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The Antonelli Versus Hicks Elasticity of Complementarity and Inverse Input Demand Systems

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  • H. Youn Kim

Abstract

A true measure of input substitution associated with exogenous changes in input quantities requires that the output level be held constant. To this effect, this study presents the Antonelli elasticity of complementarity characterised by the distance function. The more common Hicks elasticity of complementarity assumes that marginal cost is constant and hence does not capture pure substitution effects. The two elasticities of complementarity are related to inverse demand systems and are shown to be equivalent under constant returns to scale. A framework for estimating the Antonelli elasticity from the uncompensated demand system is presented. Estimation results reveal substantial bias of input substitutability with the use of Hicks' measure.

Suggested Citation

  • H. Youn Kim, 2000. "The Antonelli Versus Hicks Elasticity of Complementarity and Inverse Input Demand Systems," Australian Economic Papers, Wiley Blackwell, vol. 39(2), pages 245-261, June.
    • Handle: RePEc:bla:ausecp:v:39:y:2000:i:2:p:245-261
    DOI: 10.1111/1467-8454.00089
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    Cited by:

    1. Stern, David I., 2010. "Derivation of the Hicks, or direct, elasticity of substitution using the input distance function," Economics Letters, Elsevier, vol. 108(3), pages 349-351, September.
    2. Charles Blackorby & Daniel Primont & R. Russell, 2007. "The Morishima gross elasticity of substitution," Journal of Productivity Analysis, Springer, vol. 28(3), pages 203-208, December.
    3. David Stern, 2011. "Elasticities of substitution and complementarity," Journal of Productivity Analysis, Springer, vol. 36(1), pages 79-89, August.
    4. Gary Wong & Qiao Yu, 2001. "Inverse Demand Systems for Composite Liquid Assets: Evidence from China," School of Economics and Finance Discussion Papers and Working Papers Series 097, School of Economics and Finance, Queensland University of Technology.
    5. Daniel Graham & H. Kim, 2008. "An empirical analytical framework for agglomeration economies," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 42(2), pages 267-289, June.
    6. Irz, Xavier T. & Stevenson, James R., 2012. "Efficiency and Farm Size in Philippine Aquaculture. Analysis in a Ray Production Frontier Framework," Bio-based and Applied Economics Journal, Italian Association of Agricultural and Applied Economics (AIEAA), vol. 1(2), pages 1-24, August.
    7. Graham, Daniel J., 2007. "Variable returns to agglomeration and the effect of road traffic congestion," Journal of Urban Economics, Elsevier, vol. 62(1), pages 103-120, July.
    8. Rangkakulnuwat, Poomthan & Wang, H. Holly & Ahn, Sung K., 2007. "The inverse imported factor demand system in Thailand: A cointegration analysis," Economics Letters, Elsevier, vol. 94(3), pages 402-407, March.
    9. Elie Appelbaum & Ulrich Kohli, 1997. "Import Price Uncertainty And The Distribution Of Income," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 620-630, November.
    10. Park, Timothy A., 2008. "Evaluating Labor Productivity in Food Retailing," Agricultural and Resource Economics Review, Northeastern Agricultural and Resource Economics Association, vol. 37(2), pages 1-13.
    11. Anthony J. Glass & Amangeldi Kenjegaliev & Karligash Kenjegalieva, 2022. "Comparisons of deposit types and implications of the financial crisis: Evidence for U.S. banks," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(1), pages 641-664, January.
    12. Lohr, Luanne & Park, Timothy A., 2009. "Labor Pains: Valuing Seasonal versus Year-Round Labor on Organic Farms," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 34(2), pages 1-16, August.
    13. Stern, David I., 2008. "Derivation of the Hicks Elasticity of Substitution from the Input Distance Function," MPRA Paper 12414, University Library of Munich, Germany.
    14. T. Daniel Woodbury, 2020. "The provision of infrastructure: benefit–cost criteria for optimizing local governments," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 27(3), pages 552-574, June.

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