A New Analytical Framework for the Fertilization Problem

Abstract

A novel control model for technical and economic analysis of fertilizer recommendations is based on Liebig's Law of the Minimum, Mitscherlich's relative yield theory, and the notions of yield plateau and soil fertility carry-over. The empirical model consists of a multistage separable programming specification which maximizes the discounted stream of net revenues subject to crop response and fertility carry-over functions. The model is applied to the wheat-soybean cropping system in Southern Brazil. It is found that, while the optimal fertility target levels are within a small range of those determined by Brazilian agronomists, their maintenance recommendations could be substantially improved.

Spatial Dynamics of Water and Nitrogen Management in Irrigated Agriculture

“…The estimated regressions provide excellent fit with R 2 values ranging from 0.78 to 0.95, and all estimated parameter values are significant at the 95% level or higher. Graphical analysis of the regressions indicate functional fits lying within bands defined by data in alternate years, and all exhibit global properties consistent with the generalized conceptual model in Lanzer and Paris (1981).…”

“…Corn yield y t , nitrogen emissions n et , and nitrogen carryovers n t+1 as functions of applied water w t and applied nitrogen n at for initial soil nitrogen n t = 160 kg/ha in year t Additional concerns arise at the field-level with spatial variability. As outlined in Lanzer and Paris (1981; figure 1), a general conceptual model of yield production functions exhibits convex-concave behavior initially, followed by a yield plateau and then possibly a yield decline. In the uniform case, only the concave portion is economically relevant, hence functional forms constituting local approximations (e.g., Taylor series approximations via polynomials) may be reasonable as the optimization model can appropriately bound the inputs.…”

A Comparison of Risk Efficiency Criteria in Evaluating Groundnut Performance in Drought‐prone Areas

“…In general, these functions were too inflexible to model the lower tails of the distribution and did not predict well outside the range of the data, or, in the case of the Mitscherlich and other growth functions, the non-linear estimation process did not converge. In addition, both linear and quadratic response and plateau functions were estimated (Lanzer and Paris 1981); inflexion points for the first three growth phases were at RA W> 1. No inflexion point could be established for the fourth growth phase.…”

Decomposition of the Factors Determining Changes in China’s Maize Yields

“…The current study used a crop response model to estimate the relationships between maize yield and its determinants, which are often based on data from field experiments (Ackello-Ogutu et al 1985, Frank et al 1990, Lanzer & Paris 1981. Unlike in field experiments, however, we must assume the availability of nutrients for each crop, as provided from chemical fertilizer.…”

“…The empirical literature has discussed in depth the best functional form to use for a crop response model (e.g., quadratic, Von Liebig, Mitscherlich-Baule) toward reaching the goal of accurately pinpointing the optimal input levels for nutrients and/or water (Ackello-Ogutu et al 1985, Frank et al 1990, Lanzer & Paris 1981. However, the number of explanatory variables included in such forms is quite limited and thus insufficient for the purposes of this study.…”