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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
  • 82 Downloads

Abstract

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.

Notes

Acknowledgements

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.

References

  1. Abraham KG (2003) Toward a cost-of-living index: progress and prospects. J Econ Perspect 17(1):45–58CrossRefGoogle Scholar
  2. Abraham KG, Greenlees JS, Moulton BR (1998) Working to improve the consumer price index. J Econ Perspect 12(1):27–36CrossRefGoogle Scholar
  3. Blackorby C, Donaldson D (1999) Market demand curves and Dupuit–Marshall consumers’ surpluses: a general equilibrium analysis. Math Soc Sci 37(2):139–163CrossRefGoogle Scholar
  4. Boskin MJ, Dulberger ER, Gordon RJ, Griliches Z, Jorgenson DW (1998) Consumer prices, the consumer price index, and the cost of living. J Econ Perspect 12(1):3–26CrossRefGoogle Scholar
  5. Bruce N (1977) A note on consumer’s surplus, the divisia index, and the measurement of welfare changes. Econometr J Econometr Soc 45(4):1033–1038CrossRefGoogle Scholar
  6. Chipman JS, Moore JC (1976) The scope of consumer’s surplus arguments. In: Tang AM, Westfield FM, Worley JS (eds) Welfare and time in economics: essays in honor of Nicholas Georgescu-Roegen. Lexington Books, Lexington, pp 69–123Google Scholar
  7. Deaton A, Heston A (2010) Understanding PPPs and PPP-based national accounts. Am Econ J Macroecon 2(4):1–35CrossRefGoogle Scholar
  8. Diewert WE (1976) Exact and superlative index numbers. J Econometr 4(2):115–145CrossRefGoogle Scholar
  9. Diewert WE (1988) The early history of price index research.  https://doi.org/10.3386/w2713
  10. Diewert WE (1998) Index number issues in the consumer price index. J Econ Perspect 12(1):47–58CrossRefGoogle Scholar
  11. Dupuit J (1844) On the measurement of the utility of public works. Int Econ Pap 2:83–110 [translated and reprinted in Readings in Welfare Economics (Kenneth J. Arrow and Tibor Scitovsky, eds.), 1969, 255–283, Homewood]Google Scholar
  12. Harberger AC (1971) Three basic postulates for applied welfare economics: an interpretive essay. J Econ Lit 9(3):785–797Google Scholar
  13. Hausman JA (1981) Exact consumer’s surplus and deadweight loss. Am Econ Rev 71(4):662–676Google Scholar
  14. Hausman JA (2003) Sources of bias and solutions to bias in the consumer price index. J Econ Perspect 17(1):23–44CrossRefGoogle Scholar
  15. Hayashi T (2013) Smallness of a commodity and partial equilibrium analysis. J Econ Theory 148(1):279–305CrossRefGoogle Scholar
  16. Hicks JR (1941) The rehabilitation of consumers’ surplus. Rev Econ Stud 8(2):108–116CrossRefGoogle Scholar
  17. Hicks JR (1946) Value and capital: an inquiry into some fundamental principles of economic theory. Clarendon Press, OxfordGoogle Scholar
  18. Hulten CR (1973) Divisia index numbers. Econometr J Econometr Soc 41(6):1017–1025CrossRefGoogle Scholar
  19. Hurwicz L, Uzawa H (1971) On the integrability of demand functions. In: Chipman JS (ed) Preferences, utility, and demand. Harcourt Brace Jovanovich, New York, pp 114–148Google Scholar
  20. Lebow DE, Rudd JB (2003) Measurement error in the consumer price index: where do we stand? J Econ Lit 41(1):159–201CrossRefGoogle Scholar
  21. Marshall A (1961) Principles of economics, 9th edn. Macmillan, New York (first published in 1890)Google Scholar
  22. Mas-Colell A, Whinston MD, Green JR (1995) Microeconomic theory, vol 1. Oxford University Press, New YorkGoogle Scholar
  23. McKenzie GW (1976) Measuring gains and losses. J Polit Econ 84(3):641–646CrossRefGoogle Scholar
  24. McKenzie GW (1979) Consumer’s surplus without apology: comment. Am Econ Rev 69(3):465–468Google Scholar
  25. McKenzie GW, Pearce IF (1976) Exact measures of welfare and the cost of living. Rev Econ Stud 43(3):465–468CrossRefGoogle Scholar
  26. McKenzie GW, Pearce IF (1982) Welfare measurement: a synthesis. Am Econ Rev 72(4):669–682Google Scholar
  27. Miyake M (2006) On the applicability of Marshallian partial-equilibrium analysis. Math Soc Sci 52(2):176–196CrossRefGoogle Scholar
  28. Moulton BR (1996) Bias in the consumer price index: what is the evidence? J Econ Perspect 10(4):159–177CrossRefGoogle Scholar
  29. Nordhaus WD (1998) Quality change in price indexes. J Econ Perspect 12(1):59–68CrossRefGoogle Scholar
  30. Persky J (1998) Retrospectives: price indexes and general exchange values. J Econ Perspect 12(1):197–205CrossRefGoogle Scholar
  31. Pollak RA (1998) The consumer price index: a research agenda and three proposals. J Econ Perspect 12(1):69–78CrossRefGoogle Scholar
  32. Schultze CL (2003) The consumer price index: conceptual issues and practical suggestions. J Econ Perspect 17(1):3–22CrossRefGoogle Scholar
  33. Silberberg E (1972) Duality and the many consumer’s surpluses. Am Econ Rev 62(5):942–952Google Scholar
  34. Vives X (1987) Small income effects: a Marshallian theory of consumer surplus and downward sloping demand. Rev Econ Stud 54(1):87–103CrossRefGoogle Scholar
  35. Willig RD (1976) Consumer’s surplus without apology. Am Econ Rev 66(4):589–597Google Scholar
  36. Willig RD (1979) Consumer’s surplus without apology: reply. Am Econ Rev 69(3):469–474Google Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Osaka City UniversityOsakaJapan

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