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Translation homotheticity

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  • 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.

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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 11 (1998)
Issue (Month): 3 ()
Pages: 629-641

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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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Cited by:
  1. 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.
  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, 05.
  3. Fare, Rolf & Li, Sung Ko, 2001. "A nonparametric test of translation homotheticity," Economics Letters, Elsevier, vol. 72(3), pages 341-345, September.
  4. Valentin Zelenyuk, 2013. "Scale Efficiency and Homotheticity: Equivalence of Primal and Dual Measures," CEPA Working Papers Series WP022013, School of Economics, University of Queensland, Australia.
  5. Atakelty Hailu & Robert Chambers, 2012. "A Luenberger soil-quality indicator," Journal of Productivity Analysis, Springer, vol. 38(2), pages 145-154, October.
  6. Walter Briec & Nicolas Peypoch, 2007. "Biased Technical Change and Parallel Neutrality," Journal of Economics, Springer, vol. 92(3), pages 281-292, December.
  7. Rolf Fare & Daniel Primont, 2006. "Directional duality theory Directional duality theory," Economic Theory, Springer, vol. 29(1), pages 239-247, September.
  8. Quiggin, John & Chambers, R.G.Robert G., 2004. "Invariant risk attitudes," Journal of Economic Theory, Elsevier, vol. 117(1), pages 96-118, July.
  9. Walter Briec & Laurent Cavaignac, 2009. "An extension of the multi-output state-contingent production model," Economic Theory, Springer, vol. 39(1), pages 43-64, April.
  10. 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.
  11. A. Mantovi, 2013. "Differential duality," Economics Department Working Papers 2013-EP05, Department of Economics, Parma University (Italy).
  12. Fare, Rolf & Grosskopf, Shawna & Zelenyuk, Valentin, 2002. "Finding Common Ground: Efficiency Indices," MPRA Paper 28004, University Library of Munich, Germany, revised Jan 2005.

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