By Dr. Arthur Vogt, Dipl. math. János Barta (auth.)

ISBN-10: 366213179X

ISBN-13: 9783662131794

ISBN-10: 3790824569

ISBN-13: 9783790824568

Arthur Vogt has committed loads of his medical efforts to either individual and paintings of Irving Fisher. This ebook, written with J� nos Barta, offers a good effect of Fisher's nice contributions to the idea of the fee index at the one hand. nonetheless, it maintains Fisher's paintings in this topic alongside the strains which a number of authors drew with appreciate to cost index conception on the grounds that Fisher's dying fifty years ago.

"This is a hugely instructive e-book on either the historical past and thought of size in economics. it is very a wealthy resource of attention-grabbing houses of roughly popular indices and recognized males, particularly Irving Fisher, than an exact mathematical textual content at the axiomatic foundations of indices." (*From the Foreword by means of Wolfgang Eichhorn)*

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**Additional info for The Making of Tests for Index Numbers: Mathematical Methods of Descriptive Statistics**

**Example text**

5. Withdrawal or entry as to prices A price index should be unaffected by the withdrawal or entry of a price ratio agreeing with the index. Thus, if the price index of a certain number of goods, not including sugar, should be 105 in 1910 as compared with 1900, and the price of sugar itself 2. Traditional Treating of Properties of Price Indices 51 should be 105 in 1910 as compared with 1900, then the inclusion of sugar in the calculation of the index number ought not to change the index from 105.

E. that there is a statement B besides the axioms. However we call a statement C a theorem even when it can be deducted from the axioms alone without any further assumption. g. the statement "The identity element of a group is unique" a theorem. In fact, this theorem can be proved from one group axiom alone. 2 we propose the new axiom system {Pl. g. 1, we call certain of its "axioms" tests or theorems. 2. 25). Of course, not all theorems can be proved in such an easy way. 25). 4 Fisher's Properties The motto to this second chapter shows Fisher's opinion about desired properties of indices.

52) this is not obvious. The exponent E has to be 1 for n=l in order that the price-relative-preserving theorem is fulfilled. g. the index by Vartia (1976). It is to mention that the algorithms defining the indices by Ikle (1972) and Martini (1992) do not lead to "direct" index formulae. But there are even more "bad" or not interesting indices or, stated in the words of Divisia (1965:261): ... which gives a double infinity of possible indices. Without good economic reasons it is - believe us - nothing else than an algebraical phantasmagoria.

### The Making of Tests for Index Numbers: Mathematical Methods of Descriptive Statistics by Dr. Arthur Vogt, Dipl. math. János Barta (auth.)

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