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This article in AJ

  1. Vol. 73 No. 4, p. 733-737
    Received: Oct 24, 1980

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A Dynamic Model for Technical and Economic Analysis of Fertilizer Recommendations1

  1. Edgar A. Lanzer,
  2. Quirino Paris and
  3. William A. Williams2



The rationale of this study was to jointly estimate response functions for N, P, and K for wheat and soybean cropping in southern Brazil and carryover functions for residual fertility. The two sets of functions were then combined in a dynamic model having general applicability for optimizing fertilizer recommendations. The model is composed of (a) a yield-nutrient response function incorporating Liebig's Law of the Minimum and Mitscherlich's relative yield theory, (b) fertility carryover functions for P and K, and (c) a multiperiod economic programming model which combines crop yield response and carryover functions with crop and fertilizer prices. Important implications are that (a) the Law of the Minimum assume no nutrient substitution, (b) the relative yield theory allows pooling response data from different experiments, and (c) the fertilization problem is treated as a dynamic process that utilizes revised measures of soil fertility as they become available through soil tests. The crop response was specified as a piecewise linear and plateau function while the fertility carryover was postulated as a fist order difference equation, incorporating an exponentially declining process of soil fertility. The solution of the overall dynamic model took the form of a multiperiod linear programming problem.

The N, P, and K response functions for wheat (Triticum aestivum L.) and soybean (Glycine max L.) yields were generated from 38 fertilizer field experiments conducted at Rio Grande do sul and Santa Catarina states in southern Brazil between 1968 and 1976. The seven experiments that were repeated for 4 years provided the information for estimating the carryover effects of P and K fertilization.

The results indicate that the optimal target levels of soil fertility are in accordance with those recommended locally. The maintenance applications recommended, however, are substantially different than the optimal quantities determined by the dynamic model presented here. The model calls for a reduction of the current maintenance application for both N and P of 10 kg/ha and an increase for K of 12 kg/ha. This would result in a U.S. dollars saving of $27/ha 1 year.

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