By Wolfgang Eichhorn
We desire to thank Georg Hasenkamp for worthy reviews on an previous draft of the manuscript and Steven Diamond for his kindness in interpreting the manu script and supplying recommendation concerning the kind of the exposition. we're additionally thankful to overlook Ingeborg Kasper for her cautious typing of the manu script. Contents 1. advent four 2. cost Indices based purely on costs 2. 1 Definition, Examples, Implications four 2. 2 Characterizations of Pri~e Indices 15 three. expense Indices reckoning on costs and amounts 22 three. 1 Definition, Examples 23 three. 2 Fisher's procedure of exams 29 three. three Implications and Characterizations 35 three. four Independence and Inconsistency of Fisher's exams forty four three. five normal answer of the Inconsistency challenge fifty four four. cost degrees, cost Indices, and Fisher's Equation fifty nine of alternate four. 1 Definition, Examples, Implications 60 four. 2 Characterizations of cost degrees sixty four four. three Fisher's Equation of alternate Reconsidered seventy two Bibliography five. eighty three 6. Index 88 1. creation within the face of the industrial, political, and social difficulties resul ting from world-wide inflation, theories of the fee index have won new awareness. This newfound curiosity in expense indices stems from the truth that all such indices are designed to function yardsticks for measuring the fee habit of products and prone. that's, all expense indices relate to the concept that of the 'purchasing strength of money'. If costs raise, then the worth of the unit of cash declines, i. e.
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Additional resources for Theory of the Price Index: Fisher’s Test Approach and Generalizations
After the detailed analysis of such yardsticks of price levels changes, we now turn to the concept of a price level itself. 1 , we present a general definition of a price level Several examples and a few additional conditions on price levels are also introduced. 2 to characterize important classes of price levels. 3, I. Fisher's famous equation of exchange, which makes use of the price level concep~ is analyzed in detail and its validity is assessed. We shall show that the version of Fisher's equation of exchange considered in most textbooks is not correct.
5) . used in the above proof cannot be called price indices since no function satisfies all five axioms at the same time. 1. s)E . ° real constants, 0 (g ,E ,g,E) E S\) = 1. 8). P1"'" k be an arbitrary number k of price indices. 0). 17). 2 Fisher's System of Tests Historically, the following properties of a function ~served as 'tests' for assessing the quality of a potential price index. Named after I. Fisher, most of these tests (including certain weakened test versions) are stated as functional equations which are valid for o 0 4n all (g ,E ,51,E) e: ffi++ T1: Proportinality Test: See ( 3.
Aczel [1966, pp. 39, 213 ff]). 16) satisfies the Determinateness Test T3 if and only if c 1 = only if ~(A1, ... ,An) s 1• ... 12). 0). The following theorem, however, provides a characterization of 1. 10). 10). 25) into the Factor Reversal Test T5, we obtain g£ o g 12 000 5112 tha t i s , ( 3 . 4 Independence and Inconsistency of Fisher's Tests The following non-existence theorem was published by A. ~'" 1R 1+ which satisfies tests T1, T2, and TS' at the same time. Proof: (A. 181-182]): Three time periods are considered.