IDEAS home Printed from https://ideas.repec.org/p/par/dipeco/2016-ep01.html
   My bibliography  Save this paper

Smooth preferences, symmetries and expansion vector fields

Author

Listed:
  • A. Mantovi

Abstract

Tyson (2013) introduces the notion of symmetry vector field for a smooth preference relation, and establishes necessary and sufficient conditions for a vector field on consumption space to be a symmetry vector field. The structure of a such a condition is discussed on both geometric and economic grounds. It is established that symmetry vector fields do commute (i.e. have vanishing Lie bracket) for additive and joint separability. The marginal utility of money is employed as a normalization of the expansion vector field (Mantovi (2013) which results in the fundamental (expansion-) symmetry vector field. Finally, a characterization of symmetry vector fields is given in terms of their action on the distance function, and a pattern of complete response is discussed for additive preferences. Examples of such constructions are explicitly worked out. Potential implications of the results are discussed.

Suggested Citation

  • A. Mantovi, 2016. "Smooth preferences, symmetries and expansion vector fields," Economics Department Working Papers 2016-EP01, Department of Economics, Parma University (Italy).
    • Handle: RePEc:par:dipeco:2016-ep01
    as

    Download full text from publisher

    File URL: http://www.swrwebeco.unipr.it/RePEc/pdf/I_2016-01.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fuss, Melvyn & McFadden, Daniel, 1978. "Production Economics: A Dual Approach to Theory and Applications (II): Applications of the Theory of Production," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, volume 2, number fuss1978a.
    2. King, Robert G. & Plosser, Charles I. & Rebelo, Sergio T., 1988. "Production, growth and business cycles : II. New directions," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 309-341.
    3. W. M. Gorman, 1968. "The Structure of Utility Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(4), pages 367-390.
    4. -, 2001. "Macroeconomic policies in the Caribbean," Sede Subregional de la CEPAL para el Caribe (Estudios e Investigaciones) 27476, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
    5. Christensen, Laurits R & Jorgenson, Dale W & Lau, Lawrence J, 1975. "Transcendental Logarithmic Utility Functions," American Economic Review, American Economic Association, vol. 65(3), pages 367-383, June.
    6. Sato, Ryuzo, 1976. "Self-Dual Preferences," Econometrica, Econometric Society, vol. 44(5), pages 1017-1032, September.
    7. Pollak, Robert A, 1972. "Generalized Separability," Econometrica, Econometric Society, vol. 40(3), pages 431-453, May.
    8. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    9. Fuss, Melvyn & McFadden, Daniel & Mundlak, Yair, 1978. "A Survey of Functional Forms in the Economic Analysis of Production," Histoy of Economic Thought Chapters, in: Fuss, Melvyn & McFadden, Daniel (ed.),Production Economics: A Dual Approach to Theory and Applications, volume 1, chapter 4, McMaster University Archive for the History of Economic Thought.
    10. Andrea Mantovi, 2013. "On the commutativity of expansion and substitution effects," Journal of Economics, Springer, vol. 110(1), pages 83-105, September.
    11. Chambers,Robert G., 1988. "Applied Production Analysis," Cambridge Books, Cambridge University Press, number 9780521314275, October.
    12. Tyson, Christopher J., 2013. "Preference symmetries, partial differential equations, and functional forms for utility," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 266-277.
    13. Miguel-Angel Martín & Agustín Herranz, 2004. "Human capital and economic growth in Spanish regions," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 10(4), pages 257-264, November.
    14. Cornes,Richard, 1992. "Duality and Modern Economics," Cambridge Books, Cambridge University Press, number 9780521336017, October.
    15. King, Robert G. & Plosser, Charles I. & Rebelo, Sergio T., 1988. "Production, growth and business cycles : I. The basic neoclassical model," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 195-232.
    16. Samuelson, Paul A & Swamy, S, 1974. "Invariant Economic Index Numbers and Canonical Duality: Survey and Synthesis," American Economic Review, American Economic Association, vol. 64(4), pages 566-593, September.
    17. Debreu, Gerard, 1972. "Smooth Preferences," Econometrica, Econometric Society, vol. 40(4), pages 603-615, July.
    18. Miles S. Kimball & Matthew D. Shapiro, 2008. "Labor Supply: Are the Income and Substitution Effects Both Large or Both Small?," NBER Working Papers 14208, National Bureau of Economic Research, Inc.
    19. 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.
    20. Tyson, Christopher J., 2013. "Preference symmetries, partial differential equations, and functional forms for utility," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 266-277.
    21. Angus Deaton, 1979. "The Distance Function in Consumer Behaviour with Applications to Index Numbers and Optimal Taxation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 46(3), pages 391-405.
    22. Fuss, Melvyn & McFadden, Daniel (ed.), 1978. "Production Economics: A Dual Approach to Theory and Applications," Elsevier Monographs, Elsevier, edition 1, number 9780444850133.
    23. Fuss, Melvyn & McFadden, Daniel, 1978. "Production Economics: A Dual Approach to Theory and Applications (I): The Theory of Production," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, volume 1, number fuss1978.
    24. Silberberg, Eugene, 1972. "Duality and the Many Consumer's Surpluses," American Economic Review, American Economic Association, vol. 62(5), pages 942-952, December.
