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This paper estimates nitrogen fertilizer demand elasticities for Danish crop farms using the dual profit function approach on micro panel data. The model includes several farm- specific parameters, allowing us to estimate the mean demand elasticity and test for homogeneity of elasticities across panel farms. The mean own-price elasticity for nitrogen is -0.45, and there is a significant standard deviation from this mean for individual farms of 0.24. Heterogeneity of demand elasticities implies that regulating fertilizer application through mandated uniform percentage reductions, as is currently used in Danish nitrogen regulation, increases abatement costs relative to tax regulation. Somewhat surprisingly, this causes the abatement costs of quota regulation to be only 8% larger than with tax regulation. Simulation results indicate that the primary threat to the efficiency of uniform reduction schemes comes from inaccurate estimation of baselines rather than from heterogeneity of elasticities. [ABSTRACT FROM AUTHOR]