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Iteration and Sensitivity for a Spatial Equilibrium Problem with Linear Supply and Demand Functions

Author

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  • Caulton L. Irwin

    (West Virginia University, Morgantown, West Virginia)

  • Chin W. Yang

    (West Virginia University, Morgantown, West Virginia)

Abstract

We investigate a set of spatial equilibrium conditions which apply, for example, to a multiregional, multicommodity market or to a physical system of interconnected sources and sinks. Under additional hypotheses, the equilibrium conditions are the Kuhn-Tucker conditions for a concave, quadratic programming problem. For the case in which the equilibrium conditions do not correspond to a programming problem, an iterative process for obtaining a solution is discussed. This iteration is motivated by the Project Independence Evaluation System (PIES) energy model algorithm. An algorithmic method to determine the sensitivity of an equilibrium solution vector to data perturbations is described. Both the sensitivity analysis and the convergence of the iterative solution method are based upon a solvability lemma, which guarantees that a solution of the equilibrium conditions may be expressed in terms of the problem data. Nondegeneracy assumptions for the inter-regional flows are unnecessary for this discussion. An example of the equilibrium problem which arose in modeling the supply and demand of eastern coal is briefly described.

Suggested Citation

  • Caulton L. Irwin & Chin W. Yang, 1982. "Iteration and Sensitivity for a Spatial Equilibrium Problem with Linear Supply and Demand Functions," Operations Research, INFORMS, vol. 30(2), pages 319-335, April.
    • Handle: RePEc:inm:oropre:v:30:y:1982:i:2:p:319-335
    DOI: 10.1287/opre.30.2.319
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    Citations

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    Cited by:

    1. C. W. Yang & Ken Hung, 2010. "Stability Of Rents And Returns As A Source Of Internal Financing: Evidence From Appalachian Coal Producers," Accounting & Taxation, The Institute for Business and Finance Research, vol. 2(1), pages 33-46.
    2. Chin- Wei Yang & Dwight B. Means JR & George E. Moody, 1993. "Tax Rates and Total Tax Revenues From Local Property Taxes," Public Finance Review, , vol. 21(4), pages 355-377, October.
    3. Chin W. Yang, 1990. "An Evaluation of the Maxwell-Boltzmann Entropy Model of the Appalachian Steam Coal Market," The Review of Regional Studies, Southern Regional Science Association, vol. 20(1), pages 21-29, Winter.
    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. Chin W. Yang, 1989. "A Note on the Musgravian Transformation," Eastern Economic Journal, Eastern Economic Association, vol. 15(3), pages 229-234, Jul-Sep.

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