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General Equilibrium with Fixed Household Structure and Production

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Abstract

We consider exogenously given firms and multi-member households operating in a competitive market environment. Households are endowed with resources (commodity bundles) and shares of firm ownership. Household members are characterized by individual preferences, possibly with intra-household consumption externalities. Household decisions adhere to the collective rationality model.

  • The existence of general equilibrium and the validity of the first welfare theorem are investigated.

  • We take a first pass at a general equilibrium model with multi-member households and production.

  • The existence proof relies on induced household preferences for aggregate household consumption, so that household choices and production plans reside in the same Euclidean space.

  • Equilibrium welfare is also addressed.

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Notes

  1. 1.

    Alternative models of household decision making have been introduced by Lundberg and Pollak (1993, 1994) and Apps and Rees (2009), among others.

  2. 2.

    See Gersbach and Haller (1999, 2001, 2005, 2009, 2010, 2011), Gori (2010), Gori and Villanacci (2011), Haller (2000).

  3. 3.

    \(\parallel \!\cdot \! \parallel _d\) denotes the Euclidean norm on a d-dimensional Euclidean space. We use the notation \(\gg ,\,>\) and \(\ge \) for vector inequalities.

  4. 4.

    At the macro level, the value of household production is significant and could be around 35% of GDP in developed countries (see Apps and Rees (2009), p. 32).

References

  • Aliprantis, C., Brown, D., & Burkinshaw, D. (1987). Edgeworth equilibria in production economies. Journal of Economic Theory, 43, 252–291.

    Article  Google Scholar 

  • Allingham, M. (1975). General equilibrium. London and Basingstoke: The MacMillan Press.

    Google Scholar 

  • Apps, P. F., & Rees, R. (2009). Public economics and the household. Cambridge, UK: Cambridge University Press.

    Google Scholar 

  • Arrow, K. J., & Debreu, G. (1954). Existence of an equiibrium for a competitive economy. Econometrica, 22, 265–290.

    Article  Google Scholar 

  • Becker, G. S. (1965). A theory of the allocation of time. Economic Journal, 75, 493–517.

    Article  Google Scholar 

  • Böhm, V. (1974). The core of an economy with production. Review of Economic Studies, 41, 429–436.

    Article  Google Scholar 

  • Chiappori, P.-A. (1988). Rational household labor supply. Econometrica, 56, 63–89.

    Google Scholar 

  • Chiappori, P.-A. (1992). Collective labor supply and welfare. Journal of Political Economy, 100, 437–467.

    Article  Google Scholar 

  • Debreu, G. (1982). Existence of competitive equilibrium. In K. J. Arrow & M. D. Intriligator (Eds.), Handbook of mathematical economics (Vol. 2). Amsterdam: North-Holland.

    Google Scholar 

  • Debreu, G., & Scarf, H. (1963). A limit theorem on the core of an economy. International Economic Review, 4, 235–246.

    Article  Google Scholar 

  • Gersbach, H., & Haller, H. (1999). Allocation among multi-member households: Issues, cores and equilibria. In A. Alkan, C. D. Aliprantis, & N. C. Yannelis (Eds.), Current trends in economics: Theory and applications. Heidelberg: Springer-Verlag, Berlin.

    Google Scholar 

  • Gersbach, H., & Haller, H. (2001). Collective decisions and competitive markets. Review of Economic Studies, 68, 347–368.

    Article  Google Scholar 

  • Gersbach, H., & Haller, H. (2005). When inefficiency begets efficiency. Economic Theory, 25, 105–121.

    Article  Google Scholar 

  • Gersbach, H., & Haller, H. (2009). Bargaining power and equilibrium consumption. Social Choice and Welfare, 33, 665–690.

    Google Scholar 

  • Gersbach, H., & Haller, H. (2010). Club theory and household formation. Journal of Mathematical Economics, 46, 715–724.

    Article  Google Scholar 

  • Gersbach, H., & Haller, H. (2011). Bargaining cum voice. Social Choice and Welfare, 36, 199–225.

    Google Scholar 

  • Gersbach, H., & Haller, H. (2012). “Hard Workers” and labor restrictions. Journal of Population Economics, 25, 469–494.

    Article  Google Scholar 

  • Gilles, R. P., & Diamantaras, D. (2003). To trade or not to trade: Economies with a variable number of tradeables. International Economic Review, 44, 1173–1204.

    Article  Google Scholar 

  • Gori, M. (2010). Endogenous household formation and inefficiency in a general equilibrium model. Working Paper, Dipartimento di Matematica per le Decisioni, Università degli Studi di Firenze.

    Google Scholar 

  • Gori, M., & Villanacci, A. (2011). A bargaining model in general equilibrium. Economic Theory, 46, 327–375.

    Article  Google Scholar 

  • Haller, H. (1991). Corporate production and shareholder cooperation under uncertainty. International Economic Review, 32, 823–842.

    Article  Google Scholar 

  • Haller, H. (2000). Household decisions and equilibrium efficiency. International Economic Review, 41, 835–847.

    Article  Google Scholar 

  • Hildenbrand, W. (1974). Core and equilibria of a large economy. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Kehoe, T. J. (1985). Multiplicity of equilibria and comparative statics. Quarterly Journal of Economics, 100, 119–147.

    Article  Google Scholar 

  • Lundberg, S., & Pollak, R. A. (1993). Separate spheres bargaining and the marriage market. Journal of Political Economy, 101, 988–1011.

    Article  Google Scholar 

  • Lundberg, S., & Pollak, R. A. (1994). Non-cooperative bargaining models of marriage. American Economic Review, Papers and Proceedings, 84, 132–137.

    Google Scholar 

  • Sato, N. (2009). Existence of competitive equilibrium in economies with multi- member households. Economics Bulletin, 29, 1760–1771.

    Google Scholar 

  • Xiong, S., & Zheng, C. Z. (2007). Core equivalence theorem with production. Journal of Economic Theory, 137, 246–270.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Management, Technology and Economics, ETH Zürich, Zürich, Switzerland

    Hans Gersbach

  2. Department of Economics, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA

    Hans Haller

Authors
  1. Hans Gersbach
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  2. Hans Haller
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Correspondence to Hans Gersbach .

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Gersbach, H., Haller, H. (2017). General Equilibrium with Fixed Household Structure and Production. In: Groups and Markets. Springer, Cham. https://doi.org/10.1007/978-3-319-60516-6_5

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