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On the commutativity of expansion and substitution effects

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  • Andrea Mantovi

Abstract

The reversibility of sequential economic choices concerning production and consumption is addressed. A geometric approach to substitution effects and output/income effects is set forth in terms of vector fields on bundle space. By means of suitable fixing relations the 0-homogeneity of such problems can be circumvented, so as to define global parametrizations of effects, for which Lie brackets measure the departure from commutativity. A couple of propositions are established, assessing the benchmark relevance of homothetic models. Application to Farrell decompositions, as tailored by Bogetoft et al. (Eur J Oper Res 168:450–462, 2006 ), results in complete agreement with the results found by such Authors. The theoretical relevance of the approach is thoroughly discussed. Copyright Springer-Verlag Wien 2013

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  • Andrea Mantovi, 2013. "On the commutativity of expansion and substitution effects," Journal of Economics, Springer, vol. 110(1), pages 83-105, September.
    • Handle: RePEc:kap:jeczfn:v:110:y:2013:i:1:p:83-105
    DOI: 10.1007/s00712-013-0337-5
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    References listed on IDEAS

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    10. Robert G. Chambers, 2002. "Exact nonradial input, output, and productivity measurement," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(4), pages 751-765.
    11. Bogetoft, Peter & Fare, Rolf & Obel, Borge, 2006. "Allocative efficiency of technically inefficient production units," European Journal of Operational Research, Elsevier, vol. 168(2), pages 450-462, January.
    12. Luenberger, David G, 1996. "Welfare from a Benefit Viewpoint," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(3), pages 445-462, April.
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    Cited by:

    1. Giacomo Corneo & Sergio Vergalli, 2013. "Editorial: The economics of irreversible choices," Journal of Economics, Springer, vol. 110(1), pages 1-3, September.
    2. A. Mantovi, 2013. "On the geometry of luxury," Economics Department Working Papers 2013-EP02, Department of Economics, Parma University (Italy).
    3. Andrea Mantovi, 2016. "Smooth preferences, symmetries and expansion vector fields," Journal of Economics, Springer, vol. 119(2), pages 147-169, October.
    4. Andrea Mantovi, 2014. "On Luxury and Equilibrium," Review of Economic Analysis, Digital Initiatives at the University of Waterloo Library, vol. 6(2), pages 87-118, December.
    5. Giacomo Corneo & Sergio Vergalli, 2016. "Taxes, subsidies, regulation in dynamic models," Journal of Economics, Springer, vol. 119(2), pages 97-99, October.
    6. A. Mantovi, 2013. "Differential duality," Economics Department Working Papers 2013-EP05, Department of Economics, Parma University (Italy).

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    More about this item

    Keywords

    Partial equilibrium; Homotheticity; Substitution effect; Output effect; Income effect; Technical efficiency; Allocative efficiency; D00; D11; D20;
    All these keywords.

    JEL classification:

    • D00 - Microeconomics - - General - - - General
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D20 - Microeconomics - - Production and Organizations - - - General

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