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Translation homotheticity

Author

Listed:
  • Robert G. Chambers

    (Department of Agricultural and Resource Economics, 2200 Symons Hall, University of Maryland, College Park, MD 20742-5535, USA)

  • Rolf Färe

    (Department of Economics, Southern Illinois University, Carbondale, IL 62901-4515, USA)

Abstract

The concept of translation homotheticity is introduced and defined. It is demonstrated that translation homotheticity is necessary and sufficient for: disposable surplus to be independent of the reference utility, Luenberger's compensating and equivalent benefits to be independent of the reference utility and always equal to one another, the risk premium to be independent of reference-level utility, absolute indexes of income inequality to be reference free, and social-welfare functionals to satisfy invariance with respect to the choice of a common origin. Translation homotheticity is also sufficient for Hicks' many-market consumer surplus measure to be a second-order approximation to disposable surplus, compensating benefit, and equivalent benefit. If preferences are translation homothetic and appropriately quadratic, Hicks, many-market consumer surplus measure is exact for these welfare measures.

Suggested Citation

  • Robert G. Chambers & Rolf Färe, 1998. "Translation homotheticity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(3), pages 629-641.
    • Handle: RePEc:spr:joecth:v:11:y:1998:i:3:p:629-641
    Note: Received: October 24, 1996; revised version: March 3, 1997
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    Citations

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    Cited by:

    1. Chambers, Robert G. & Quiggin, John, 2001. "Primal and Dual Approaches to the Analysis of Risk Aversion," Working Papers 197602, University of Maryland, Department of Agricultural and Resource Economics.
    2. Robert G. Chambers & John Quiggin, 2007. "Dual Approaches to the Analysis of Risk Aversion," Economica, London School of Economics and Political Science, vol. 74(294), pages 189-213, May.
    3. Juan Aparicio & Jesus T. Pastor, 2012. "Benefit function and individual preferences. A generalization of the zero-maximum principle," Economics and Business Letters, Oviedo University Press, vol. 1(1), pages 12-20.
    4. Molinos-Senante, María & Maziotis, Alexandros & Sala-Garrido, Ramón, 2014. "The Luenberger productivity indicator in the water industry: An empirical analysis for England and Wales," Utilities Policy, Elsevier, vol. 30(C), pages 18-28.
    5. R. Fare & S. Grosskopf, 2000. "On Separability of the Profit Function," Journal of Optimization Theory and Applications, Springer, vol. 105(3), pages 609-620, June.
    6. Atakelty Hailu & Robert Chambers, 2012. "A Luenberger soil-quality indicator," Journal of Productivity Analysis, Springer, vol. 38(2), pages 145-154, October.
    7. Briec, Walter & Mussard, Stéphane, 2020. "Improvement of technical efficiency of firm groups," European Journal of Operational Research, Elsevier, vol. 283(3), pages 991-1001.
    8. Soloaga, Isidro, 2000. "The treatment of non-essential inputs in a Cobb-Douglas technology : an application to Mexican rural household-level data," Policy Research Working Paper Series 2499, The World Bank.
    9. Fare, Rolf & Li, Sung Ko, 2001. "A nonparametric test of translation homotheticity," Economics Letters, Elsevier, vol. 72(3), pages 341-345, September.
    10. Briec, Walter & Mussard, Stéphane, 2014. "Efficient firm groups: Allocative efficiency in cooperative games," European Journal of Operational Research, Elsevier, vol. 239(1), pages 286-296.
    11. Rolf Fare & Daniel Primont, 2006. "Directional duality theory Directional duality theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 239-247, September.
    12. Färe, Rolf & Grosskopf, Shawna & Hayes, Kathy J. & Margaritis, Dimitris, 2008. "Estimating demand with distance functions: Parameterization in the primal and dual," Journal of Econometrics, Elsevier, vol. 147(2), pages 266-274, December.
    13. Ball, V.E. & Färe, R. & Grosskopf, S. & Margaritis, D., 2015. "The role of energy productivity in U.S. agriculture," Energy Economics, Elsevier, vol. 49(C), pages 460-471.
    14. A. Mantovi, 2013. "Differential duality," Economics Department Working Papers 2013-EP05, Department of Economics, Parma University (Italy).
    15. Chambers, Robert G. & Quiggin, John, 1999. "Production Insurance and Input Use: An Analytical Framework," Working Papers 197859, University of Maryland, Department of Agricultural and Resource Economics.
    16. Valentin Zelenyuk, 2014. "Scale efficiency and homotheticity: equivalence of primal and dual measures," Journal of Productivity Analysis, Springer, vol. 42(1), pages 15-24, August.
    17. Walter Briec & Nicolas Peypoch, 2007. "Biased Technical Change and Parallel Neutrality," Journal of Economics, Springer, vol. 92(3), pages 281-292, December.
    18. Walter Briec & Marc Dubois & Stéphane Mussard, 2021. "Technical efficiency in firm games with constant returns to scale and $$\alpha $$ α -returns to scale," Annals of Operations Research, Springer, vol. 304(1), pages 35-62, September.
    19. Fare, Rolf & Grosskopf, Shawna & Zelenyuk, Valentin, 2002. "Finding Common Ground: Efficiency Indices," MPRA Paper 28004, University Library of Munich, Germany, revised Jan 2005.
    20. Walter Briec & Laurent Cavaignac, 2009. "An extension of the multi-output state-contingent production model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(1), pages 43-64, April.
    21. Quiggin, John & Chambers, R.G.Robert G., 2004. "Invariant risk attitudes," Journal of Economic Theory, Elsevier, vol. 117(1), pages 96-118, July.

    More about this item

    JEL classification:

    • D20 - Microeconomics - - Production and Organizations - - - General
    • D60 - Microeconomics - - Welfare Economics - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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