A new Procedure for Determining Economic and Non-economic Zones of Production Function for Nitrogen Fertilizer Input

Classical and neoclassical viewpoints in production and growth theory dominated the issue of capital and labor substitution in the normative progress of the production function, while ignoring other inputs, called intermediate factors. In the context of emerging global priorities related to planetary boundaries and the Sustainable Development Goals (SDGs), there is a need to upgrade marginal production analysis to explicitly incorporate nitrogen use pathways. To address this gap, the study extends (i) a novel procedure based on the microeconomic relationship between marginal product ( ) and average product ( ). Specifically, MP of nitrogen fertilizer ( ) is formulated as a function of the proportional change in nitrogen application rate, the elasticity of nitrogen use with respect to cropland size, and the marginal effect of the cropland-to-nitrogen ratio on the average product of nitrogen fertilizer ( ); (ii) two distinct pathways of nitrogen- saving/farm-expansion and nitrogen-intensive/farm-expansion. The performance of the procedure is examined by using three waves of cross-sectional data from corn farms in Michigan, USA. The results showed that a higher level of the nitrogen-saving/farm-expansion strategy keeps farms within the economic zone (Stage II) of the production function, as indicated by a positive marginal effect. These results indicate yield losses of approximately 223 kg/ha, 43 kg/ha, and 34 kg/ha for corn farms applying nitrogen at average rates of 53 kg/ha, 142 kg/ha, and 165 kg/ha, respectively. The nitrogen-intensive/farm-expansion strategy causes, depending on the nitrogen rate, the farm position to vary between the economic zone (Stage II) and the zone of negative return (Stage III) of the production function if the marginal effect responds negatively. The outcomes of the new procedure underscore the importance of targeting nitrogen management policies to specific production stages, supporting sustainable intensification that maintains yields while mitigating environmental risks in Michigan’s corn systems.