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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 the consumer located at each fixed distance from the central business district. In contrast, with a continuum of agents, average land rent goes up for consumers at each fixed distance close to the central business district, is constant at some intermediate distance, and decreases for locations farther away. Therefore, there is a qualitative difference between the two types of models, and this difference is potentially testable.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 7312.

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Date of creation: 22 Feb 2008
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Handle: RePEc:pra:mprapa:7312

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

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  1. repec:cup:cbooks:9780521805247 is not listed on IDEAS
  2. Marcus Berliant & Courtney LaFountain, 2004. "Space in General Equilibrium," Urban/Regional, EconWPA 0408002, EconWPA, revised 27 Jun 2005.
  3. Robert E. Lucas & Esteban Rossi-Hansberg, 2002. "On the Internal Structure of Cities," Econometrica, Econometric Society, Econometric Society, vol. 70(4), pages 1445-1476, July.
  4. Raa, M.H. ten & Berliant, M., 1991. "On the continuum approach of spatial and some local public goods or product differentiation models," Open Access publications from Tilburg University urn:nbn:nl:ui:12-381947, Tilburg University.
  5. repec:cup:cbooks:9780521801386 is not listed on IDEAS
  6. Fujita,Masahisa, 1989. "Urban Economic Theory," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521346627.
  7. 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, Elsevier, vol. 55(1), pages 95-120, October.
  8. Berliant, M. & Fujita, M., 1990. "Alonso'S Discrete Population Model Of Land Use: Efficient Allocations And Competitive Equilibria," RCER Working Papers 217, University of Rochester - Center for Economic Research (RCER).
  9. Berliant, Marcus, 1985. "Equilibrium models with land : A criticism and an alternative," Regional Science and Urban Economics, Elsevier, Elsevier, vol. 15(2), pages 325-340, June.
  10. Papageorgiou, Yorgos Y. & Pines, David, 1990. "The logical foundations of urban economics are consistent," Journal of Economic Theory, Elsevier, Elsevier, vol. 50(1), pages 37-53, February.
  11. Kamecke,Ulrich, 1987. "Mean-City a consistent approximation of bid rent equilibria," Discussion Paper Serie A, University of Bonn, Germany 138, University of Bonn, Germany.
  12. 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, Elsevier, vol. 21(4), pages 639-645, December.
  13. 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, Elsevier, vol. 20(4), pages 473-508, February.
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