Cost function and positive mathematical programming

Quirino Paris


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.


positive mathematical programming; solution uniqueness; supply elasticities; calibrating model

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