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Solution Of Spatial Trading Systems With Concave Cubic Programming

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

Abstract

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.

Suggested Citation

  • MacAulay, T. Gordon & Batterham, Robert L. & Fisher, Brian S., 1989. "Solution Of Spatial Trading Systems With Concave Cubic Programming," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 33(3), pages 1-17, December.
    • Handle: RePEc:ags:ajaeau:22998
    DOI: 10.22004/ag.econ.22998
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    References listed on IDEAS

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    1. 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, February.
    2. MacKinnon, James G., 1975. "An algorithm for the generalized transportation problem," Regional Science and Urban Economics, Elsevier, vol. 5(4), pages 445-464, December.
    3. B. S. Fisher, 1981. "The Impact of Changing Marketing Margins on Farm Prices," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 63(2), pages 261-263.
    4. 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(1), pages 1-9, April.
    5. Stella Dafermos & Anna Nagurney, 1984. "Sensitivity Analysis for the General Spatial Economic Equilibrium Problem," Operations Research, INFORMS, vol. 32(5), pages 1069-1086, October.
    6. Richard Asmuth & B. Curtis Eaves & Elmor L. Peterson, 1979. "Computing Economic Equilibria on Affine Networks with Lemke's Algorithm," Mathematics of Operations Research, INFORMS, vol. 4(3), pages 209-214, August.
    7. Rowse, John, 1981. "Solving the generalized transportation problem," Regional Science and Urban Economics, Elsevier, vol. 11(1), pages 57-68, February.
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    Cited by:

    1. Drynan, Ross G. & Perich, M. & Batterham, Robert L. & Whelan, S.P., 1994. "The Effects of Policy Changes on the Production and Sales of Milk in New South Wales," Review of Marketing and Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 62(02), pages 1-15, August.
    2. Batterham, Robert L. & MacAulay, T. Gordon, 1994. "Price-Linked Farm And Spatial Equilibrium Models," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 38(2), pages 1-28, August.

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