Social Choice and Welfare

, Volume 52, Issue 1, pp 127–159 | Cite as

Welfare evaluations and price indices with path dependency problems

  • Tsuyoshi SasakiEmail author
Original Paper


In cases where multiple prices change, this paper develops methods for calculating compensating and equivalent variations from the prices, the consumption bundle, and the wealth elasticities of demand for goods. The methods are a natural extension and generalization of the method in Willig (Am Econ Rev 66(4):589–597, 1976), and have the ability to provide second-order approximations of compensating and equivalent variations. In addition, this paper considers two types of price paths: indifference price paths, along which utility levels are kept constant, and iso-price-ratio paths, along which prices change proportionally. Along these two paths, changes in consumer surplus, compensating variation, and equivalent variation are easily calculated, and that there are interesting and precise relationships among them. Furthermore, the methods and relationships above correspond to those of the Laspeyres–Konüs and Paasche–Konüs true cost of living price indices and the Divisia indices.



I am deeply grateful to Robert D. Willig, Makoto Mori, Tetsuya Nakajima, Minoru Kitahara, Ryosuke Okazawa, the editors, and anonymous reviewers for their helpful comments and suggestions.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Osaka City UniversityOsakaJapan

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