9780765604590

Introductory Mathematical Economics

by ;
  • ISBN13:

    9780765604590

  • ISBN10:

    0765604590

  • Edition: 1st
  • Format: Hardcover
  • Copyright: 7/22/2015
  • Publisher: Routledge

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Summary

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.

Table of Contents

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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