Abstract
When supply and demand curves for a single commodity are approximately linear in each ofN regions and interregional transportation costs are linear, then equilibrium trade flows can be computed by solving a quadratic program of special structure. An equilibrium trade flow exists in which the routes carrying positive flow form a forest, and this solution can be efficiently computed by a tree growing algorithm.
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References
C.R. Glassey, “Explicit duality for convex homogeneous programs”,Mathematical Programming 10 (1976) 176–191.
P. Samuelson, “Spatial price equilibrium and linear programming”,American Economic Review 42 (1952) 283–303.
T. Takayama and G.G. Judge,Spatial and temporal price and allocation models (North-Holland, Amsterdam, 1971).
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Glassey, C.R. A quadratic network optimization model for equilibrium single commodity trade flows. Mathematical Programming 14, 98–107 (1978). https://doi.org/10.1007/BF01588953
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DOI: https://doi.org/10.1007/BF01588953