Introductory Mathematical Economics

This work provides a concise and comprehensive grounding in the principles of mathematical economics. It uses matrix algebra and calculus as the basis for explaining its core models: Input-Output, Linear Programming, Inventory Control, Game Theory, Markov Chains, and Regression Analysis. These basic models are then supported through numerous solved, "real world" examples related to business and economic problems. The book has no prerequisites other than high school algebra. It can be used as either a main text or a supplemental text for undergraduate courses, and is also useful for graduate-level students and professional economists.

Preface

vii

Acknowledgments

ix

Vectors and Matrices

1

(40)

Vectors

1

(3)

Geometric Representation of Vectors

4

(1)

Some Types of Vectors

5

(1)

Length (Magnitude) of Vectors

6

(1)

Distance

6

(1)

Linear Combination of Vectors

7

(1)

Linear Independence of Vectors

8

(1)

The Concept of Basis

9

(1)

Matrices

10

(4)

Types of Matrices

14

(2)

The Determinants

16

(5)

Matrix Inversion

21

(2)

Solving Systems of Simultaneous Equations

23

(11)

Eigenvalues, Eigenvectors, and Diagonalization of Matrices

34

(4)

Problems

38

(3)

Derivatives and Applications

41

(27)

The Concept of Derivative

41

(10)

Higher-Order Derivatives

51

(1)

Partial Differentiation

52

(3)

Implicit Differentiation

55

(1)

Higher-Order Partial Derivatives

55

(2)

Total Differentials

57

(5)

Total Derivatives

62

(3)

Problems

65

(3)

The Input-Output Model

68

(27)

The Input-Output Table

68

(4)

The Assumptions of the Input-Output Model

72

(3)

The Mathematical Structure of the Input-Output Model

75

(4)

Multipliers in the Input-Output Model

79

(6)

The Economic Impacts of a New Industry

85

(2)

Backward and Forward Linkages

87

(3)

Prices in the Open Input-Output Model

90

(4)

Problems

94

(1)

Optimization Theory: The Calculus Approach

95

(27)

Optimization of Functions of One Variable

95

(5)

Optimization of Functions of Several Variables

100

(9)

Constrained Optimization of Functions of Several Variables

109

(11)

Problems

120

(2)

The Inventory Model

122

(20)

The Economic Order Quantity (EOQ) Model

122

(9)

The Optimal Order Quantity Model

131

(5)

Inventory With Planned Shortage

136

(4)

Problems

140

(2)

Dynamic Techniques

142

(27)

Definite and Indefinite Integration

142

(7)

First-Order Linear Difference Equations

149

(6)

Second-Order Linear Difference Equations

155

(5)

First-Order Linear Differential Equations

160

(4)

Second-Order Linear Differential Equations

164

(3)

Problems

167

(2)

Linear Programming 1: The Simplex Method

169

(36)

A Problem's Formulation and Assumptions

169

(6)

Graphical Solution of Linear Programming Problems

175

(3)

The Simplex Method: Maximization Problems

178

(11)

The Simplex Method: Minimization Problems

189

(5)

Problems in the Simplex Method

194

(8)

Problems

202

(3)

Linear Programming II: Sensitivity Analysis, Duality, and Integer Programming

205

(38)

Sensitivity Analysis

205

(12)

Duality

217

(11)

Integer Programming

228

(4)

Appendix

232

(8)

Problems

240

(3)

References

243

(2)

Index

245

(5)

About the Author

250

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Introductory Mathematical Economics

Summary

Table of Contents

Supplemental Materials