A dual profit model is used to characterize the Entre Douro e Minho (EDM) region agriculture. The data comes from budgets for twelve representative farms. Positive Mathematical Programming (PMP) is applied. First, shadow prices of fixed inputs are obtained for each farm from a linear program (LP) forcing base year (1994) net output and fixed input allocations. Second, the Maximum Entropy (ME) technique is used to recover the restricted profit functions. The model purely reproduces observed net output and fixed input data. A short run profit function is derived for the region from aggregation of the model. The corresponding long run profit function is also derived. The profit model reveals an inelastic response to prices in the short run, and a more elastic response in the long run. Nitrogen and water appear as complements. The inelasticity of nitrogen response to its own price precludes taxing nitrogen to control its use. In contrast, pricing water is an effective strategy, not only to control water use but also nitrogen use. The Water Framework Directive (WFD) recommends both strategies.water, agricultural economics, elasticities, positive mathematical programming, maximum entropy

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