By Wolfgang Eichhorn
We desire to thank Georg Hasenkamp for precious reviews on an prior draft of the manuscript and Steven Diamond for his kindness in analyzing the manu script and offering suggestion concerning the sort of the exposition. we're additionally thankful to overlook Ingeborg Kasper for her cautious typing of the manu script. Contents 1. creation four 2. cost Indices based simply on costs 2. 1 Definition, Examples, Implications four 2. 2 Characterizations of Pri~e Indices 15 three. cost Indices counting on costs and amounts 22 three. 1 Definition, Examples 23 three. 2 Fisher's method 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. rate degrees, cost Indices, and Fisher's Equation fifty nine of trade four. 1 Definition, Examples, Implications 60 four. 2 Characterizations of fee 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 associated fee index have received new cognizance. This newfound curiosity in cost indices stems from the truth that all such indices are designed to function yardsticks for measuring the fee habit of products and providers. that's, all expense indices relate to the idea that of the 'purchasing strength of money'. If costs bring up, then the worth of the unit of cash declines, i. e.
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Sample text
16), since ~ is multiplicative. 18) where c 1L£2, ... ,cn are real constants. 20): 9'. 18) do not satisfy the Proportionality Test T1, we know that tests T1, T2', T4, and T5 cannot be satisfied by any function ~at the same time. Since T3 is not required, our proof does not include any continuity (or differentiability) assumption. 26) in section 3,4. 12) is uniquely determined by tests T2, T3, T4, and T5. 4). -16), whenever a scalar argument of ~ varies in a sufficiently small interval with left boundary O.
T1 T1' T2 x x x x x x x x T2' x x x x x x x x x x x x x x T5 x x x T4 x x x T3 Does nonDoes strict existence non-existence theorem exist? theorem exist? , Does strict existence non-existence theorem exist? theorem exist? 1) always presumes the system of tests F = {T1, T1', T2, T3', T3, T4, T5, T5 i }. It is feasible, of course, to change the test system. I. 6) as a special case of the Circular Test T2. 10) satisfies T1, T3, T4, T5, and the Time Reversal Test, but not the Circular Test. Therefore, the Time Reversal Test is irrelevant to the solution of the inconsistency problem of Fisher's tests.
2). 4) - at the point (1, ••. ,1). A multiplicative function ~ : 1R~++ 1R++ which is continuous at a single point, can always be written as (see J. Aczel [1966, pp. 12) g(SIrJ2) and respectively. 9) • • - 39 - R. Frisch [1930, p. 10) under rather strong regularity assumptions on 9'using the theory of partial differential equations. (3 • 3. 1 4 ) Remark: R. 10) that the Base Test T2', the Commensurability Test T4, and the Determinateness Test T3 "cannot be fulfilled at the same time (if the index number possesses partial derivatives)".
