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Cost function and positive mathematical programming

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  • Paris, Quirino

Abstract

A line of research in Positive Mathematical Programming (PMP) has pursued the goal of estimating a cost function capable of reproducing the base-year results in a sample of farms. Originally, the PMP approach estimated a “myopic” cost function, that is, a cost relation depending only on the output levels observed during a production cycle. No input price entered this type of cost function. In this paper we define and estimate a proper cost function that calibrates the economic results of a sample of farms. In the process, we demonstrate the existence of a unique solution of the PMP problem when observed output quantities and limiting input prices are taken as calibrating benchmarks. Furthermore, the paper shows how to obtain endogenous output supply elasticities that calibrate with available exogenous information in the form of previously estimated elasticities for an entire region or sector. This framework is applied to a sample of Italian farms that admit no production for some of the crop activities. This PMP model can be used to explore farmers’ response to various policy decisions involving output prices, environmental constraints, limiting input supply, and other government interventions.

Suggested Citation

  • Paris, Quirino, 2017. "Cost function and positive mathematical programming," Bio-based and Applied Economics Journal, Italian Association of Agricultural and Applied Economics (AIEAA), vol. 6(1), May.
    • Handle: RePEc:ags:aieabj:276284
    DOI: 10.22004/ag.econ.276284
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    References listed on IDEAS

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    1. Richard E. Howitt, 1995. "Positive Mathematical Programming," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 77(2), pages 329-342.
    2. Qureshi, M. Ejaz & Ahmad, Mobin-ud-Din & Whitten, Stuart M. & Kirby, Mac, 2014. "A multi-period positive mathematical programming approach for assessing economic impact of drought in the Murray–Darling Basin, Australia," Economic Modelling, Elsevier, vol. 39(C), pages 293-304.
    3. Henseler, Martin & Wirsig, Alexander & Herrmann, Sylvia & Krimly, Tatjana & Dabbert, Stephan, 2009. "Modeling the impact of global change on regional agricultural land use through an activity-based non-linear programming approach," Agricultural Systems, Elsevier, vol. 100(1-3), pages 31-42, April.
    4. Cortignani, Raffaele & Severini, Simone, 2009. "Modeling farm-level adoption of deficit irrigation using Positive Mathematical Programming," Agricultural Water Management, Elsevier, vol. 96(12), pages 1785-1791, December.
    5. Richard E. Howitt, 1995. "A Calibration Method For Agricultural Economic Production Models," Journal of Agricultural Economics, Wiley Blackwell, vol. 46(2), pages 147-159, May.
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