Mathematical Methods and Models for Economists

Book 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.

Customer Reviews:

Ambivalent .......2007-05-25

I found this book to be overkill for the Chicago Ph.D. courses other than econometrics. Proofs are emphasized to the point of neglecting examples, and are not terribly lucid. The book would seem difficult to read anyhow other than as a reference on the rare occasion where you need a very rigorous definition of a given mathematical process (this is how I have used it). Good to have on the shelf since it is the standard bearer in the field, but Simon and Blume will give you everything you need if you are looking to prepare broadly. The few omitted items in constrained optimization will be taught to you in the course of your studies anyhow!

Comprehensive, specially for a Penn PD in Economics.......2006-10-29

Very good book to have if you plan to be an economist!

good for the PhD.......2006-10-06

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.

Great service.......2005-10-03

The book got there on due date and in perfect condition. Great service.

A good overview.......2004-10-01

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.

A note on "The Myth of Institutionalist Method.": An article from: Journal of Economic Issues

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A note on "The Myth of Institutionalist Method.": An article from: Journal of Economic Issues
Charles J. Whalen
Manufacturer: Association for Evolutionary Economics
ProductGroup: Book
Binding: Digital
ASIN: B00095N56W
Release Date: 2005-07-28

Book Description

This digital document is an article from Journal of Economic Issues, published by Association for Evolutionary Economics on March 1, 1996. The length of the article is 1490 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

From the supplier: Institutionalist economists have practiced qualitative methods in their analyses which are considered outmoded by mainstream economists. These methods include single and comparative participant observation, case analysis, interviews and surveys. While these methods are deemed sufficient in analyzing some economic fields, their used are discouraged by conventional economists who prefer quantitative methods. Despite their preference, institutionalists do not use any special analytical methods in their practice.

Citation Details
Title: A note on "The Myth of Institutionalist Method."
Author: Charles J. Whalen
Publication: Journal of Economic Issues (Refereed)
Date: March 1, 1996
Publisher: Association for Evolutionary Economics
Volume: v30 Issue: n1 Page: p279(4)

Distributed by Thomson Gale

Customer Reviews:

Hair of the Dog: Tales from Aboard a Russian Trawler.......2006-05-25

She gave a detailed of how the journey would go through out the ship voyage and gives reader a great idea of how brave she was on the ship. This book does not only show the readers that even you only spend most of the time on the ship that you can still have fun and this a once a life time experience. You can imagine how people who sail or working on the ship most of the time, and how they spent their time. It's a great and fuuny book and gives me a imagination of how her journey is.

From a Former Interpreter Aboard Russian Trawlers.......2001-12-31

This is a special book and a very enjoyable read. Oakley perservered in getting it published and we are all the beneficiaries. Give yourself a treat and get a glimpse of US-Soviet relations that few Americans have witnessed. This book is not just a factual account of life at sea; it is a view into the Russian soul and psyche. You will not regret it.

Customer Reviews:

Amazing!! You will never see Jerusalem in the same light.......1998-12-14

If you have never read Aryeh Kaplan before you are in for a treat. He opens up the mystical (G-ds intended meaning), deeper meaning of the Bible to those uninitiated in Hebrew, Torah, Talmud or Kabbalah. What the true meaning of Jerusalem has to Jews and the world and to the final resurrection predicted by Judaism is all packed into this little book. Read It and Grow.

Henry Sidgwick - Eye of the Universe: An Intellectual Biography

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Henry Sidgwick - Eye of the Universe: An Intellectual Biography
Bart Schultz
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0521829674

Book Description

Henry Sidgwick is one of the great intellectual figures of 19th century Britain. He was first and foremost a great moral philosopher, whose masterwork Methods of Ethics is still widely studied today. But he was many other things besides, writing on religion, economics, politics, education and literature. He was deeply involved in the founding of first college for women at the University of Cambridge. He was a leading figure in parapsychology. He was also much concerned with the sexual politics of his close friend John Addington Symonds, a pioneer of gay studies. Through his famous student, G.E. Moore, a direct line can be traced from Sidgwick and his cirlce to the Bloomsbury group. Bart Schultz has written a magisterial overview of this great Victorian sage--the first comprehensive study, offering quite new critical perspectives on the life and the work. Sidgwick's ethical work is revealed as a necessarily guarded statement of his deepest philosphical convictions and doubts. All other areas of his writings are covered and presented in the context of the late Victorian culture of imperialism. ' This biography, or 'Goethean reconstruction' will be eagerly sought out by readers interested in philosophy, Victorian studies, political theory, the history of ideas, educational theory, the history of psychology and gender and gay studies. Bart Schultz is Fellow and Lecturer in the Division of the Humanities and Special Programs Coordinator in the Graham School of General Studies at the University of Chicago.

