Corn yield response to phosphorus fertilizer in Michigan: a metamodeling approach for phosphorus management policies

Phosphorus (P) pollution from nonpoint sources is a persistent agricultural externality. P fertilizer use in excess of crop removal leads to soil P accumulation and increases chance of P runoff from agricultural fields. For fertilizer-intensive crops such as corn, effective nutrient management can partly mitigate the externality associated with fertilizer use. In states such as Michigan with abundant freshwater resources that are vulnerable to P pollution and where corn is grown intensively, understanding yield response is instrumental for P management policies. We analyze corn yield response to P fertilizer and control for soil P. We use farmer survey data from 1650 corn farmers in Michigan and a crop-simulation model to obtain data in a metamodeling approach to estimate yield function. Using the estimated function in profit maximization set up, we calculate agronomically and economically optimal profit-maximizing P application rates for Michigan, across agricultural regions, and across different soil types. We find that corn yield responds to P only in low soil P (0–5 ppm or mg kg −1 ) fields and the economically optimal P rate for Michigan is [63, 68] kg ha −1 or [53, 61] lbs acre −1 for low soil P fields and would be zero for fields with adequate soil P. For existing soil P levels in Michigan, the self-reported P application of Michigan corn farmers exceeds the profit-maximizing P application rate. We compare our analysis results with self-reported survey data to demonstrate excess P applications. Since many fields in Michigan have high soil P, additional P application in excess of crop removal increases risks of eutrophication. We also find that 10 % increase in P prices faced by farmers would lead to 3.1 % reduction in the economically optimal P application rate. Based on these results, we discuss suitable policy options such as fertilizer “usage fee” and tailored fertilizer recommendations. • We use survey and crop-simulation data to estimate corn yield response to P. • Calibrated crop-simulation model is run under experimental design. • We calculate economically optimal P application rate and elasticity across prices. • Given Michigan soil P levels, self-reported average P application rate is high.