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A Note on Allen’s Arc Elasticity with Arithmetic, Geometric and Harmonic Means


  • Chin Yang
  • Anthony Loviscek
  • Hui Cheng


  • Ken Hung


Discussion and debate on the application of Allen’s arc elasticity has continued into the 21st century. This note demonstrates three points. First, perceived differences between Allen’s geometric mean elasticity and a constant demand elasticity based on an assumed isoelastic demand curve are negligible for small changes in price and quantity, which comprise the vast majority of such changes. Second, in some cases of rapid security or commodity price movements, the harmonic mean may provide the most accurate elasticity estimates across measures of central tendency. Third, because the arithmetic and harmonic means serve as bounds for the geometric mean, an elasticity based on the geometric mean may be considered a prudent choice among these three on this basis alone. Copyright International Atlantic Economic Society 2012

Suggested Citation

  • Chin Yang & Anthony Loviscek & Hui Cheng & Ken Hung, 2012. "A Note on Allen’s Arc Elasticity with Arithmetic, Geometric and Harmonic Means," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 40(2), pages 161-171, June.
  • Handle: RePEc:kap:atlecj:v:40:y:2012:i:2:p:161-171
    DOI: 10.1007/s11293-012-9315-5

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    References listed on IDEAS

    1. Panagariya, Arvind & Shah, Shekhar & Mishra, Deepak, 2001. "Demand elasticities in international trade: are they really low?," Journal of Development Economics, Elsevier, vol. 64(2), pages 313-342, April.
    2. J. Gallego-Diaz, 1944. "A Note on the Arc Elasticity of Demand," Review of Economic Studies, Oxford University Press, vol. 12(2), pages 114-115.
    3. Shane Miller & Eckhard Platen, 2010. "Real-World Pricing for a Modified Constant Elasticity of Variance Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(2), pages 147-175.
    4. Greenblatt, Jeffery B. & Succar, Samir & Denkenberger, David C. & Williams, Robert H. & Socolow, Robert H., 2007. "Baseload wind energy: modeling the competition between gas turbines and compressed air energy storage for supplemental generation," Energy Policy, Elsevier, vol. 35(3), pages 1474-1492, March.
    5. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    6. C. C. Holt & P. A. Samuelson, 1946. "The Graphic Depiction of Elasticity of Demand," Journal of Political Economy, University of Chicago Press, vol. 54, pages 354-354.
    7. Natalya Ketenci & Idil Uz, 2011. "Bilateral and regional trade elasticities of the EU," Empirical Economics, Springer, vol. 40(3), pages 839-854, May.
    8. Sofia Berto Villas-Boas, 2009. "An empirical investigation of the welfare effects of banning wholesale price discrimination," RAND Journal of Economics, RAND Corporation, vol. 40(1), pages 20-46.
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    More about this item


    Demand elasticity; Allen’s geometric mean arc elasticity; Arithmetic mean arc elasticity; Harmonic mean arc elasticity; JEL; D01; C13;

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General


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