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Discrete Spatial Price Equilibrium

  • Sven Erlander
  • Jan T. Lundgren
Part of the Advances in Spatial Science book series (ADVSPATIAL)

Abstract

In this paper we consider how the flow of a single commodity is distributed between regional markets in a transportation network. We assume that there is an unlimited number of price-taking ’shippers’ who can enter the market and ship a single unit of commodity between some supply and demand points whenever there is a profit to be made. A common assumption made for this problem is that the shippers in the system behave rationally. In this case, a shipment of the commodity will usually take place only if the procurement costs at the supply market plus the transportation costs are less than, or equal, to the price obtained for the commodity at the demand market. If perfect competition prevails, no shipments will be made if procurement costs plus transportation costs are greater then the price obtained at the demand market. These are the equilibrium conditions defining a spatial price equilibrium model. The classical way to derive the conditions, according to Samuelson (1952) and Takayama and Judge (1971), is to formulate a mathematical program, and to obtain the equilibrium conditions as the optimal conditions of the mathematical program.

Keywords

Transportation Network Demand Point Active Shipper Trade Pattern Shipment Plan 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Beckmann, M.J. and McGuire, C.B. and Winsten, C.B. (1956), Studies in the Economics of Transportation, Yale University Press, New Haven, CT.Google Scholar
  2. Bernstein, D. and Smith, T.E. (1994), ‘Programmability of discrete network equilibria’, SOR-94-19, Princeton University, NJ.Google Scholar
  3. Dial R.B. (1971), ‘A probabilistic multipath traffic assignment model which obviates path enumeration’, Transportation Research, vol. 5, pp. 83–111.CrossRefGoogle Scholar
  4. Erlander, S. (1985), ‘On the principle of monotone likelihood and loglinear models’, Mathematical Programming, vol. 21, pp. 137–151.CrossRefGoogle Scholar
  5. Erlander, S. (1990), ‘Efficient population behavior and the simultaneous choices of origins, destinations and routes’, Transportation Research, vol. 24B, pp. 363–373.Google Scholar
  6. Erlander, S. and Lundgren, J.T. (1992), ‘Spatial price equilibrium and efficiency’, Department of Mathematics, LiTH-MAT-R-1992-39, Linköping University, Linköping.Google Scholar
  7. Erlander, S. and Smith, T.E. (1990), ‘General representation theorems for efficient population behavior’, Applied Mathematics and Computation, vol. 36, pp. 173–217.CrossRefGoogle Scholar
  8. Erlander, S. and Stewart, N.F. (1990), The Gravity Model in Transportation Analysis — Theory and Extensions, VSP, Utrecht, The Netherlands.Google Scholar
  9. Fisk, C. (1980), ‘Some developments in equilibrium traffic assignment’, Transportation Research, vol. 14B, pp. 243–255.Google Scholar
  10. Florian, M. and Los, M. (1982), ‘A new look at spatial price equilibrium models’, Regional Science and Urban Economics, vol. 12, pp. 579–597.CrossRefGoogle Scholar
  11. Harker, P.T. (1988), ‘Dispersed spatial price equilibrium’, Environment and Planning A, vol. 20, pp. 353–368.CrossRefGoogle Scholar
  12. Rosenthal, R.W. (1973), ‘The network equilibrium problem in integers’, Networks, vol. 3, pp. 53–59.CrossRefGoogle Scholar
  13. Roy, J.R. (1990), ‘A dispersed equilibrium commodity trade model’, The Annals of Regional Science, vol. 24, pp. 13–28.CrossRefGoogle Scholar
  14. Samuelson, P.A. (1952), ‘Spatial price equilibrium and linear programming’, The American Economic Review, vol. 42, pp. 283–303.Google Scholar
  15. Sheffi, Y. (1985), Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods, Prentice-Hall, Englewood Cliffs.Google Scholar
  16. Smith, T.E. (1978), ‘A cost-efficiency principle of spatial interaction behavior’, Regional Science and Urban Economics, vol. 8, pp. 313–337.CrossRefGoogle Scholar
  17. Smith, T.E. (1983), ‘A cost-efficiency approach to the analysis of congested spatial-interaction behavior’, Environment and Planning A, vol. 15, pp. 435–464.CrossRefGoogle Scholar
  18. Smith, T.E. (1988), ‘A cost-efficiency theory of dispersed network equilibria’, Environment and Planning A, vol. 20, pp. 231–266.CrossRefGoogle Scholar
  19. Smith, T.E. (1993), Private communication.Google Scholar
  20. Takayama, T. and Judge, G.G. (1971), Spatial and Temporal Price Allocation Models, North-Holland, Amsterdam.Google Scholar
  21. Wilson, A.G. (1970), Entropy in Urban and Regional Modelling, Pion, London.Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1998

Authors and Affiliations

  • Sven Erlander
    • 1
  • Jan T. Lundgren
    • 1
  1. 1.Department of MathematicsLinköping UniversityLinköpingSweden

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