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On Marginal Returns and Inferior Inputs

Author

Listed:
  • Paolo Bertoletti

    (Department of Economics and Quantitative Methods, University of Pavia)

  • Giorgio Rampa

    (Department of Economics and Quantitative Methods, University of Pavia)

Abstract

A necessary and sufficient condition for an input to be inferior is that, taking into account the input adjustment, an increase of its price raises the marginal productivity of all inputs. Contrary to a widespread opinion, it is not necessary that (some) inputs are “rivals” (i.e., that some marginal productivity cross derivative is negative). We discuss these facts and illustrate them by introducing a few simple functional forms for the production function. Our results suggest that the existence of inferior inputs is naturally associate to the presence of increasing returns, and possibly make the case for inferiority considerably stronger.

Suggested Citation

  • Paolo Bertoletti & Giorgio Rampa, 2011. "On Marginal Returns and Inferior Inputs," Quaderni di Dipartimento 145, University of Pavia, Department of Economics and Quantitative Methods.
    • Handle: RePEc:pav:wpaper:145
    as

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    File URL: http://dem-web.unipv.it/web/docs/dipeco/quad/ps/RePEc/pav/wpaper/q145.pdf
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    References listed on IDEAS

    as
    1. Takayama,Akira, 1985. "Mathematical Economics," Cambridge Books, Cambridge University Press, number 9780521314985, November.
    2. H. A. John Green, 1961. "Direct Additivity And Consumers' Behaviour," Oxford Economic Papers, Oxford University Press, vol. 13(2), pages 132-136.
    3. repec:bla:manchs:v:68:y:2000:i:5:p:503-15 is not listed on IDEAS
    4. Cornes,Richard, 1992. "Duality and Modern Economics," Cambridge Books, Cambridge University Press, number 9780521336017, November.
    5. Cowell, Frank A., 2006. "Microeconomics: Principles and Analysis," OUP Catalogue, Oxford University Press, number 9780199267774.
    6. Deaton,Angus & Muellbauer,John, 1980. "Economics and Consumer Behavior," Cambridge Books, Cambridge University Press, number 9780521296762, November.
    7. Fisher, Franklin M., 1990. "Normal goods and the expenditure function," Journal of Economic Theory, Elsevier, vol. 51(2), pages 431-433, August.
    8. Gil S. Epstein & Uriel Spiegel, 2000. "A Production Function with an Inferior Input," Manchester School, University of Manchester, vol. 68(5), pages 503-515, September.
    9. Leroux, Alain, 1987. "Preferences and normal goods: A sufficient condition," Journal of Economic Theory, Elsevier, vol. 43(1), pages 192-199, October.
    10. Christian E. Weber, 2001. "A Production Function with an Inferior Input: Comment," Manchester School, University of Manchester, vol. 69(6), pages 616-622, December.
    11. repec:bla:manchs:v:69:y:2001:i:6:p:616-22 is not listed on IDEAS
    12. Paolo Bertoletti, 2005. "Elasticities of Substitution and Complementarity: A Synthesis," Journal of Productivity Analysis, Springer, vol. 24(2), pages 183-196, October.
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    More about this item

    Keywords

    inferior and normal inputs; marginal productivity; homotheticity.;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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