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A General Theory of Price and Quantity Aggregation and Welfare Measurement

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  • Claude Hillinger

Abstract

The paper presents a general theory of the aggregation of prices and quantities that unifies the field and relates topics that in the past have been treated separately and unsatisfactorily, or not at all. The theory does without the common but unrealistic assumptions of homotheticity, or representative agents and is valid with or without an explicit utility maximization assumption. Two different derivations are given, one in continuous time, using Divisia integrals, and one employing more traditional discrete arguments. The unifying concept is the money metric, which is interpreted as a partial welfare indicator, rather than as a comprehensive welfare measure. On this basis, a consistent set of chained price and quantity indexes for a set of additive time series, such as those in the national income and product accounts, is derived. All variants of the theory lead to Törnqvist indexes defined on the appropriate data set. A numerical example confirms that in the non-homothetic case, these indexes are superior both to Fisher’s ‘ideal’ index and to the consumer surplus approximation.

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Bibliographic Info

Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 818.

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Date of creation: 2002
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Handle: RePEc:ces:ceswps:_818

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Keywords: chain indexes; consumer surplus; cost-of-living; divisia integral; money metric price index; quantity index; real consumption; Törnqvist index;

References

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  1. Diewert, W Erwin, 1978. "Superlative Index Numbers and Consistency in Aggregation," Econometrica, Econometric Society, Econometric Society, vol. 46(4), pages 883-900, July.
  2. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, Elsevier, vol. 4(2), pages 115-145, May.
  3. Apps, Patricia F & Rees, Ray, 1997. "Collective Labor Supply and Household Production," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 105(1), pages 178-90, February.
  4. Diewert, W E, 1992. "Exact and Superlative Welfare Change Indicators," Economic Inquiry, Western Economic Association International, Western Economic Association International, vol. 30(4), pages 562-82, October.
  5. Chiuri, M C & Simmons, P J, 1997. "Universal Decentralisation: A Demand System for Collective and Unitary Models with Household Public Goods," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 107(441), pages 372-89, March.
  6. Jorgenson, Dale W, 1990. "Aggregate Consumer Behavior and the Measurement of Social Welfare," Econometrica, Econometric Society, Econometric Society, vol. 58(5), pages 1007-40, September.
  7. Daniel T. Slesnick, 1998. "Empirical Approaches to the Measurement of Welfare," Journal of Economic Literature, American Economic Association, vol. 36(4), pages 2108-2165, December.
  8. Samuelson, Paul A & Swamy, S, 1974. "Invariant Economic Index Numbers and Canonical Duality: Survey and Synthesis," American Economic Review, American Economic Association, American Economic Association, vol. 64(4), pages 566-93, September.
  9. Diewert, W E, 1976. "Harberger's Welfare Indicator and Revealed Preference Theory," American Economic Review, American Economic Association, American Economic Association, vol. 66(1), pages 143-52, March.
  10. Claude Hillinger, 2001. "Money Metric, Consumer Surplus and Welfare Measurement," German Economic Review, Verein für Socialpolitik, Verein für Socialpolitik, vol. 2(2), pages 177-193, 05.
  11. Samuelson, Paul A, 1974. "Complementarity-An Essay on the 40th Anniversary of the Hicks-Allen Revolution in Demand Theory," Journal of Economic Literature, American Economic Association, vol. 12(4), pages 1255-89, December.
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