Introductory Mathematical Economics

by Mouhammed; Adil H.

• ISBN13: 9780765604590
• ISBN10: 0765604590
• Format: Hardcover
• Copyright: 2015-07-22
• Publisher: Routledge

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