Secrets of the Night Sky: Most Amazing Things in the Universe You Can See with the Naked Eye, The

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A great basic astronomy read for the casual observer.
Great author.
A wonderful book
General knowledge only
sky at night

Secrets of the Night Sky: Most Amazing Things in the Universe You Can See with the Naked Eye, The
Bob Berman
Manufacturer: Harper Paperbacks
ProductGroup: Book
Binding: Paperback

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ASIN: 006097687X

Amazon.com

You don't need expensive instruments to appreciate the beauty of the night sky, as Bob Berman exuberantly demonstrates in Secrets of the Night Sky. Berman takes you on a tour of the night sky, pointing out its highlights and its history, along with a wealth of practical tips and tricks, such as how to categorize satellites that appear overhead. Secrets of the Night Sky is not only a how-to manual for enjoying the celestial sphere but is also a painless introduction to the science of cosmology. With a flair for analogies, Berman imparts a visceral understanding of the scale of stellar objects. And in case your explorations do lead you to buy a telescope, the book's appendices contain a variety of no-nonsense advice that may save you from getting fleeced.

Book Description

From blue moons to Betelgeuse, it's all in this witty, fact-packed, profusely illustrated guide to the heavens by the author of Discover magazine's popular "Night Watchman" column.

Customer Reviews:

A great basic astronomy read for the casual observer........2006-01-30

I first read this book when in the Navy stationed in Japan, I would read it on the train to and from Tokyo and Yokosuka. It was light, enjoyable reading about what you can see in the night sky. Now I am reading again to refresh my memory of constellations, stars, Jupiters moons and how to see satellites. My daughter loves stars and I want to refresh my basic knowlege so I can stimulate her curiosity as we view the sights together. I cannot think of a better text to do so. It is a quick read and filled with intersting facts about spacial relationships, space travel and just the magnitude of it all. If there is a down spot it would be the frequent analogies of size and distance which really become meaningless after a point. Still the text will give the lay reader a vocubulary and understanding of the night sky in an easy to read, fun text, what more can you ask for?

Great author........2005-02-24

This book is one of the most informative and entertaining I have ever read. The author provides the information is such a way that you want to keep reading about why there are really more than 24 hours in a day. Anyway, it's a great book, very interesting, very well written. Buy it.

A wonderful book.......2003-09-18

I have been in amateur astronomy for 15 years, and this is one of my favorite books, for beginner or astronomy hobbyist. This is, mercifully, NOT a textbook. You can learn your way around the sky with Raymo's "365 Starry Nights" (also an excellent book), but Berman supplies the humor. The beauty of the night sky is, unfortunatly, a "secret," as few people know anything about it! Let Bob Berman describe the scene up there, get yourself a star chart, and get outdoors!

General knowledge only.......2003-06-14

This book is probably intended for the vast masses that want and look for general information about the universe. The writer indeed contribute a little bit of amazing information about the sizes of stars but many pages are wasted on tidbits which contribute nothing for the science of astronomy. The book is written in light English with not so many words in every page. The diagrams and pictures are of a very low quality and it is very difficult to understand the names of the stars in the diagrams. The pictures are simply disappointing and the paper quality is low as well. The book is as far as possible from a scientific book. Don't come closer to this book if you are after the science of astronomy.

sky at night.......2003-04-12

Very good book for the lovers of sky , especially at night..
beautiful examination and imagination... lovely and kind

The Starry Room: Naked Eye Astronomy in the Intimate Universe

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A modern-day classic

The Starry Room: Naked Eye Astronomy in the Intimate Universe
Fred Schaaf
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

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Book Description

Inspiring, enriching essays describe the amazing features of the night sky, telling beginning star-gazers where to look for and how to find specific celestial objects with the naked eye. No particular knowledge of astronomy is needed to understand the book and most technical expressions are explained as they appear in the text. 5 illustrations.

