IDEAS home Printed from https://ideas.repec.org/p/ifs/ifsewp/05-06.html
   My bibliography  Save this paper

Household Nash equilibrium with voluntarily contributed public goods

Author

Listed:
  • Valérie Lechene

    (Institute for Fiscal Studies and University College London)

  • Ian Preston

    (Institute for Fiscal Studies and University College London)

Abstract

We study noncooperative models with two agents and several voluntarily contributed public goods. We focus on interior equilibria in which neither agent is bound by non negativity constraints, establishing the conditions for existence and uniqueness of the equilibrium. While adding-up and homogeneity hold, negativity and symmetry properties are generally violated. We derive the counterpart to the Slutsky matrix, and show that it can be decomposed into the sum of a symmetric and negative semidefinite matrix and another the rank of which never exceeds the number of public goods plus one. Under separability of the public goods the deviation from symmetry is at most rank two.

Suggested Citation

  • Valérie Lechene & Ian Preston, 2005. "Household Nash equilibrium with voluntarily contributed public goods," IFS Working Papers W05/06, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:ifsewp:05/06
    as

    Download full text from publisher

    File URL: http://www.ifs.org.uk/wps/wp0506.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Becker, Gary S, 1974. "A Theory of Social Interactions," Journal of Political Economy, University of Chicago Press, vol. 82(6), pages 1063-1093, Nov.-Dec..
    2. M. Browning & P. A. Chiappori, 1998. "Efficient Intra-Household Allocations: A General Characterization and Empirical Tests," Econometrica, Econometric Society, vol. 66(6), pages 1241-1278, November.
    3. Eduardo Ley, 1996. "On the private provision of public goods: a diagrammatic exposition," Investigaciones Economicas, Fundación SEPI, vol. 20(1), pages 105-123, January.
    4. Bergstrom, Ted C. & Blume, Larry & Varian, Hal, 1992. "Uniqueness of Nash equilibrium in private provision of public goods : An improved proof," Journal of Public Economics, Elsevier, vol. 49(3), pages 391-392, December.
    5. Martin Browning & Pierre-André Chiappori & Valérie Lechene, 2006. "Collective and Unitary Models: A Clarification," Review of Economics of the Household, Springer, vol. 4(1), pages 5-14, March.
    6. Chiappori, Pierre-Andre, 1991. "Nash-Bargained Household Decisions: A Rejoinder," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(3), pages 761-762, August.
    7. Browning, Martin & Francois Bourguignon & Pierre-Andre Chiappori & Valerie Lechene, 1994. "Income and Outcomes: A Structural Model of Intrahousehold Allocation," Journal of Political Economy, University of Chicago Press, vol. 102(6), pages 1067-1096, December.
    8. Angus Deaton, 1991. "Price Elasticities from Survey Data: Extensions and Indonesian Results," International Economic Association Series, in: Marc Nerlove (ed.), Issues in Contemporary Economics, chapter 10, pages 253-283, Palgrave Macmillan.
    9. Paul A. Samuelson, 1956. "Social Indifference Curves," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 70(1), pages 1-22.
    10. McElroy, Marjorie B & Horney, Mary Jean, 1990. "Nash-Bargained Household Decisions: Reply," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(1), pages 237-242, February.
    11. Diewert, W. E., 1977. "Generalized slutsky conditions for aggregate consumer demand functions," Journal of Economic Theory, Elsevier, vol. 15(2), pages 353-362, August.
    12. Warr, Peter G., 1983. "The private provision of a public good is independent of the distribution of income," Economics Letters, Elsevier, vol. 13(2-3), pages 207-211.
    13. Browning, Martin & Meghir, Costas, 1991. "The Effects of Male and Female Labor Supply on Commodity Demands," Econometrica, Econometric Society, vol. 59(4), pages 925-951, July.
    14. Manser, Marilyn & Brown, Murray, 1980. "Marriage and Household Decision-Making: A Bargaining Analysis," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(1), pages 31-44, February.
    15. Bergstrom, Theodore & Blume, Lawrence & Varian, Hal, 1986. "On the private provision of public goods," Journal of Public Economics, Elsevier, vol. 29(1), pages 25-49, February.
    16. Fraser, Clive D., 1992. "The uniqueness of Nash equilibrium in the private provision of public goods : An alternative proof," Journal of Public Economics, Elsevier, vol. 49(3), pages 389-390, December.
    17. Chiappori, Pierre-Andre, 1988. "Nash-Bargained Households Decisions: A Comment," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(4), pages 791-796, November.
    18. James Banks & Richard Blundell & Arthur Lewbel, 1997. "Quadratic Engel Curves And Consumer Demand," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 527-539, November.
