By J. Aczél

ISBN-10: 902772377X

ISBN-13: 9789027723772

ISBN-10: 9400937490

ISBN-13: 9789400937499

Recently I taught brief classes on practical equations at numerous universities (Barcelona, Bern, Graz, Hamburg, Milan, Waterloo). My objective was once to introduce crucial equations and techniques of answer via real (not artifi­ cial) purposes which have been contemporary and with which I had anything to do. so much of them occurred to be on the topic of the social or behavioral sciences. All have been initially solutions to questions posed through experts within the respective utilized fields. the following I provide a a little bit prolonged model of those lectures, with newer effects and purposes integrated. As earlier wisdom simply the elemental proof of calculus and algebra are meant. components the place slightly extra (measure concept) is required and sketches of lengthier calcula­ tions are set in nice print. i'm thankful to Drs. J. Baker (Waterloo, Ont.), W. Forg-Rob (Innsbruck, Austria) and C. Wagner (Knoxville, Tenn.) for serious comments and to Mrs. Brenda legislation for care­ ful computer-typing of the manuscript (in numerous versions). A notice on numbering of statements and references: The numbering of Lemmata, Propositions, Theorems, Corollaries and (separately) formulae starts off anew in every one part. If quoted in one other part, the part quantity is further, e.g. (2.10) or Theorem 1.2. References are quoted by means of the final names of the authors and the final digits of the 12 months, e.g. Daroczy-Losonczi [671. 1 1. An aggregation theorem for allocation difficulties. Cauchy equation for single-and multiplace services. extension theorems.

Show description

Read or Download A Short Course on Functional Equations: Based Upon Recent Applications to the Social and Behavioral Sciences PDF

Similar economic theory books

Property and Contract in Economics: The Case for Economic - download pdf or read online

This e-book argues that the lately deceased Capitalism-Socialism debate used to be wrong-headed from the start - like a 'debate' over deepest or public possession of slaves. The query used to be now not deepest or public slavery, yet slavery as opposed to self-ownership. equally, this publication argues that the query isn't even if humans may be deepest staff (capitalism) or public staff (socialism) yet no matter if humans could be employed or rented as staff in any respect as opposed to continuously being together self-employed as employee-owned businesses.

Firms, Markets and Hierarchies: The Transaction Cost - download pdf or read online

This ebook examines transaction fee economics, the influential theoretical standpoint on companies and that used to be the topic of Oliver Williamson's seminal book,Markets and Hierarchies (1975). Written by way of major economists, sociologists, and political scientists, the essays amassed right here replicate the fruitful highbrow alternate that's taking place around the significant social technological know-how disciplines.

Download e-book for kindle: The Evolutionary Foundations of Economics by Kurt Dopfer

Evolutionary economics is attracting expanding curiosity as a manner of figuring out the techniques which generate specific varieties of fiscal actions and buildings. This assortment brings jointly economists who're on the vanguard of this new box of enquiry to supply the main complete and authoritative survey to be had.

Read e-book online Economics and Cognitive Science PDF

Economics, facing psychological techniques of determination makers is a part of cognitive technological know-how; conversely, cognitive technology, confronted with constraints on info processing, is a part of economics. In July 1990, the Cecoia 2 convention used to be organised in Paris to additional discover the connections among the 2.

Additional info for A Short Course on Functional Equations: Based Upon Recent Applications to the Social and Behavioral Sciences

Example text

Multiplicative, logarithmic functions. a(r)v(x) + v(r) = a(x)v(r) + v(x) 27 . L T Since u and thus v is not constant, a =1= equation (6) becomes aa(rx) - a = aa(r)a(x) - aa(r) ) o. +) , (13) (only one unknown function left). Functions satisfying (13) are called multiplicative. Also this equation can be reduced to the Cauchy equation or to (8). It is clear that we will do the latter by taking logarithms of both sides of (13). For this we have to establish that a is everywhere positive. Actually, a(x) 0 is a solution of (13) but we exclude this (since, by (12) and (7), it would cause u to be constant).

F = 0 of (14) so we The case where the dependent variable also has a ratio scale, that is, it transforms by a (homogeneous) linear transformation too (while the independent variables still undergo equal linear transformations), gives the functional equation u(rx) = R(r)u(x) (r EIR++, x EIR~+; u : 1R~+ ~ 1R++, 1R: 1R++ ~ 1R++) (18) (cf. (12)). This is simply the special case P(r) = 0 (r EIR++), u(x) >0 (x EIR~+) of (2). So from (8) L(r) =0 in (7), from (15) b = 0 (since that was the M(r) ¢:1 case) in (14) and from (17) R(r) 1 (since b = 0 in (16) would contradict u(x) > 0) and f is positive valued in (7) and (14) and b > 0 in (16).

Then we get (10). So the following holds. , Independent scales. Price Levels. Characters. ill Corollary 4. ) then in Theorem 1 u(xu···,x n ) = n :E Ci log Xi +b , i=1 or U(Xl"··'X n ) = a n n c. Xi' +b , i=l where a,b,cl, ... ,c n are arbitrary real constants. This too has been obtained by Luce (64] under the supposition that u is everywhere continuous. Our next case is where the independent variables all have interval scales with the same unz"t but with independent zeros, while the dependent variable also has an interval scale.

Download PDF sample

A Short Course on Functional Equations: Based Upon Recent Applications to the Social and Behavioral Sciences by J. Aczél

by Anthony

Rated 4.42 of 5 – based on 37 votes