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When worlds collide: Different comparative static predictions of continuous and discrete agent models with land

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  • Berliant, Marcus
  • Sabarwal, Tarun

Abstract

This paper presents a difference in the comparative statics of general equilibrium models with land when there are finitely many agents, and when there is a continuum of agents. Restricting attention to quasi-linear and Cobb-Douglas utility, it is shown that with finitely many agents, an increase in the (marginal) commuting cost increases land rent per unit (that is, land rent averaged over the consumer's equilibrium parcel) paid by each consumer. In contrast, with a continuum of agents, average land rent goes up close to the central business district, is constant at some intermediate distance, and decreases for consumers farther away. Therefore, there is a qualitative difference between the two types of models, and this difference is potentially testable.

Suggested Citation

  • Berliant, Marcus & Sabarwal, Tarun, 2007. "When worlds collide: Different comparative static predictions of continuous and discrete agent models with land," MPRA Paper 3393, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:3393
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    References listed on IDEAS

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    1. Berliant, Marcus & ten Raa, Thijs, 1991. "On the continuum approach of spatial and some local public goods or product differentiation models: Some problems," Journal of Economic Theory, Elsevier, vol. 55(1), pages 95-120, October.
    2. Fujita,Masahisa, 1991. "Urban Economic Theory," Cambridge Books, Cambridge University Press, number 9780521396455, January.
    3. Kamecke Ulrich, 1993. "Mean City--A Consistent Approximation of Bid Rent Equilibria," Journal of Urban Economics, Elsevier, vol. 33(1), pages 48-67, January.
    4. Berliant, Marcus, 1991. "Comments on: 'On the foundations of land use theory: Discrete versus continuous populations' by Y. Asami, M. Fujita and T.E. Smith," Regional Science and Urban Economics, Elsevier, vol. 21(4), pages 639-645, December.
    5. Papageorgiou, Yorgos Y. & Pines, David, 1990. "The logical foundations of urban economics are consistent," Journal of Economic Theory, Elsevier, vol. 50(1), pages 37-53, February.
    6. Berliant, Marcus & Fujita, Masahisa, 1992. "Alonso's Discrete Population Model of Land Use: Efficient Allocations and Competitive Equilibria," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(3), pages 535-566, August.
    7. Asami, Y. & Fujita, M. & Smith, T. E., 1991. "On the foundations of land use theory : Discrete versus continuous populations," Regional Science and Urban Economics, Elsevier, vol. 20(4), pages 473-508, February.
    8. Marcus Berliant & Courtney LaFountain, 2004. "Space in General Equilibrium," Urban/Regional 0408002, University Library of Munich, Germany, revised 27 Jun 2005.
    9. Berliant, Marcus, 1985. "Equilibrium models with land : A criticism and an alternative," Regional Science and Urban Economics, Elsevier, vol. 15(2), pages 325-340, June.
    10. Robert E. Lucas & Esteban Rossi-Hansberg, 2002. "On the Internal Structure of Cities," Econometrica, Econometric Society, vol. 70(4), pages 1445-1476, July.
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    Cited by:

    1. Berliant, Marcus, 2007. "Prospects for a unified urban general equilibrium theory," Regional Science and Urban Economics, Elsevier, vol. 37(4), pages 466-471, July.
    2. RĂ©mi Lemoy & Charles Raux & Pablo Jensen, 2016. "Exploring the polycentric city with multi-worker households: an agent-based microeconomic model," Post-Print hal-00602087, HAL.

    More about this item

    Keywords

    Large Urban Economies; Comparative Statics; Continuous and Discrete Agent Models;

    JEL classification:

    • R13 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - General Equilibrium and Welfare Economic Analysis of Regional Economies
    • R14 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Land Use Patterns
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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