SOLUTION OF SPATIAL TRADING SYSTEMS WITH CONCAVE CUBIC PROGRAMMING

Standard spatial equilibrium activity analysis models, as developed by Takayama and Judge (1971), are based on linear supply and demand functions and fixed input-output coefficients. Such models are suitable for multiple market level trading systems where the fixed input-output coefficients are appropriate. A primal-dual price form of these models is developed in which the assumption of constant per unit costs of transformation is relaxed. In the case when the average cost curves of transformation are quadratic in nature the problem becomes one that will be termed cubic programming (that is, a cubic objective function and linear and/or quadratic constraints) which is solved in a concave region of the solution space. In the paper, the formulation of a simplified spatial equilibrium model with quadratic average costs of transformation is presented and solved. A discussion of possible applications of such a model is also presented.