Abstract
Empirical applications of the quadratic programming form of spatial equilibrium commodity model have proliferated recently. However, the quality and performance of this modeling methodology have received little attention either in the form of stability analysis or validation analysis. In particular, a legitimate sensitivity analysis of the stability properties of the optimal solutions of such mathematical models is lacking. This paper attempts to meet this, need by conducting a two-step sensitivity analysis. First, a mathematical derivation of the stability conditions is performed based on the Kuhn-Tucker theorem. Second, these conditions are then embodied in a three-way factorial analysis. Such an approach is considered valuable for conducting future sensitivity analyses of commodity models of this type, especially where the Monte Carlo technique is not applicable.
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References
Cutler, L., andD.S. Pass: A Computer Program for Quadratic Mathematical Models to be Used for Aircraft Design and Other Applications Involving Linear Constraints. Santa Monica 1971.
Enke, S.: Equilibrium Among Spatially Separated Markets: Solution to Electric Analog. Econometrica, 1951, 40–47.
Graybill, F.A.: Theory and Application of the Linear Model. North Scituate 1976, 481–575.
Irwin, C., andC. W. Yang: Iteration and Sensitivity for a Spatial Equilibrium Problem with Linear Supply and Demand Functions. Operations Research,30, 1982, 319–335.
Labys, W.C.: Commodity Markets and Models: The Range of Experience. Stabilizing World Commodity Markets. Ed. by F.G. Adams and S. Klein. Lexington 1978.
Labys, W.C. (ed.): Quantitative Models of Commodity Markets. Cambridge 1975.
Labys, W., andC.W. Yang: A Quadratic Programming Model of the Appalachian Steam Coal Market. Energy Economics2, 1980, 86–95.
Mutchler, P.H., et al. (ed.): Competitive Transportation Costs of Supplying Low-Sulfur Fuels to Mid-western and Eastern Domestic Energy Market. Washington, D.C., 1972.
National Coal Association: Steam-Electric Plant Factors. Washington, D.C., 1974.
Samuelson, P.A.: Spatial Price Equilibrium and Linear Programming. American Economic Review, 1952, 283–303.
Silberberg, E.: A Theory of Spatially Separated Markets. International Economic Review, 1970, 343–348.
Takayama, T., andG. Judge: Spatial and Temporal Price and Allocation Model. Amsterdam 1971, 129–152.
U.S. Bureau of Mines: Mineral Year Book. Washington, D.C., 1974.
Wallis, A.W., andH.V. Robert: Statistics: A New Approach. Glencoe 1956, 475–483.
Yang, C.W.: The Stability of Interregional Trade Flows in Allocation Models: The Case of Quadratic Programs. Proceedings of the Conference on Computer Modeling. Ed. by W.G. Vogt and M.H. Mickle. Pittsburgh 1979a, 1527–1531.
—: A Critical Analysis of Spatial Commodity Modeling: The Case of Coal. Unpublished Ph.D. Dissertation, West Virginia University, Morgantown 1979b.
Yang, C.W., andW.C. Labys: Stability of Appalachian Coal Shipments Under Policy Variation. The Energy Journal, 1981, 111–128.
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Yang, C.W., Labys, W.C. A sensitivity analysis of the stability properties of the QP commodity model. Empirical Economics 7, 93–107 (1982). https://doi.org/10.1007/BF02506827
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DOI: https://doi.org/10.1007/BF02506827