On the Geometry and the Numerical Approximation of Cost of Living and Real Income Indices

Part of the Advanced Studies in Theoretical and Applied Econometrics book series (ASTA, volume 25)


The economic theory of the “true” cost of living and real income index numbers is described and illustrated geometically in the logarithmic price-income space. Special attention is paid to the real income index evaluated at the geometric means of the prices in the two periods and to the cost of living index evaluated at the utility level which is associated with these geometric mean prices and geometric mean income. It is shown that this particular pair of index numbers is the only pair which satisfies a certain simple set of axioms. It is also shown how these index numbers can be approximated on the basis of observable price-quantity data. The approximation is accurate up to the second order in price and income log-changes.


Real Income Index Number Utility Level Indifference Curve Equality Sign 
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  1. Fisher, I.: 1922, The Making of Index Numbers, Houghton Mifflin Company, Boston-New York.Google Scholar
  2. Kloek, T.: 1966, Indexcijfers: Enige Methodologische Aspecten, Ph.D. dissertation, Rotterdam.Google Scholar
  3. Rajaoja, V.: 1958, A Study in the Theory of Demand Functions and Price Indexes, Societas Scientiarum Fennica, Helsinki.Google Scholar
  4. Theil, H.: 1967, Economics and Information Theory, Rand McNally & Company, Chicago and North-Holland Publishing Company, Amsterdam.Google Scholar
  5. Törnqvist, L.: 1936, “The Bank of Finland’s Consumption Price Index,” Bank of Finland Monthly Bulletin, 10, 1–8.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1992

Authors and Affiliations

  1. 1.University of ChicagoChicagoUSA

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