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Exact and Superlative Price and Quantity Indicators

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Author Info
Diewert, Erwin
Mizobuchi , Hideyuki

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Abstract

The traditional economic approach to index number theory is based on a ratio concept. The Konüs true cost of living index is a ratio of cost functions evaluated at the same utility level but with the prices of the current period in the cost function that appears in the numerator and the prices of the base period in the denominator cost function. The Allen quantity index is also a ratio of cost functions where the utility levels vary but the price vector is held constant in the numerator and denominator. There is a corresponding theory for differences of cost functions that was initiated by Hicks and the present paper develops this approach. Diewert defined superlative price and quantity indexes as observable indexes which were exact for a ratio of unit cost functions or for a ratio of linearly homogeneous utility functions. The present paper looks for counterparts to his results in the difference context, for both flexible homothetic and flexible nonhomothetic preferences. The Bennet indicators of price and quantity change turn out to be superlative for the nonhomothetic case. The underlying preferences are of the translation homothetic form discussed by Balk, Chambers, Dickenson, Färe and Grosskopf.

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Publisher Info
Paper provided by UBC Department of Economics in its series UBC Departmental Archives with number erwin_diewert-2009-1.

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Length: 46 pages
Date of creation: 07 Jan 2009
Date of revision: 07 Jan 2009
Handle: RePEc:ubc:bricol:erwin_diewert-2009-1

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Related research
Keywords: Price and quantity aggregates; index number theory; equivalent and compensating variations; exact and superlative indexes; flexible functional forms;

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Find related papers by JEL classification:
C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
D60 - Microeconomics - - Welfare Economics - - - General

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  1. Barnett, William A. & Diewert, W. Erwin & Zellner, Arnold, 2009. "Introduction to Measurement with Theory," MPRA Paper 14868, University Library of Munich, Germany. [Downloadable!]
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This page was last updated on 2009-10-30.

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