We develop a modeling framework, based on discrete‐time dynamic optimization, to study the effect of legacy nutrient stores and soil nutrient dynamics on optimal nutrient management and agri‐environmental policy in crop production. Three alternative measures are studied to reduce nutrient loss: reduced fertilization, nonlegume catch crop cultivation and gypsum amendment. According to our results, landowner can bring down excessively high phosphorus stocks causing environmental damage within decades, by simultaneous optimization of the nitrogen and phosphorus fertilizers on the economic basis of profit maximization. Our results suggest that nitrogen loss abatement with catch crops is socially optimal, whereas the use of gypsum is well justified as a temporary measure on soils with high soil phosphorus levels. A dynamic tax‐subsidy‐scheme, which takes into account the current soil nutrient levels and field attributes such as soil texture, can enforce the socially optimal outcome. The welfare losses of the static steady‐state‐based tax‐subsidy‐schemes are increasing functions of the legacy nutrient stores and soil's ability to hold nutrients.

中文翻译：

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通过氮和磷的施肥，农作物的收获和石膏的处理来管理遗留的养分

我们基于离散时间动态优化开发了一个建模框架，以研究传统养分存储和土壤养分动态对作物生产中最佳养分管理和农业环境政策的影响。研究了三种减少养分流失的替代措施：减少施肥，种植非豆类作物和种植石膏。根据我们的结果，通过在利润最大化的经济基础上同时优化氮磷肥，土地所有者可以减少数十年来对环境造成损害的过多磷储备。我们的结果表明，采用农作物减产氮在社会上是最佳的，而在高磷水平的土壤上使用石膏作为临时措施是合理的。动态的税收补贴方案，考虑到当前土壤养分水平和田间属性（例如土壤质地），可以强制实现社会最优结果。静态的，基于稳态的税收补贴方案的福利损失正在增加传统养分库的功能以及土壤养分的能力。