The Index Number Problem

Construction Theorems

Sydney Afriat

A classic work from an eminent scholar who is a leading authority on the theory of economic index numbers
New approach to The Index Number Problem
Combines the author's major contributions with new material on index numbers

The Index Number Problem

Construction Theorems

Sydney Afriat

Description

A theft amounting to L1 was a capital offence in 1260 and a judge in 1610 affirmed the law could not then be applied since L1 was no longer what it was. Such association of money with a date is well recognized for its importance in very many connections. Thus arises the need to know how to convert an amount at one date into the right amount at another date: in other words, a price index.

The longstanding question concerning how such an index should be constructed is known as 'The Index Number Problem'. The ordinary consumer price index represents a practical response to this need. However the search for a true price index has given rise to extensive thought and theory to which an impressive number of economists have each contributed a word, or volume. However, there have been hold-ups at a basic level, which are addressed in this book. The approach brings the subject into involvement with utility construction on the basis of finite data, in a form referred to as 'Afriat's Theorem' but now with utility subject to constant (and also possibly approximate) returns.

The Index Number Problem

Construction Theorems

Sydney Afriat

Preface
Acknowledgements
Introduction
I The Index Number Problem
I. The New Formula
II. The Power Algorithm
III. Combinatorics
IV. Consistency
V. Illustration
Bibliography
II Construction Theorems
1. The system of inequalities ars > xs - xr
2. Principles of Choice and Preference
3. Utility construction-revisited
4. The construction of separable utility functions from expenditure data
5. The Connection between Demand and Utility
6. Revealed Preference Revealed
Appendix: Terminology
Appendix 1. Constant returns, conical, homogeneous
Appendix 2. Notation
Appendix 3. Cost Efficient, Cost Effective
Appendix 4. Part, Chapter, Section
Note: RES 2011 Conference Preliminary to 'Afriat's Theorem and the Index Number Problem'

The Index Number Problem

Construction Theorems

Sydney Afriat

Author Information

Sydney Afriat, Visiting Professor, University of Siena

Sydney Afriat was awarded a State Bursary at school for two years at Pembroke College, Cambridge. He graduated in mathematics and part physics and spent an interval during WWII at the National Physical Laboratory, Teddington, High Speed Section, Aerodynamics Division, directed by J. H. C. He was released at end of the war and whilst studying for his DPhil at Queen's College, Oxford, he became research assistant to the economist J. R. Bellerby, and then joined the Department of Applied Economics at Cambridge. He has held positions at many universities including Jerusalem, Princeton, Rice, Yale, Purdue, UNC, Waterloo, Ottawa, and Berkeley. He has been Visiting Fellow at All Souls, Oxford, Izaak Walton Killam Memorial Fellow, an Academic Visitor at the London School of Economics, Visiting Fellow at Macquarie University NSW, Visiting Professor at the Institute of Social and Economic Research, Osaka and at the University of Siena, and Jean Monnet Fellow at the European University Institute.

The Index Number Problem

Construction Theorems

Sydney Afriat

Reviews and Awards

"A sort of collected works... much to enjoy for both theorists and historians" -- Journal of Economic Literature

"Sydney Afriat, long acclaimed for his deep and elegant contributions to economic theory, provides in this book for the first time a definitive answer to the problem of converting a sum of money at one date into the appropriate amount at another, the resolution of which has defied the finest minds in economics for three generations." -- Michael Allingham, Fellow, Magdalen College, Oxford University

"Trying to remain on the saddle versus riding the horse anywhere you wish. Learning index number formulas for standard applications versus being equipped for much more. Thats the Afriat difference. His deep insights provide sound footing and fertile ground for future research." -- Ali Dogramaci, Bilkent University

"A remarkable achievement! Afriat shows that the standard approach to index numbers is misleading and defective, and he then provides us with a new and comprehensive treatment of the issues." -- Edward Nell, Malcolm B Smith Professor of Economics, New School For Social Research

"A brilliant guide to measuring the unmeasurable - a feast for the mathematically inclined." -- Paul Streeten, Professor Emeritus, Boston University