    19. Kemp, Murray C., 1984. "A note of the theory of international transfers," Economics Letters, Elsevier, vol. 14(2-3), pages 259-262.
    20. Richard C. Cornes & Emilson C. D. Silva, 1999. "Rotten Kids, Purity, and Perfection," Journal of Political Economy, University of Chicago Press, vol. 107(5), pages 1034-1040, October.
    21. Chen, Zhiqi & Woolley, Frances, 2001. "A Cournot-Nash Model of Family Decision Making," Economic Journal, Royal Economic Society, vol. 111(474), pages 722-748, October.
    22. Blundell,R. W. & Preston,Ian & Walker,Ian (ed.), 1994. "The Measurement of Household Welfare," Cambridge Books, Cambridge University Press, number 9780521451956.
    23. McElroy, Marjorie B & Horney, Mary Jean, 1981. "Nash-Bargained Household Decisions: Toward a Generalization of the Theory of Demand," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(2), pages 333-349, June.
    24. Bergstrom, Theodore C, 1989. "A Fresh Look at the Rotten Kid Theorem--and Other Household Mysteries," Journal of Political Economy, University of Chicago Press, vol. 97(5), pages 1138-1159, October.
    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. Laurens Cherchye & Thomas Demuynck & Bram De Rock, 2011. "Revealed Preference Analysis of Non‐Cooperative Household Consumption," Economic Journal, Royal Economic Society, vol. 121(555), pages 1073-1096, September.
    2. Claude d’Aspremont & Rodolphe Dos Santos Ferreira, 2014. "Household behavior and individual autonomy: an extended Lindahl mechanism," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 643-664, April.
    3. Cherchye, L.J.H. & Demuynck, T. & de Rock, B., 2009. "Degrees of Cooperation in Household Consumption Models : A Revealed Preference Analysis," Other publications TiSEM 097597d5-7724-4d31-b044-e, Tilburg University, School of Economics and Management.
    4. Laurens CHERCHYE & Thomas DEMUYNCK & Bram DE ROCK, 2010. "Noncooperative household consumption with caring," Working Papers of Department of Economics, Leuven ces10.34, KU Leuven, Faculty of Economics and Business (FEB), Department of Economics, Leuven.
    5. Lechene, Valérie & Preston, Ian, 2011. "Noncooperative household demand," Journal of Economic Theory, Elsevier, vol. 146(2), pages 504-527, March.
    6. Laurens Cherchye & Sam Cosaert & Thomas Demuynck & Bram De Rock, 2020. "Group Consumption with Caring Individuals," The Economic Journal, Royal Economic Society, vol. 130(627), pages 587-622.
    7. Martin Browning & Pierre-André Chiappori & Valérie Lechene, 2010. "Distributional Effects in Household Models: Separate Spheres and Income Pooling," Economic Journal, Royal Economic Society, vol. 120(545), pages 786-799, June.
    8. d’ASPREMONT, Claude & DOS SANTOS FERREIRA, Rodolphe, 2009. "Household behavior and individual autonomy," LIDAM Discussion Papers CORE 2009022, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Gutierrez, Federico H., 2018. "A Sharing Model of the Household: Explaining the Deaton-Paxson Paradox and Computing Household Indifference Scales," GLO Discussion Paper Series 166, Global Labor Organization (GLO).
    10. Sabrina Bruyneel & Laurens Cherchye & Bram De Rock, 2012. "Collective consumption models with restricted bargaining weights: an empirical assessment based on experimental data," Review of Economics of the Household, Springer, vol. 10(3), pages 395-421, September.
    11. Valérie Lechene & Ian Preston, 2007. "Demand properties in household Nash equilibrium," IFS Working Papers W07/01, Institute for Fiscal Studies.
    12. Opata, Patience I. & Ezeibe, Adaku B. & Ume, Chikwuma O., 2020. "Impact of women’s share of income on household expenditure in southeast Nigeria," African Journal of Agricultural and Resource Economics, African Association of Agricultural Economists, vol. 15(1), March.
    13. Castilla, Carolina, 2010. "Intra-Household Resource Management Structure and Income-Hiding under Incomplete Information," 2010 Annual Meeting, July 25-27, 2010, Denver, Colorado 61607, Agricultural and Applied Economics Association.
    14. Claude d’Aspremont & Rodolphe Dos Santos Ferreira, 2019. "Enlarging the collective model of household behavior: A revealed preference analysis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(1), pages 1-19, July.
    15. Valerie Lechene & Martin Browning & Pierre-Andre Chiappori, 2006. "Quelques resultats sur l`effet des transferts cibles," Economics Series Working Papers 294, University of Oxford, Department of Economics.
    16. Marcel Fafchamps & Agnes R. Quisumbing & IFPRI, 2006. "Household Formation and Marriage Markets," Economics Series Working Papers GPRG-WPS-039, University of Oxford, Department of Economics.