Customer Reviews:

A modern-day classic.......2005-04-14

There are three books I read again every year: Baseball Anecdotes by Daniel Okrent and Steve Wulf; Be True to Your School by Bob Greene; and the Starry Room by Fred Schaaf. Only one of them moves me to tears on the very first page. If you have ever stood at the edge of the woods at night, gazed up at the stars, and trembled with reverence and awe, perhaps even fear - Fred Schaaf's prose will not only return you to that sacred moment but sweep you up and into the midst of that very sky. The intimate universe awaits.

Eyes on the universe: A history of the telescope

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A very 'readable' history of the telescope, from Asimov.
Asimov and the history of aperature envy.

Eyes on the universe: A history of the telescope
Isaac Asimov
Manufacturer: Houghton Mifflin
ProductGroup: Book
Binding: Unknown Binding

Astronomy | Astronomy | Science | Subjects | Books

Telescopes | Experiments, Instruments & Measurement | Science | Subjects | Books
ASIN: 0395207169

Customer Reviews:

A very 'readable' history of the telescope, from Asimov........1997-08-18

Issac Asimov's affection for astronomy sparkles throughout this thoroughly researched and very entertaining book. An impression of the instrument's dramatic impact on civilisation, is left with the reader. My copy was lost five years ago and I still pine for it. No doubt, had Asimov written 'A Brief History of Time' then quantum physicists would be more widely understood

Asimov and the history of aperature envy........1997-08-14

Written on the eve of construction of the Hubble Space Telescope, Eyes on the Universe traces the development of optical telescopes from the human eye and Galileo's first night out to design considerations for HST. Find out why Galileo went blind, how Newton built the first reflector and why Lord Rosse got clouded out. Learn how giant telescopes and the replacement of the eyepiece with cameras allowed modern astronomers to storm the heavens and change our concepts about the size, age and origins of the cosmos. An excellent history and easy read for scientist and non-scientist alike, Asimov proves why he made tons more money writing science fact than science fiction

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The Space Shuttle (Eye on the Universe)
Jacqueline Langille , and Bobbie Kalman
Manufacturer: Crabtree Publishing Company
ProductGroup: Book
Binding: Paperback

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ASIN: 0865056889

Book Description

Discover what it is like to live and work aboard the space shuttle. Fabulous color photographs and diagrams show the shuttle, its living conditions and its role in our future.

The Life of an Astronaut (Eye on the Universe)

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The Life of an Astronaut (Eye on the Universe)
Niki Walker
Manufacturer: Crabtree Publishing Company
ProductGroup: Book
Binding: Paperback

General | Science, Nature & How It Works | Children's Books | Subjects | Books

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ASIN: 0865056935

Book Description

Who hasn't wondered what it's like to be an astronaut? This book explains how candidates train to become astronauts or "star sailors." It looks at how they prepare for a mission, what they do in space, and what they experience along the way. Kids will love discovering how astronauts eat, sleep, and spend their day in weightless conditions. Engaging photographs and clearly written text will help hopeful young astronauts decide if they, too, have the "right stuff."

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The Sun (Eye on the Universe)
Niki Walker
Manufacturer: Crabtree Publishing Company
ProductGroup: Book
Binding: Paperback

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ASIN: 0865056927

Book Description

The Sun rises. The Sun sets. If you think that's all there is to know about this heavenly body, prepare to be amazed! This book explains what type of star the Sun is, what fuels its enormous energy, and what the Sun's position is in our galaxy. Kids will be intrigued to learn about eclipses, solar activity, and space weather but, more importantly, they'll gain an insight into the crucial relationship between the Sun and Earth. Spectacular photographs and illustrations complement the easy-to-read text to help young readers understand the complex life of the Sun.

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The holy city seen through holy eyes

Jerusalem, Eye of the Universe
Aryeh Kaplan
Manufacturer: Union of Orthodox Jewish Congregations of Ame
ProductGroup: Book
Binding: Paperback

General | Judaism | Religion & Spirituality | Subjects | Books
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ASIN: 1879016125

Customer Reviews:

The holy city seen through holy eyes .......2005-05-20

Aryeh Kaplan sees Jerusalem as both historical center of the Jewish people and cosmic center for redemption of the world.
This is a concise and deep reflection on the Holy City.

Eyes on the Universe (The Story of Science)

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Eyes on the Universe (The Story of Science)
George Reed
Manufacturer: Benchmark Books (NY)
ProductGroup: Book
Binding: Library Binding

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ASIN: 0761411542

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