A Note on Separability of the Profit Function


Based on the concept of translation elasticity we restate in this note the Fare and Grosskopf’s [1] conditions for additive separability of the profit function. We show that for the profit function to be additively separable, the technology must satisfy both simultaneous input-and-output translation homotheticity and graph translation homotheticity.

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Färe, R. and Karagiannis, G. (2014) A Note on Separability of the Profit Function. Theoretical Economics Letters, 4, 702-704. doi: 10.4236/tel.2014.48089.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Fare, R. and Grosskopf, S. (2000) On Separability of the Profit Function. Journal of Optimization Theory and Applications, 105, 609-620. http://dx.doi.org/10.1023/A:1004693107475
[2] Balk, B.M., Fare, R. and Karagiannis, G. (2014) On Directional Scale Elasticities. Journal of Productivity Analysis. (forthcoming). http://dx.doi.org/10.1007/s11123-014-0399-6
[3] Luenberger, D.G. (1995) Microeconomic Theory. McGraw-Hill, New York.
[4] Chambers, R.G., Chung, Y. and Fare, R. (1998) Profit, Directional Distance Functions, and Nelrovian Efficiency. Journal of Optimization Theory and Applications, 98, 351-364.
[5] Lau, L.J. (1972) Profit Functions for Technologies with Multiple Inputs and Outputs. Review of Economics and Statistics, 54, 281-289. http://dx.doi.org/10.2307/1937989
[6] Chambers, R.G. (2002) Exact Nonradial Input, Output and Productivity Measurement. Economic Theory, 20, 751-765. http://dx.doi.org/10.1007/s001990100231
[7] Briec, W. and Kerstens, K. (2004)A Luenberger-Hicks-Moorsteen Productivity Indicator: Its Relation to the Hicks-Moorsteen Productivity Index and the Luenberger Productivity Indicator. Economic Theory, 23, 925-939. http://dx.doi.org/10.1007/s00199-003-0403-2

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