Mathematical Methods and Models for Economists | 
 enlarge | Author: Angel De La Fuente
Publisher: Cambridge University Press
Category: Book
List Price: $58.00
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Rating:  13 reviews
Sales Rank: 160798
Media: Paperback
Edition: 0
Pages: 848
Number Of Items: 1
Shipping Weight (lbs): 3
Dimensions (in): 9.9 x 6.9 x 1.5
ISBN: 0521585295
Dewey Decimal Number: 330.0151
EAN: 9780521585293
Publication Date: February 15, 2000
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Product Description
This book is intended as a textbook for a first-year Ph. D. course in mathematics for economists and as a reference for graduate students in economics. It provides a self-contained, rigorous treatment of most of the concepts and techniques required to follow the standard first-year theory sequence in micro and macroeconomics. The topics covered include an introduction to analysis in metric spaces, differential calculus, comparative statics, convexity, static optimization, dynamical systems and dynamic optimization. The book includes a large number of applications to standard economic models and over two hundred fully worked-out problems.
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| Customer Reviews: Read 8 more reviews...
 Excellent book May 15, 2000
oleg kirsanov (London, UK)
12 out of 18 found this review helpful
Excellent book for mathematicians who are working in a field of economics, economists, who are solving applied problems. All math algorithms for economics included. Highly recommended for not only students
Great value, for the right user September 28, 2003
Gorman
4 out of 6 found this review helpful
I used this book extensively during my first year Ph.D. Econ. It has almost all the basics of the math I used. I agree that it is not a novel-style, Math. Maturity is required and as any First Edition has some typos (but to discover them -by constructing counterexamples- is a great way to show yourself you are understading the concepts and questioning all the assumptions). It has a good presentation of the Berge's (Theorem of the Maximum) and Static Optimization. Its section on dynamic optimization is mostly under continuum time, that I find not too popular nowadays. It is a great reading for the summer before Grad.School but never hesitate to consult lower-level books also -e.g. Simon and Blume. After this, I would read either Debreu's Theory of Value Math. Chapters or Takayama's.
good for the PhD October 6, 2006
Timothy McBabe (germany)
1 out of 3 found this review helpful
This summarizes well the tools for the first year. I'm glad I have it after discovering that Simon and Blume is too basic.
It is important to note that if sth seems too difficult it may not be relevant. Even if it is there are always a lot of solutions which help practising.
this is a great book.
 A good overview October 1, 2004
Dr. Lee D. Carlson (Saint Louis, Missouri USA)
16 out of 18 found this review helpful
Mathematical economics has been around for about 175 years, although as a discipline it has only been recognized for about five decades. Professional economists have had various levels of confidence in its validity and applicability, and mathematical economists have been criticized for the esoteric nature of the mathematics they deploy and some have been ostracized from academic departments for this very reason. This book emphasizes the mathematical tools, these being primarily the theory of optimization and dynamical systems, but the author does find time to discuss applications. Some of these could be classified as "classical" applications, but some are very contemporary in their scope and intersect the work done in financial engineering.
Part 1 of the book introduces the reader to the necessary background in real analysis, topology, differential calculus, and linear algebra. All of this mathematics is straightforward and can be found in many books.
In chapter 5, the author considers static economic models, which are described by collections of parametrized systems of equations. The equations are dependent on parameters describing the environment and `endogenous' variables. The goal is to find the values of the endogenous variables at equilibrium, and to find out if the equilibrium solutions are unique. In addition, it is interest to find out how the solution set changes when the parameters are changed. This is what the author calls `comparative statics'. Linear models are considered first, their analysis being amenable to the techniques of linear and multilinear algebra. The comparative statics for linear models is straightforward, with the shift in equilibrium as a parameter is change readily calculated. The comparative statics of nonlinear models involves the use of the implicit function theorem, and the author derives a formula for doing comparative statics in differentiable models. The discussion here, involving concepts such as transversality, critical points, regular values, and genericity, should be viewed as a warm-up to a more advanced treatment using differential topology.
The author studies static optimization in chapter 7, with the postulate of rationality assumed throughout. This allows the study of the behavior of economic agents to be reduced to a constrained optimization problem. The techniques of nonlinear programming are used to find solutions to the constrained optimization problem. Throughout this chapter one sees discussion of the ubiquitous `agent' who is embedded in a collection of possible environments, and is able to carry out a certain collection of actions.
The author finally gets to economic applications in chapter 8, wherein the author studies the behavior of a single agent under a set of restrictions imposed on it by its environment. This rather simplistic study is then generalized to the case of many interacting agents who are taken to be rational. The concept of `equilibrium', so entrenched in economic theory and economic modeling, makes its appearance here. In a condition of equilibrium, no agent has an incentive to change its behavior, and the actions of each individual are mutually compatible. Some of the usual concepts of equilibrium are discussed in the chapter, such as Walrasian equilibrium in exchange economies, and Nash equilibrium in game theory. The (subjective) preferences of consumers are modeled by binary relations and differentiable utility functions. The differentiability allows the techniques of chapter 7 to be used. The author asks the reader to work through some examples of `imperfect' competition at the end of the chapter.
After a straightforward review of dynamical systems in chapters 9 and 10, the author discusses applications of dynamical systems in chapter 11. He begins with a discussion of a dynamic IS-LM model, using assumptions on the evolution of the money supply, the formation of expectations, and price dynamics. This model consists of two first-order ordinary differential equations, and the author studies its fixed-point structure via a standard phase-space analysis. This analysis allows the author to study the effect of a change in parameters, such as change in the rate of money creation, i.e. the effects of a certain monetary policy. Also discussed are `perfect-foresight models', which address the difficult issue of boundary conditions in economic models based on dynamical systems. Two of these models are discussed, one is a stock price model based on the no-arbitrage principle from finance, and the other is a model of exchange-rate determination. The stock price model is the most interesting discussion in the book. It requires one to specify how expectations are formed, and, depending on how this is done, some very unexpected results occur. For example, if the agents have adaptive expectations, the author shows that the forecast error is predictable, and that agents who understand the structure of the model will have an incentive to deviate from the predicted behavior. This behavior on the part of the agents will invalidate the theory since the agents will have an incentive to compute the trajectory of prices, contrary to the assumption of the model. The author concludes that this is in direct conflict with the assumption that individuals are rational and maximize utility, i.e. that in a world without uncertainty, adaptive expectations are inconsistent with the assumption of rationality. The author avoids this problem by assuming that `perfect foresight' holds for the agents, i.e. the agents form expectations that are consistent with the structure of the model. He shows that the assumption of perfect foresight eliminates the inconsistency that was found in the adaptive expectations model. In the perfect foresight model, every agent uses the correct model to predict prices, and no agent has any incentive to act differently. The author then uses this model to study the response of share prices to a change in the tax rate on dividends. The rest of the chapter discusses neoclassical growth models and the software language Mathematica is introduced as a tool for solving nonlinear differential equations.
I did not read the last two chapters of the book, which cover dynamic optimization and its applications, and so I will omit their review.
Excellent self-contained book February 18, 2001
5 out of 5 found this review helpful
For the first time (at least as far as I know) there is a fully self-contained book on all major mathematical tools needed for intermediary to advanced topics in economics (it even has a small section on logic and methods of proof!). Unfortunatly, there is no treatment whatsoever of integration and measure theory, which is regretable.
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