions
A Further Look at the Bordered Hessian
Absolute versus Relative Extrema
Exercise 12.4
Utility Maximization and Consumer Demand
First-Order Condition
Second-Order Condition
Comparative-Static Analysis
Proportionate Changes in Prices and Income
Exercise 12.5
Homogeneous Functions
Linear Homogeneity
Cobb-Douglas Production Function
Extensions of the Results
Exercise 12.6
Least-Cost Combination of Inputs
First-Order Condition
Second-Order Condition
The Expansion Path
Homothetic Functions
Elasticity of Substitution
CES Production Function
Cobb-Douglas Function as a Special Case of the CES Function
Exercise 12.7
Further Topics in Optimization
Nonlinear Programming and Kuhn-Tucker Conditions
Step 1: Effect of Nonnegativity Restrictions
Step 2: Effect of Inequality Constraints
Interpretation of the Kuhn-Tucker Conditions
The n-Variable, m-Constraint Case
Exercise 13.1
The Constraint Qualification
Irregularities at Boundary Points
The Constraint Qualification
Linear Constraints
Exercise 13.2
Economic Applications
War-Time Rationing
Peak-Load Pricing
Exercise 13.3
Sufficiency Theorems in Nonlinear Programming
The Kuhn-Tucker Sufficiency Theorem: Concave Programming
The Arrow-Enthoven Sufficiency Theorem: Quasiconcave Programming
A Constraint-Qualification Test
Exercise 13.4
Maximum-Value Functions and the Envelope Theorem
The Envelope Theorem for Unconstrained Optimization
The Profit Function
Reciprocity Conditions
The Envelope Theorem for Constrained Optimization
Interpretation of the Lagrange Multiplier
Duality and the Envelope Theorem
The Primal Problem
The Dual Problem
Duality
Roy's Identity
Shephard's Lemma
Exercise 13.6
Some Concluding Remarks
PART FIVE DYNAMIC ANALYSIS
Economic Dynamics and Integral Calculus
Dynamics and Integration
Indefinite Integrals
The Nature of Integrals
Basic Rules of Integration
Rules of Operation
Rules Involving Substitution
Exercise 14.2
Definite Integrals
Meaning of Definite Integrals
A Definite Integral as an Area under a Curve
Some Properties of Definite Integrals
Another Look at the Indefinite Integral
Exercise 14.3
Improper Integrals
Infinite Limits of Integration
Infinite Integrand
Exercise 14.4
Some Economic Applications of Integrals
From a Marginal Function to a Total Function
Investment and Capital Formation
Present Value of a Cash Flow
Present Value of a Perpetual Flow
Exercise 14.5
Domar Growth Model
The Framework
Finding the Solution
The Razor's Edge
Exercise 14.6
Continuous Time: First-Order Differential Equations
First-Order Linear Differential Equations with Constant Coefficient and Constant Term
The Homogeneous Case
The Nonhomogeneous Case
Verification of the Solution
Exercise 15.1
Dynamics of Market Price
The Framework
The Time Path
The Dynamic Stability of Equilibrium
An Alternative Use of the Model
Exercise 15.2
Variable Coefficient and Variable Term
The Homogeneous Case
The Nonhomogeneous Case
Exercise 15.3
Exact Differential Equations
Exact Differential Equations
Method of Solution
Integrating Factor
Solution of First-Order Linear Differential Equations
Exercise 15.4
Nonlinear Differential Equations of the First Order and First Degree
Exact Differential Equations
Separable Variables
Equations Reducible to the Linear Form
Exercise 15.5
The Qualitative-Graphic Approach
The Phase Diagram
Types of Time Path
Exercise 15.6
Solow Growth Model
The Framework
A Qualitative-Graphic Analysis
A Quantitative Illustration
Exercise 15.7
Higher-Order Differential Equations
Second-Order Linear Differential Equations with Constant Coefficients and Constant Term
The Particular Integral
The Complementary Function
The Dynamic Stability of Equilibrium
Exercise 16.1
Complex Numbers and Circular Functions
Imaginary and Complex Numbers
Complex Roots
Circular Functions
Properties of the Sine and Cosine Functions
