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Solution Of Spatial Trading Systems With Concave Cubic Programming

  • MacAulay, T. Gordon
  • Batterham, Robert L.
  • Fisher, Brian S.
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    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.

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    Article provided by Australian Agricultural and Resource Economics Society in its journal Australian Journal of Agricultural Economics.

    Volume (Year): 33 (1989)
    Issue (Month): 03 (December)

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    Handle: RePEc:ags:ajaeau:22998
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    1. Rowse, John, 1981. "Solving the generalized transportation problem," Regional Science and Urban Economics, Elsevier, vol. 11(1), pages 57-68, February.
    2. Larry J. Martin, 1981. "Quadratic Single And Multi-Commodity Models Of Spatial Equilibrium: A Simplified Exposition," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 29(1), pages 21-48, 02.
    3. Piggott, Roley R. & Small, Annette M. & Dumsday, Robert G. & Wright, Vic, 1987. "Short-Run Costs And Throughput Variability For A Nsw Abattoir," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 31(01), April.
    4. MacKinnon, James G., 1975. "An algorithm for the generalized transportation problem," Regional Science and Urban Economics, Elsevier, vol. 5(4), pages 445-464, December.
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