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Journal of Economics

, Volume 109, Issue 3, pp 303–313 | Cite as

On inferior inputs and marginal returns

  • Paolo BertolettiEmail author
  • Giorgio Rampa
Article

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.

Keywords

Inferior and normal inputs Marginal productivity Homotheticity 

JEL Classification

D11 D21 D24 

References

  1. Avriel M, Diewert WE, Schaible S, Zang I (1988) Generalized concavity. Plenum Press, New YorkCrossRefGoogle Scholar
  2. Barten AP, Bohn V (1982) Consumer theory. In: Arrow KJ, Intriligator MD (eds) Handbook of mathematical economics, vol II, chap 9. North-Holland, Amsterdam, pp 381–430CrossRefGoogle Scholar
  3. Bear DVT (1972) A further note on factor inferiority. South Econ J 38:409–413CrossRefGoogle Scholar
  4. Beattie BR, Taylor CR (1985) The economics of production. Wiley, New YorkGoogle Scholar
  5. Bertoletti P (2005) Elasticities of substitution and complementarity: a synthesis. J Prod Anal 24:183–196CrossRefGoogle Scholar
  6. Bilas RA, Massey FA (1972) A note on factor inferiority. South Econ J 38:407–408CrossRefGoogle Scholar
  7. Chipman JS (1977) An empirical implication of Auspitz-Lieben–Edgeworth–Pareto complementarity. J Econ Theory 14:228–231CrossRefGoogle Scholar
  8. Cornes R (1992) Duality and modern economics. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  9. Cowell F (2006) Microeconomics. Principles and analysis. Oxford University Press, OxfordGoogle Scholar
  10. Deaton A, Muellbauer J (1980) Economics and consumer behavior. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  11. Epstein GS, Spiegel U (2000) A production function with an inferior input. Manch School 68:503–515CrossRefGoogle Scholar
  12. Fisher F (1990) Normal goods and the expenditure function. J Econ Theory 51:431–433CrossRefGoogle Scholar
  13. Frisch R (1965) Theory of Production. D. Reidel Publishing Company, DordrechtGoogle Scholar
  14. Green HAJ (1961) Direct additivity and consumers’ behaviour. Oxf Econ Pap 13:132–136Google Scholar
  15. Hicks JR (1946) Value and capital, 2nd edn. Clarendon Press, OxfordGoogle Scholar
  16. Hicks JR (1956) A revision of demand theory. Oxford University Press, OxfordGoogle Scholar
  17. Katz ML, Rosen HS (1998) Microeconomics, 3rd edn. McGraw-Hill, New YorkGoogle Scholar
  18. Leroux A (1987) Preferences and normal goods: a sufficient condition. J Econ Theory 43:192–199CrossRefGoogle Scholar
  19. Puu T (1971) Some comments on “inferior” (regressive) inputs. Swed J Econ 73:241–251CrossRefGoogle Scholar
  20. Quah JK-H (2007) The comparative statics of constrained optimization problems. Econometrica 75:401–431CrossRefGoogle Scholar
  21. Rowe JW Jr (1977) Some further comments on input classification. Scand J Econ 79:488–496CrossRefGoogle Scholar
  22. Samuelson PA (1947) Foundations of economic analysis. Harvard University Press, CambridgeGoogle Scholar
  23. Takayama A (1985) Mathematical economics. Cambridge University Press, CambridgeGoogle Scholar
  24. Varian HR (1996) Intermediate microeconomics. A modern approach, 4th edn. W.W. Norton& Company, New YorkGoogle Scholar
  25. Varian HR (1992) Microeconomic analysis, 3rd edn. W.W. Norton& Company, New YorkGoogle Scholar
  26. Weber CE (2001) A production function with an inferior input: comment. Manch School 69:616–622CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Dipartimento di economia politica e metodi quantitativi, Facoltà di EconomiaUniversity of PaviaPaviaItaly

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