Euler Relations
Alternative Representations of Complex Numbers
Exercise 16.2
Analysis of the Complex-Root Case
The Complementary Function
An Example of Solution
The Time Path
The Dynamic Stability of Equilibrium
Exercise 16.3
A Market Model with Price Expectations
Price Trend and Price Expectations
A Simplified Model
The Time Path of Price
Exercise 16.4
The Interaction of Inflation and Unemployment
The Phillips Relation
The Expectations-Augmented Phillips Relation
The Feedback from Inflation to Unemployment
The Time Path of π
Exercise 16.5
Differential Equations with a Variable Term
Method of Undetermined Coefficients
A Modification
Exercise 16.6
Higher-Order Linear Differential Equations
Finding the Solution
Convergence and the Routh Theorem
Exercise 16.7
Discrete Time: First-Order Difference Equations
Discrete Time, Differences, and Difference Equations
Solving a First-Order Difference Equation
Iterative Method
General Method
Exercise 17.2
The Dynamic Stability of Equilibrium
The Significance of b
The Role of A
Convergence to Equilibrium
Exercise 17.3
The Cobweb Model
The Model
The Cobwebs
Exercise 17.4
A Market Model with Inventory
The Model
The Time Path
Graphical Summary of the Results
Exercise 17.5
Nonlinear Difference Equations---The Qualitative-Graphic Approach
Phase Diagram
Types of Time Path
A Market with a Price Ceiling
Exercise 17.6
Higher-Order Difference Equations
Second-Order Linear Difference Equations with Constant Coefficients and Constant Term
Particular Solution
Complementary Function
The Convergence of the Time Path
Exercise 18.1
Samuelson Multiplier-Acceleration Interaction Model
The Framework
The Solution
Convergence versus Divergence
A Graphical Summary
Exercise 18.2
Inflation and Unemployment in Discrete Time
The Model
The Difference Equation in p
The Time Path of p
The Analysis of U
The Long-Run Phillips Relation
Exercise 18.3
Generalizations to Variable-Term and Higher-Order Equations
Variable Term in the Form of cmt
Variable Term in the Form ctn
Higher-Order Linear Difference Equations
Convergence and the Schur Theorem
Exercise 18.4
Simultaneous Differential Equations and Difference Equations
The Genesis of Dynamic Systems
Interacting Patterns of Change
The Transformation of a High-Order Dynamic Equation
Solving Simultaneous Dynamic Equations
Simultaneous Difference Equations
Matrix Notation
Simultaneous Differential Equations
Further Comments on the Characteristic Equation
Exercise 19.2
Dynamic Input-Output Models
Time Lag in Production
Excess Demand and Output Adjustment
Capital Formation
Exercise 19.3
The Inflation-Unemployment Model Once More
Simultaneous Differential Equations
Solution Paths
Simultaneous Difference Equations
Solution Paths
Exercise 19.4
Two-Variable Phase Diagrams
The Phase Space
The Demarcation Curves
Streamlines
Types of Equilibrium
Inflation and Monetary Rule a la Obst
Exercise 19.5
Linearization of a Nonlinear Differential-Equation System
Taylor Expansion and Linearization
The Reduced Linearization
Local Stability Analysis
Exercise 19.6
Optimal Control Theory
The Nature of Optimal Control
Illustration: A Simple Macroeconomic Model
Pontryagin's Maximum Principle
Alternative Terminal Conditions
Fixed Terminal Point
Horizontal Terminal Line
Truncated Vertical Terminal Line
Truncated Horizontal Terminal Line
Exercise 20.2
Autonomous Problems
Economic Applications
Lifetime Utility Maximization
Exhaustible Resource
Exercise 20.4
Infinite Time Horizon
Neoclassical Optimal Growth Model
The Current-Value Hamiltonian
Constructing a Phase Diagram
Analyzing the Phase Diagram
Limitations of Dynamic Analysis
The Greek Alphabet
Mathematical Symbols
A Short Reading List
Answers to Selected Exercises
Index
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