Studies in Economic Theory : STUDIES IN ECONOMIC THEORY - Karl Vind

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Studies in Economic Theory

By: Karl Vind

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Hardcover | 13 November 2002

At a Glance

Hardcover
296 Pages

Dimensions(cm)
23.5 x 15.88 x 2.54

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The work on this book started many years ago as an attempt to simplify and unify some results usually taught in courses in mathematical economics. The economic interpretation of the re- sults were representations of preferences as sums or integrals and the decomposition of preferences into utilities and probabilities. It later turned out that t.he approach taken in the earlier versions were also the proper approach in generalizing from preferences which were total preorders to preferences which were not total or tran- sitive. The same mathematics would even in that situation give representations which were additive. It would also give decomposi- tions where concepts of uncertainty appeared. Early versions of some of the results appeared as Working Pa- pers No. 135, 140, 150, and 176 from The Center for Research in Management Science, Berkeley. A first version of chapters 2, 4, 6, 7, and 8 appeared 1969 with the title" Mean Groupoids" 177]. They are essentially unchanged -except for some notes especially in chapter 6. Another version appeared 1990 as 178]. Chapter 10 contains results from the same versions and from 181]. Chapter 11 by Birgit Grodal is based on 91] by Grodal and Jp, an-Francois Mertens. Chapters 11 and 12 - also by Birgit Gro- dal -contains the results from the earlier versions, but have been extended (by Karl Vind) to take into account the new corollaries of the results in the other chapters.

Industry Reviews

From the reviews of the first edition:

"The most important contribution of this book is to formalize, simplify and unify concepts of uncertainity that occur in mathematical economics. ... This well-written book provides an elegant and serious introduction to the basic concepts and results of representations of preferences as sums and integrals. It discusses in detail the decomposition of preferences into utilities and probabilities. This lively presentation ... is impressive. The book will serve as an inspiration for further research and can be recommended ... ." (P.R. Parthasarathy, Zentralblatt MATH, Vol. 1080, 2006)

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You Can Find This Book In

Non-Fiction Psychology Mathematics Probability & Statistics Economics Economic Theory & Philosophy Econometrics Economic Statistics Calculus & Mathematical Analysis Numerical Analysis

Introduction	p. 1
Economics	p. 1
Statistics	p. 1
Mathematics	p. 2
Summary of results	p. 4
Applications	p. 6
Basic Mathematics	p. 7
Totally preordered sets	p. 9
Introduction	p. 9
Order relations	p. 9
Basic concepts	p. 9
Completion	p. 14
Representation	p. 16
Topological concepts	p. 18
The order topology	p. 20
Representation	p. 23
	p. 23
Basic concepts	p. 23
Ordered sets	p. 24
Topology and order topology	p. 24
Ordered topological spaces	p. 24
Lexicographic orders	p. 25
Removing gaps	p. 25
Further results	p. 25
Preferences and preference functions	p. 27
Introduction	p. 27
Representations and representation theorem	p. 27
Notes	p. 29
Totally preordered product sets	p. 31
Introduction	p. 31
Independence assumptions	p. 31
Order topologies on product sets	p. 33
Existence of real continuous order homomorphisms	p. 37
Note	p. 38
A subset of a product set	p. 39
Introduction	p. 39
Independence	p. 40
A total preorder on the set S(A)	p. 40
The Thomsen and the Reidemeister conditions	p. 43
Note	p. 45
The Reidemeister and Thomsen conditions	p. 45
Mean groupoids	p. 49
Introduction	p. 49
Definition of a commutative mean groupoid	p. 49
Completion of commutative mean groupoid	p. 52
The Aczél Fuchs theorem	p. 54
Extension of a commutative mean groupoid	p. 57
The bisymmetry equation	p. 59
Notes	p. 60
History and other results	p. 60
Classifying commutative mean groupoids	p. 61
Lexicographic "mean groupoids"	p. 61
Totally ordered mixture spaces	p. 61
Reducible	p. 62
Products of mean groupoids	p. 62
Completion	p. 62
Measurement of magnitudes	p. 63
The bisymmetry equation	p. 63
Counter example (Andrew Gleason, Harvard)(1)	p. 65
Products of two sets as a mean groupoid	p. 69
Introduction	p. 69
Thomsen's and Reidemeister's conditions	p. 70
(S, >=) = (X x Y/
Table of Contents provided by Publisher. All Rights Reserved.

Studies in Economic Theory

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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