    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. Lechene, Valérie & Preston, Ian, 2011. "Noncooperative household demand," Journal of Economic Theory, Elsevier, vol. 146(2), pages 504-527, March.
    2. Chiappori, Pierre-André & Donni, Olivier, 2009. "Non-unitary Models of Household Behavior: A Survey of the Literature," IZA Discussion Papers 4603, Institute of Labor Economics (IZA).
    3. Xu, Zeyu, 2007. "A survey on intra-household models and evidence," MPRA Paper 3763, University Library of Munich, Germany.
    4. Chiappori, Pierre-André & Donni, Olivier, 2006. "Les modèles non unitaires de comportement du ménage : un survol de la littérature," L'Actualité Economique, Société Canadienne de Science Economique, vol. 82(1), pages 9-52, mars-juin.
    5. Valerie Lechene & Ian Preston & University College London and Institute for Fiscal Studies, 2000. "Departures from Slutsky Symmetry in Noncooperative Household Demand Models," Economics Series Working Papers 52, University of Oxford, Department of Economics.
    6. Ian Preston, 2000. "Departures from Slutsky Symmetry in Household Demand Models," Econometric Society World Congress 2000 Contributed Papers 1809, Econometric Society.
    7. Laurens CHERCHYE & Thomas DEMUYNCK & Bram DE ROCK, 2010. "Noncooperative household consumption with caring," Working Papers of Department of Economics, Leuven ces10.34, KU Leuven, Faculty of Economics and Business (FEB), Department of Economics, Leuven.
    8. Miriam Beblo & Denis Beninger, 2017. "Do husbands and wives pool their incomes? A couple experiment," Review of Economics of the Household, Springer, vol. 15(3), pages 779-805, September.
    9. Chiuri, Maria Concetta, 2000. "Individual decisions and household demand for consumption and leisure," Research in Economics, Elsevier, vol. 54(3), pages 277-324, September.
    10. Olivier Bargain & Miriam Beblo & Denis Beninger & Richard Blundell & Raquel Carrasco & Maria-Concetta Chiuri & François Laisney & Valérie Lechene & Nicolas Moreau & Michal Myck & Javier Ruiz-Castillo , 2006. "Does the Representation of Household Behavior Matter for Welfare Analysis of Tax-benefit Policies? An Introduction," Review of Economics of the Household, Springer, vol. 4(2), pages 99-111, June.
    11. Alistair Munro, 2018. "Intra†Household Experiments: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 32(1), pages 134-175, February.
    12. Jara-Díaz, Sergio & Rosales-Salas, Jorge, 2017. "Beyond transport time: A review of time use modeling," Transportation Research Part A: Policy and Practice, Elsevier, vol. 97(C), pages 209-230.
    13. Laurens Cherchye & Sam Cosaert & Thomas Demuynck & Bram De Rock, 2020. "Group Consumption with Caring Individuals," The Economic Journal, Royal Economic Society, vol. 130(627), pages 587-622.
    14. Gutierrez, Federico H., 2018. "A Sharing Model of the Household: Explaining the Deaton-Paxson Paradox and Computing Household Indifference Scales," GLO Discussion Paper Series 166, Global Labor Organization (GLO).
    15. Laurens Cherchye & Thomas Demuynck & Bram De Rock, 2011. "Revealed Preference Analysis of Non‐Cooperative Household Consumption," Economic Journal, Royal Economic Society, vol. 121(555), pages 1073-1096, September.
    16. Miriam Beblo & Denis Beninger, 2012. "Do husbands and wives pool their incomes? Experimental evidence," Working Papers of BETA 2012-10, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    17. Richard Cornes & Jun-ichi Itaya & Aiko Tanaka, 2012. "Private provision of public goods between families," Journal of Population Economics, Springer;European Society for Population Economics, vol. 25(4), pages 1451-1480, October.
    18. Pierre-André Chiappori & Costas Meghir, 2014. "Intrahousehold Inequality," NBER Working Papers 20191, National Bureau of Economic Research, Inc.
    19. Olivier Bargain & Nicolas Moreau, 2013. "The Impact of Tax-Benefit Reforms on Labor Supply in a Simulated Nash-bargaining Framework," Journal of Family and Economic Issues, Springer, vol. 34(1), pages 77-86, March.
    20. Smith, V. Kerry & Van Houtven, George, 1998. "Non-Market Valuation and the Household," RFF Working Paper Series dp-98-31, Resources for the Future.

    More about this item

    Keywords

    Nash equilibrium; Intra-household allocation; Slutsky;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    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:ifs:ifsewp:05/06. 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: Emma Hyman (email available below). General contact details of provider: https://edirc.repec.org/data/ifsssuk.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.