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Sensitivity Analysis for the General Spatial Economic Equilibrium Problem

Author

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  • Stella Dafermos

    (Brown University, Providence, Rhode Island)

  • Anna Nagurney

    (Brown University, Providence, Rhode Island)

Abstract

We consider the general spatial economic equilibrium problem where the supplies and demands at each market for each commodity may depend on the price on this as well as other prices of other commodities at other markets and the transportation cost on each link for each commodity may depend on the flow on this as well as other flows of other commodities on other links in the network. For this model we perform stability and sensitivity analysis. Assuming that the supply, demand, and transportation cost functions are monotone, we first show that the multicommodity equilibrium price pattern depends continuously upon the market supply and demand functions and the multicommodity equilibrium shipment pattern depends continuously upon the transportation cost functions. We then focus on the delicate question of predicting the direction of the change in the price and shipment pattern and the incurred supplies, demands, and transportation costs resulting from changes in the supply, demand, and transportation cost functions and we demonstrate that certain phenomena may prevail. Our analysis depends crucially on the fact that the governing equilibrium conditions can be formulated as a variational inequality.

Suggested Citation

  • Stella Dafermos & Anna Nagurney, 1984. "Sensitivity Analysis for the General Spatial Economic Equilibrium Problem," Operations Research, INFORMS, vol. 32(5), pages 1069-1086, October.
    • Handle: RePEc:inm:oropre:v:32:y:1984:i:5:p:1069-1086
    DOI: 10.1287/opre.32.5.1069
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    Citations

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    Cited by:

    1. G. Anello & M. Donato & M. Milasi, 2010. "A quasi-variational approach to a competitive economic equilibrium problem without strong monotonicity assumption," Journal of Global Optimization, Springer, vol. 48(2), pages 279-287, October.
    2. Anna Nagurney & Dana Hassani & Oleg Nivievskyi & Pavlo Martyshev, 2023. "Exchange rates and multicommodity international trade: insights from spatial price equilibrium modeling with policy instruments via variational inequalities," Journal of Global Optimization, Springer, vol. 87(1), pages 1-30, September.
    3. Nagurney, Anna & Besik, Deniz & Dong, June, 2019. "Tariffs and quotas in world trade: A unified variational inequality framework," European Journal of Operational Research, Elsevier, vol. 275(1), pages 347-360.
    4. Yang, Chin W. & Hwang, Ming J. & Sohng, Soong N., 2002. "The Cournot competition in the spatial equilibrium model," Energy Economics, Elsevier, vol. 24(2), pages 139-154, March.
    5. MacAulay, T. Gordon & Batterham, Robert L. & Fisher, Brian S., 1989. "Solution Of Spatial Trading Systems With Concave Cubic Programming," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 33(3), pages 1-17, December.
    6. Li, Dong & Nagurney, Anna & Yu, Min, 2018. "Consumer learning of product quality with time delay: Insights from spatial price equilibrium models with differentiated products," Omega, Elsevier, vol. 81(C), pages 150-168.
    7. José Holguín-Veras & Ning Xu & Miguel Jaller & John Mitchell, 2016. "A Dynamic Spatial Price Equilibrium Model of Integrated Urban Production-Transportation Operations Considering Freight Delivery Tours," Transportation Science, INFORMS, vol. 50(2), pages 489-519, May.
    8. Zhao, Lan & Nagurney, Anna, 2008. "A network equilibrium framework for Internet advertising: Models, qualitative analysis, and algorithms," European Journal of Operational Research, Elsevier, vol. 187(2), pages 456-472, June.
    9. Konur, Dinçer & Geunes, Joseph, 2012. "Competitive multi-facility location games with non-identical firms and convex traffic congestion costs," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(1), pages 373-385.
    10. Nagurney, Anna & Zhang, Ding, 1996. "On the stability of an adjustment process for spatial price equilibrium modeled as a projected dynamical system," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 43-62.
    11. T L Friesz & T Miller & R L Tobin, 1988. "Algorithms for Spatially Competitive Network Facility-Location," Environment and Planning B, , vol. 15(2), pages 191-203, June.
    12. Hu, Xiaowei & Li, Peng, 2022. "Relief and stimulus in a cross-sector multi-product scarce resource supply chain network," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 168(C).
    13. Xiaowei Hu & Peng Li, 2021. "Relief and Stimulus in A Cross-sector Multi-product Scarce Resource Supply Chain Network," Papers 2101.09373, arXiv.org, revised Nov 2022.
    14. Anna Nagurney & Patrizia Daniele & Ladimer S. Nagurney, 2020. "Refugee migration networks and regulations: a multiclass, multipath variational inequality framework," Journal of Global Optimization, Springer, vol. 78(3), pages 627-649, November.
    15. P T Harker, 1988. "Dispersed Spatial Price Equilibrium," Environment and Planning A, , vol. 20(3), pages 353-368, March.
    16. Frederic H. Murphy & Murthy V. Mudrageda, 1998. "A Decomposition Approach for a Class of Economic Equilibrium Models," Operations Research, INFORMS, vol. 46(3), pages 368-377, June.
    17. Cho, Hsun-Jung & Smith, Tony E. & Friesz, Terry L., 2000. "A reduction method for local sensitivity analyses of network equilibrium arc flows," Transportation Research Part B: Methodological, Elsevier, vol. 34(1), pages 31-51, January.
    18. Paul Berglund & Changhyun Kwon, 2014. "Solving a Location Problem of a Stackelberg Firm Competing with Cournot-Nash Firms," Networks and Spatial Economics, Springer, vol. 14(1), pages 117-132, March.
    19. Walter C. Labys & Chin-wei Yang, 1991. "Advances in the Spatial Equilibrium Modeling of Mineral and Energy Issues," International Regional Science Review, , vol. 14(1), pages 61-94, April.
    20. Anna Nagurney & David Parkes & Patrizia Daniele, 2007. "The Internet, evolutionary variational inequalities, and the time-dependent Braess paradox," Computational Management Science, Springer, vol. 4(4), pages 355-375, October.

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