Adjustment to optimal-economic fertilization doses when prices change: economic-mathematical analysis
DOI:
https://doi.org/10.29312/remexca.v16i4.3425Keywords:
analysis behind the envelope, fertilization dose, input-output price ratioAbstract
The current situation shows worrying trends that will hinder both food production and the production and use of fertilizers. By 2050, the world population will be 9 200 million; its demand for food will grow by 54% and for fertilizers by 45% compared to those of 2015. Fertilizer prices have grown considerably faster than agricultural product prices, especially since the first quarter of 2021. Price changes and the need to reduce greenhouse gas emissions modify the optimal-economic doses of fertilization, which is why it is necessary to adjust them. This research aimed to define the economic-mathematical bases for updating the optimal-economic doses of fertilization when the prices of fertilizers and agricultural products change. The method was mathematical-deductive. In addition, the theory of non-linear mathematical programming, the economic theory of profit optimization, the mathematical theorems of the envelope, and the Shephard-McKenzie lemma were applied. The ten propositions obtained constitute the results of this research, and they were obtained through a logical-mathematical process of a deductive nature. It was concluded that the response surfaces should be estimated for each crop and for each of the agricultural regions of Mexico, and it is necessary to create a computerized system that analyzes and updates the optimal-economic doses of fertilization as changes in the prices of outputs and fertilizers are observed.
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