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The elasticity of derived demand, factor substitution, and product demand: Corrections to Hicks' formula and Marshall's Four Rules

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  • Chirinko, Robert S.
  • Mallick, Debdulal

Abstract

The concept of the elasticity of substitution between capital and labor, introduced by John Hicks and Joan Robinson over 75Â years ago, has had important implications in labor economics and several areas of economic inquiry. In his The Theory of Wages (1932/1963), Hicks developed a formula that has proven very useful in relating the substitution elasticity to the derived demand for productive factors, the distribution of factor incomes, and Marshall's Four Rules. This short paper shows that the original and subsequent derivations of Hicks' celebrated formula contained a slip (that factor shares are independent of the substitution elasticity and therefore constant), presents a new derivation and a corrected formula, and demonstrates that, with the corrected formula, Marshall's First Rule based on the substitution elasticity is no longer generally valid.

Suggested Citation

  • Chirinko, Robert S. & Mallick, Debdulal, 2011. "The elasticity of derived demand, factor substitution, and product demand: Corrections to Hicks' formula and Marshall's Four Rules," Labour Economics, Elsevier, vol. 18(5), pages 708-711, October.
    • Handle: RePEc:eee:labeco:v:18:y:2011:i:5:p:708-711
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    References listed on IDEAS

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    1. M. Bronfenbrenner, 1961. "Notes On The Elasticity Of Derived Demand," Oxford Economic Papers, Oxford University Press, vol. 13(3), pages 254-261.
    2. Mario García Molina, 2005. "Capital theory and the origins of the elasticity of substitution (1932--35)," Cambridge Journal of Economics, Oxford University Press, vol. 29(3), pages 423-437, May.
    3. Daron Acemoglu, 2003. "Labor- And Capital-Augmenting Technical Change," Journal of the European Economic Association, MIT Press, vol. 1(1), pages 1-37, March.
    4. Pierre Cahuc & André Zylberberg, 2004. "Labor Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 026203316x, December.
    5. J. R. Hicks, 1963. "The Theory of Wages," Palgrave Macmillan Books, Palgrave Macmillan, number 978-1-349-00189-7.
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    Cited by:

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    2. Heijdra, Ben J. & Ligthart, Jenny E., 2007. "Fiscal policy, monopolistic competition, and finite lives," Journal of Economic Dynamics and Control, Elsevier, vol. 31(1), pages 325-359, January.
    3. Julieta Caunedo & David Jaume & Elisa Keller, 2023. "Occupational Exposure to Capital-Embodied Technical Change," American Economic Review, American Economic Association, vol. 113(6), pages 1642-1685, June.
    4. Fillmore, Ian, 2022. "A $15 federal minimum wage is outside historical experience," Research in Economics, Elsevier, vol. 76(1), pages 84-92.
    5. Hijzen, Alexander & Swaim, Paul, 2010. "Offshoring, labour market institutions and the elasticity of labour demand," European Economic Review, Elsevier, vol. 54(8), pages 1016-1034, November.

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    More about this item

    Keywords

    Derived demand Substitution elasticity Hicks' formula Marshall's Four Rules;

    JEL classification:

    • A20 - General Economics and Teaching - - Economic Education and Teaching of Economics - - - General
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D33 - Microeconomics - - Distribution - - - Factor Income Distribution
    • J23 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Labor Demand

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