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Fertilizer production functions from experimental data with associated supply and demand relationships Iowa Agriculture and Home Economics Experiment Station Research Bulletin: Volume 35, Issue 543

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Fertilizer production functions from experimental data with associated supply and demand relationships
( 2017-06-21) Heady, Earl ; Pesek, John ; Rao, V. ; Extension and Experiment Station Publications

This study includes (1) estimation of physical production functions from fertilizer experiments designed for this purpose, (2) prediction of corresponding marginal products, isoquants and isoclines, (3) estimation of economic optima under various price situations, (4) prediction of confidence regions for isoquants, isoclines and economic optima, (5) derivation of static corn supply and fertilizer demand functions and (6) estimation of gross marginal rates of substitution of fertilizer for land.

The analysis of this study is based on two sets of experiments conducted in 1959 and 1960 on corn. The experiments, conducted on Clarion, Nicollet and Webster soil series, included nitrogen (N), phosphorus (P) and potassium (K) as variable nutrients. A central composite design was used for each experiment. A quadratic function with crossproduct terms of the three nutrients was fitted to the combined data of both years. However, K was fixed at zero level for the purpose of this study. The derived production function is given by equation a, where Y denotes predicted corn yield in bushels per acre and N, P and K denote the pounds per acre of nitrogen, phosphorus and potassium, respectively.

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