1st Edition
Mathematical Analysis and Optimization for Economists
In Mathematical Analysis and Optimization for Economists, the author aims to introduce students of economics to the power and versatility of traditional as well as contemporary methodologies in mathematics and optimization theory; and, illustrates how these techniques can be applied in solving microeconomic problems.
This book combines the areas of intermediate to advanced mathematics, optimization, and microeconomic decision making, and is suitable for advanced undergraduates and first-year graduate students. This text is highly readable, with all concepts fully defined, and contains numerous detailed example problems in both mathematics and microeconomic applications. Each section contains some standard, as well as more thoughtful and challenging, exercises. Solutions can be downloaded from the CRC Press website. All solutions are detailed and complete.
Features
- Contains a whole spectrum of modern applicable mathematical techniques, many of which are not found in other books of this type.
- Comprehensive and contains numerous and detailed example problems in both mathematics and economic analysis.
- Suitable for economists and economics students with only a minimal mathematical background.
- Classroom-tested over the years when the author was actively teaching at the University of Hartford.
- Serves as a beginner text in optimization for applied mathematics students.
- Accompanied by several electronic chapters on linear algebra and matrix theory, nonsmooth optimization, economic efficiency, and distance functions available for free on www.routledge.com/9780367759018.
Preface
Author
Symbols and Abbreviations
1. Mathematical Foundations 1
2. Mathematical Foundations 2
3. Mathematical Foundations 3
4. Mathematical Foundations 4
5. Global and Local Extrema of Real-Valued Functions
6. Global Extrema of Real-Valued Functions
7. Local Extrema of Real-Valued Functions
8. Convex and Concave Real-Valued Functions
9. Generalizations of Convexity and Concavity
10. Constrained Extrema: Equality Constraints
11. Constrained Extrema: Inequality Constraints
12. Constrained Extrema: Mixed Constraints
13. Lagrangian Saddle Points and Duality
14. Generalized Concave Optimization
15. Homogeneous, Homothetic, and Almost Homogeneous Functions
16. Envelope Theorems
17. The Fixed Point Theorems of Brouwer and Kakutani
18. Dynamic Optimization: Optimal Control Modeling
19. Comparative Statics Revisited
References
Index
Biography
Michael J. Panik is Professor Emeritus in the Department of Economics and Finance at the University of Hartford, CT. He has taught courses in economic and business statistics, introductory and advanced quantitative methods, and econometrics. Dr. Panik is the author of several textbooks, monographs, and numerous articles in professional journals.
“Mathematics plays a vital role in providing the logical and foundational basis for several other branches of knowledge. This is particularly true in fields such as economics. Attempting to understand economics without a reasonable grip on mathematics is unwise.
[. . .] The book, Mathematical Analysis and Optimization for Economists, is written with a two-fold intention—on one hand, it envisages making the power and usefulness of contemporary mathematical methodologies evident to the students of economics, and on the other, it attempts at illustrating how these techniques or methodologies could be employed in the solutions of macroeconomic problems. [. . .] The book contains a good number of references for further reading and a very rich index is appended for a quick look-up. It could safely be classified as an intermediate-level textbook. [. . .] it is a very rich source of literature on mathematical analysis and optimization for economists.”
– Technometrics
