This study includes predictions of fertilizer production functions for four experiments. The experiments on Clarion and McPaul soils contain predictions of total and marginal yields, isoquants and marginal rates of substitution, isoclines and economic optima. Similar analyses for the other two experiments, conducted on Carrington soil during successive growing seasons, were not warranted because insufficient rainfall limited yield responses. The experiments included in this study were based on partially replicated factorial designs.

The experiment with corn on Clarion silt loam in 1954 included nitrogen, phosphorus and potash as variable nutrients. The production function, isoquants and isoclines are represented by equations a, b, c, d, e, f and g. In these equations (and equations listed below), N, P and K denote the pounds per acre of nitrogen, P₂O₅ and K₂0, respectively. Isoquant and isocline equations were derived for each pair of nutrients. Hence, there are three of each of these equations. The α in the isocline equations represents a constant price or substitution ratio.