Abstract
Spatial equilibrium analysis in agricultural economics has received considerable attention in the past several years (Takayama and Judge 1971; Judge and Takayama; Weinschenck, Henrichsmeyer, Aldinger; and McCarl and Spreen). When linear supply and demand functions are assumed, the spatial equilibrium problem can be formulated as a quadratic programming problem. However, in application, relatively small quadratic programming (QP) problems generally have been solved. Sometimes approximations (Duloy and Norton) or alternative solution procedures (Tramel and Seale, King and Ho) are used for larger problems because suitable large-scale quadratic programming algorithms are not available.' Reactive programming has been used (Tramel and Seale). However, there is controversy about whether or not this solution procedure achieves finite termination (see Takayama and Judge 1963, King and Ho). The purpose of this paper is to discuss a solution procedure, similar to the reactive programming, which possesses analytically established convergence properties. This procedure is based on Benders' decomposition (Benders, Geoffrion, and McCarl). The procedure presented here, originally developed by Polito, was discussed mathematically by Polito, McCarl, and Morin and used by Litzenberg.
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