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Better understanding the trade-offs/synergies between desirable and environmentally harmful (undesirable) farm outputs is relevant for future targeting and tailoring of agri-environmental policy measures. We use a hyperbolic distance function to represent the production technology employed by Swiss dairy farms in mountainous regions, thus allowing for simultaneous expansion of desirable outputs (milk and non-milk) and contraction of undesirable output (nitrogen surplus). We calculate the farm-specific shadow price of the undesirable output. The obtained shadow prices (mean value with respect to milk output was equal to 28 Swiss francs per kg of nitrogen) provide quantitative information on farmers’ costs of reducing nitrogen pollution.