IDEAS home Printed from
   My bibliography  Save this paper

Exact and Superlative Price and Quantity Indicators


  • Diewert, Erwin
  • Mizobuchi , Hideyuki


The traditional economic approach to index number theory is based on a ratio concept. The Konüs true cost of living index is a ratio of cost functions evaluated at the same utility level but with the prices of the current period in the cost function that appears in the numerator and the prices of the base period in the denominator cost function. The Allen quantity index is also a ratio of cost functions where the utility levels vary but the price vector is held constant in the numerator and denominator. There is a corresponding theory for differences of cost functions that was initiated by Hicks and the present paper develops this approach. Diewert defined superlative price and quantity indexes as observable indexes which were exact for a ratio of unit cost functions or for a ratio of linearly homogeneous utility functions. The present paper looks for counterparts to his results in the difference context, for both flexible homothetic and flexible nonhomothetic preferences. The Bennet indicators of price and quantity change turn out to be superlative for the nonhomothetic case. The underlying preferences are of the translation homothetic form discussed by Balk, Chambers, Dickenson, Färe and Grosskopf.

Suggested Citation

  • Diewert, Erwin & Mizobuchi , Hideyuki, 2009. "Exact and Superlative Price and Quantity Indicators," Economics working papers erwin_diewert-2009-1, Vancouver School of Economics, revised 07 Jan 2009.
  • Handle: RePEc:ubc:bricol:erwin_diewert-2009-1

    Download full text from publisher

    File URL:
    Download Restriction: no

    Other versions of this item:


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Barnett, William A. & Erwin Diewert, W. & Zellner, Arnold, 2011. "Introduction to measurement with theory," Journal of Econometrics, Elsevier, vol. 161(1), pages 1-5, March.
    2. W. Diewert, 2015. "Decompositions of productivity growth into sectoral effects," Journal of Productivity Analysis, Springer, vol. 43(3), pages 367-387, June.
    3. W. Erwin Diewert & Robert C. Feenstra, 2019. "Estimating the Benefits of New Products," NBER Chapters, in: Big Data for 21st Century Economic Statistics, National Bureau of Economic Research, Inc.
    4. Diewert, W. Erwin & Fox, Kevin J., 2016. "Kevin J. Fox Interview of W. Erwin Diewert," working papers erwin_diewert-2016-6, Vancouver School of Economics, revised 02 Jun 2016.
    5. Diewert, Erwin & Feenstra, Robert, 2019. "Estimating the Benefits of New Products: Some Approximations," working papers erwin_diewert-2019-3, Vancouver School of Economics, revised 13 Mar 2019.
    6. Diewert, Erwin & Fox, Kevin J. & Schreyer, Paul, 2019. "Experimental Economics and the New Commodities Problem," working papers erwin_diewert-2019-4, Vancouver School of Economics, revised 13 Mar 2019.
    7. Erik Brynjolfsson & Avinash Collis & W. Erwin Diewert & Felix Eggers & Kevin J. Fox, 2020. "Measuring the Impact of Free Goods on Real Household Consumption," AEA Papers and Proceedings, American Economic Association, vol. 110, pages 25-30, May.
    8. Robert J. Hill & Alice O. Nakamura, 2010. "Improving Inflation And Related Performance Measures For Nations: An Introduction," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(s1), pages 1-10, June.

    More about this item


    Price and quantity aggregates; index number theory; equivalent and compensating variations; exact and superlative indexes; flexible functional forms;

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
    • D60 - Microeconomics - - Welfare Economics - - - General


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ubc:bricol:erwin_diewert-2009-1. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Maureen Chin). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.