An Analysis of Optimal Agricultural Fertilizer Application Decisions in the Presence of Market and Weather Uncertainties and Nutrient Pollution
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Date
2023-01-12
Authors
Yang, Xinyuan
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Publisher
University of Waterloo
Abstract
This thesis addresses the questions of how uncertain corn market and weather factors affect optimal fertilizer application decisions of the farmer and the social planner, and what factors drive the divergence between the two. Nutrient runoff from agricultural activities has become a primary source of surface water quality deterioration worldwide. Over-application of fertilizer in agricultural production represents a non-point source pollution which is causing extensive nutrient loading in water bodies and has a severe impact on the global environment. There is evidence that farmers apply more fertilizer than is socially optimal and more than is recommended by government agencies. This thesis first investigates the farmer’s optimal fertilizer application under crop price uncertainty by constructing an inter-temporal farmer’s decision model under two alternative stochastic price processes. Closed form results are derived, which indicate that an increase in price uncertainty implies a reduction in the quantity of fertilizer applied in the farmer’s optimal decision problem. Numerous factors that could impact the optimal fertilization decision are examined as well. The farmer’s decision model is then enhanced by allowing for two possible fertilizer application times in the growing season and the inclusion of additional stochastic state variables such as rainfall and temperature, in the corn yield model. The model is parameterized for average conditions in Iowa corn growing regions. Employing a Monte Carlo approach, numerical results conclude that for a wide range of parameter assumptions the farmer’s optimal strategy is to apply fertilizer at planting rather than later as a side dressing. This thesis analyzes the impacts of price uncertainty, fertilizer cost and other economic parameters on the farmer’s optimal fertilizer application strategy. The thesis also analyzes the optimal decisions of a social planner whose objective function includes an estimate of the damages caused by nitrogen leakage and denitrification. Numerical results show that including the damages from pollution affect both the quantity and timing of fertilizer application. Assumptions about the frequency and quantity of rainfall have an important impact on the optimal decision. This is an important consideration for public policy as climate change affects weather patterns over the next decade and beyond.
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Keywords
uncertainty, nutrient pollution, social cost, weather, optimal fertilizer application, corn price