The Index Number Problem: Construction Theorems

ISBN : 9780199670581

Sydney Afriat
240 Pages
162 x 237 mm
Pub date
Feb 2014
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A theft amounting to GBP1 was a capital offence in 1260 and a judge in 1610 affirmed the law could not then be applied since GBP1 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.


I. The New Formula
II. The Power Algorithm
III. Combinatorics
IV. Consistency
V. Illustration
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 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'

About the author: 

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.

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