Methods of Mathematical Economics: Linear and Nonlinear Programming, Fixed-Point Theorems
By addebook • Nov 20th, 2008 • Category: Mathematics •
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Methods of Mathematical Economics: Linear and Nonlinear Programming, Fixed-Point Theorems (Classics in Applied Mathematics, 37) (Classics in Applied Mathematics)
by Joel N. Franklin
Methods of Mathematical Economics: Linear and Nonlinear Programming, Fixed-Point Theorems (Classics in Applied Mathematics, 37) (Classics in Applied Mathematics)
By Joel N. Franklin
Publisher: Society for Industrial Mathematics
Number Of Pages: 297
Publication Date: 2002-01-15
ISBN-10 / ASIN: 0898715091
ISBN-13 / EAN: 9780898715095
Binding: Paperback
Many advances have taken place in the field of combinatorial algorithms since Methods of Mathematical Economics first appeared two decades ago. Despite these advances and the development of new computing methods, several basic theories and methods remain important today for understanding mathematical programming and fixed-point theorems. In this easy-to-read classic, readers learn Wolfe’s method, which remains useful for quadratic programming, and the Kuhn-Tucker theory, which underlies quadratic programming and most other nonlinear programming methods. In addition, the author presents multiobjective linear programming, which is being applied in environmental engineering and the social sciences. The book presents many useful applications to other branches of mathematics and to economics, and it contains many exercises and examples. The advanced mathematical results are proved clearly and completely.
Summary: Outdated, but has a unique collection of interesting topics
Rating: 3
This text attempts to survey the core subjects in optimization and mathematical economics: linear and nonlinear programming, separating plane theorems, fixed-point theorems, and some of their applications.
This text covers only two subjects well: linear programming and fixed-point theorems. The sections on linear programming are centered around deriving methods based on the simplex algorithm as well as some of the standard LP problems, such as network flows and transportation problem. I never had time to read the section on the fixed-point theorems, but I think it could prove to be useful to research economists who work in microeconomic theory. This section presents four different proofs of Brouwer fixed-point theorem, a proof of Kakutani’s Fixed-Point Theorem, and concludes with a proof of Nash’s Theorem for n-person Games.
Unfortunately, the most important math tools in use by economists today, nonlinear programming and comparative statics, are barely mentioned. This text has exactly one 15-page chapter on nonlinear programming. This chapter derives the Kuhn-Tucker conditions but says nothing about the second order conditions or comparative statics results.
Most likely, the strange selection and coverage of topics (linear programming takes more than half of the text) simply reflects the fact that the original edition came out in 1980 and also that the author is really an applied mathematician, not an economist. This text is worth a look if you would like to understand fixed-point theorems or how the simplex algorithm works and its applications. Look elsewhere for nonlinear programming or more recent developments in linear programming.
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