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On inferior inputs and marginal returns

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  • Paolo Bertoletti
  • Giorgio Rampa

Abstract

An input is inferior if and only if an increase in its price raises all marginal productivities. A sufficient condition for input inferiority under quasi-concavity of the production function is then that there are increasing marginal returns with respect to the other input and a non-positive marginal productivity cross derivative. Thus, contrary to widespread opinion, input “competitiveness” is not needed. We discuss these facts and illustrate them by introducing a class of simple production function functional forms. Our results suggest that the existence of inferior inputs is naturally associated with increasing returns, and possibly strengthen the case for inferiority considerably. Copyright Springer-Verlag 2013

Suggested Citation

  • Paolo Bertoletti & Giorgio Rampa, 2013. "On inferior inputs and marginal returns," Journal of Economics, Springer, vol. 109(3), pages 303-313, July.
  • Handle: RePEc:kap:jeczfn:v:109:y:2013:i:3:p:303-313
    DOI: 10.1007/s00712-012-0294-4
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    References listed on IDEAS

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    1. 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.
    2. Leroux, Alain, 1987. "Preferences and normal goods: A sufficient condition," Journal of Economic Theory, Elsevier, vol. 43(1), pages 192-199, October.
    3. Takayama,Akira, 1985. "Mathematical Economics," Cambridge Books, Cambridge University Press, number 9780521314985.
    4. H. A. John Green, 1961. "Direct Additivity And Consumers' Behaviour," Oxford Economic Papers, Oxford University Press, vol. 13(2), pages 132-136.
    5. Chipman, John S., 1977. "An empirical implication of Auspitz-Lieben-Edgeworth-Pareto complementarity," Journal of Economic Theory, Elsevier, vol. 14(1), pages 228-231, February.
    6. John K.-H Quah, 2007. "The Comparative Statics of Constrained Optimization Problems," Econometrica, Econometric Society, vol. 75(2), pages 401-431, March.
    7. Epstein, Gil S & Spiegel, Uriel, 2000. "A Production Function with an Inferior Input," Manchester School, University of Manchester, vol. 68(5), pages 503-515, September.
    8. Christian E. Weber, 2001. "A Production Function with an Inferior Input: Comment," Manchester School, University of Manchester, vol. 69(6), pages 616-622, December.
    9. Rowe, John W, Jr, 1977. " Some Further Comments on Input Classifications," Scandinavian Journal of Economics, Wiley Blackwell, vol. 79(4), pages 488-496.
    10. Cornes,Richard, 1992. "Duality and Modern Economics," Cambridge Books, Cambridge University Press, number 9780521336017.
    11. Cowell, Frank A., 2006. "Microeconomics: Principles and Analysis," OUP Catalogue, Oxford University Press, number 9780199267774.
    12. Deaton,Angus & Muellbauer,John, 1980. "Economics and Consumer Behavior," Cambridge Books, Cambridge University Press, number 9780521296762.
    13. Weber, Christian E, 2001. "A Production Function with an Inferior Input: Comment," Manchester School, University of Manchester, vol. 69(6), pages 616-622, December.
    14. Fisher, Franklin M., 1990. "Normal goods and the expenditure function," Journal of Economic Theory, Elsevier, vol. 51(2), pages 431-433, August.
    15. 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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    3. A. Mantovi, 2013. "On the geometry of luxury," Economics Department Working Papers 2013-EP02, Department of Economics, Parma University (Italy).
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    5. Rocha, Felipe Freitas da & Almeida, Edmar Luiz Fagundes de, 2021. "A general equilibrium model of macroeconomic rebound effect: A broader view," Energy Economics, Elsevier, vol. 98(C).

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    More about this item

    Keywords

    Inferior and normal inputs; Marginal productivity; Homotheticity; D11; D21; D24;
    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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