    25. Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, vol. 70(3), pages 312-326, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. A. Mantovi, 2021. "Bitcoin selection rule and foundational game theoretic representation of mining competition," Economics Department Working Papers 2021-EP02, Department of Economics, Parma University (Italy).
    2. Giacomo Corneo & Sergio Vergalli, 2016. "Taxes, subsidies, regulation in dynamic models," Journal of Economics, Springer, vol. 119(2), pages 97-99, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. A. Mantovi, 2013. "Differential duality," Economics Department Working Papers 2013-EP05, Department of Economics, Parma University (Italy).
    2. Daniel McFadden, 2014. "The new science of pleasure: consumer choice behavior and the measurement of well-being," Chapters, in: Stephane Hess & Andrew Daly (ed.), Handbook of Choice Modelling, chapter 2, pages 7-48, Edward Elgar Publishing.
    3. J. Peter Neary, 2004. "Rationalizing the Penn World Table: True Multilateral Indices for International Comparisons of Real Income," American Economic Review, American Economic Association, vol. 94(5), pages 1411-1428, December.
    4. Neary, Peter, 2000. "True Multilateral Indexes for International Comparisons of Real Income: Theory and Empirics," CEPR Discussion Papers 2590, C.E.P.R. Discussion Papers.
    5. Serletis, Apostolos & Xu, Libo, 2020. "Functional monetary aggregates, monetary policy, and business cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 121(C).
    6. Barnett, William A. & Serletis, Apostolos, 2008. "Consumer preferences and demand systems," Journal of Econometrics, Elsevier, vol. 147(2), pages 210-224, December.
    7. V. Vandenberghe, 2018. "The Contribution of Educated Workers to Firms’ Efficiency Gains: The Key Role of Proximity to the ‘Local’ Frontier," De Economist, Springer, vol. 166(3), pages 259-283, September.
    8. Jean Pierre Huiban & Camille Mastromarco & Antonio Musolesi & Michel Simioni, 2016. "The impact of pollution abatement investments on production technology: new insights from frontier analysis," Working Papers hal-01512154, HAL.
    9. Sauer, J., 2007. "Monotonicity and Curvature – A Bootstrapping Approach," Proceedings “Schriften der Gesellschaft für Wirtschafts- und Sozialwissenschaften des Landbaues e.V.”, German Association of Agricultural Economists (GEWISOLA), vol. 42, March.
    10. Chambers, Robert G. & Pope, Rulon D., 1993. "A Virtually Ideal Production System: Specifying and Estimating the VIPS Model," Working Papers 197785, University of Maryland, Department of Agricultural and Resource Economics.
    11. LaFrance, Jeffrey T., 2008. "The structure of US food demand," Journal of Econometrics, Elsevier, vol. 147(2), pages 336-349, December.
    12. Bruno De Borger & Kristiaan Kerstens & Diego Prior & Ignace Van de Woestyne, 2013. "Static efficiency decompositions and capacity utilization: integrating economic and technical capacity notions," Applied Economics, Taylor & Francis Journals, vol. 45(24), pages 3529-3529, August.
    13. Stéphane Blancard & Jean-Philippe Boussemart & Walter Briec & Kristiaan Kerstens, 2006. "Short- and Long-Run Credit Constraints in French Agriculture: A Directional Distance Function Framework Using Expenditure-Constrained Profit Functions," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 88(2), pages 351-364.
    14. Gloria A. Grizzle & Ann D. Witte, 1984. "Evaluating Multidimensional Performance," Evaluation Review, , vol. 8(6), pages 777-800, December.
    15. repec:hal:spmain:info:hdl:2441/2041 is not listed on IDEAS
    16. Gabriele Dono & Luca Giraldo & Simone Severini, 2012. "The Cost of Irrigation Water Delivery: An Attempt to Reconcile the Concepts of Cost and Efficiency," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(7), pages 1865-1877, May.
    17. Florian Pelgrin & Arnaud Sylvain & Eric Heyer, 2004. "Capital operating time and working time in the production function : an evaluation on a panel firms over the period 1989-2001," SciencePo Working papers Main hal-00972838, HAL.
    18. Barnett, William A. & Serletis, Apostolos, 2008. "Measuring Consumer Preferences and Estimating Demand Systems," MPRA Paper 12318, University Library of Munich, Germany.
    19. Sauer, Johannes, 2006. "Monotonicity And Curvature - A Bootstrapping Approach," 46th Annual Conference, Giessen, Germany, October 4-6, 2006 14948, German Association of Agricultural Economists (GEWISOLA).
    20. repec:spo:wpecon:info:hdl:2441/2041 is not listed on IDEAS
    21. Eric Heyer & Florian Pelgrin & Arnaud Sylvain, 2004. "Translog ou Cobb-Douglas? Le rôle des durées d'utilisation des facteurs," Staff Working Papers 04-19, Bank of Canada.
    22. Perekhozhuk, Oleksandr, 2007. "Marktstruktur und Preisbildung auf dem ukrainischen Markt für Rohmilch," Studies on the Agricultural and Food Sector in Transition Economies, Leibniz Institute of Agricultural Development in Transition Economies (IAMO), volume 41, number 92322.

    More about this item

    Keywords

    Utility Function; Symmetry; Separability; Vector Field; Expansion Path; Distance Function;
    All these keywords.

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D04 - Microeconomics - - General - - - Microeconomic Policy: Formulation; Implementation; Evaluation
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:par:dipeco:2016-ep01. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Andrea Lasagni (email available below). General contact details of provider: https://edirc.repec.org/data/feparit.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.