Backing Economic Optimal N and P Fertilizer Rates Out of Yield Goal Based Fertilizer Recommendations.

Fertilizer recommendations are often based on yield goals, but they seldom explicitly account for crop and fertilizer prices.  The relationship between expected yield and fertilizer rate (i.e., production function or yield response curve) is required for identifying economic optimal fertilizer rates.  Further complicating economic optimal fertilizer rates are that most fertilizer recommendations for one nutrient (e.g., N) do not explicitly depend on other nutrients (e.g., P).  In a limiting factor framework, the economic optimal rate for one nutrient will not only depend on crop price and that particular nutrient, but it will also depend on the rates and prices of other nutrients as well as other yield-enhancing inputs such as irrigation water.  This research developed a method for identifying optimal economic input rates for multiple inputs in the absence of a multi-factor production function.  The mathematical framework developed for nitrogen is consistent with yield response being linear for any particular site-year, but where expected response becomes curvilinear in the face of random weather across space and time.  Additionally, the approach is fundamentally tied to the K-State nitrogen fertilizer recommendations such that the price-based-adjusted N rates are consistent with University recommendations, which do not explicitly account for prices.  Given single-factor yield response functions for various inputs (here N, P, and irrigation water) and assuming a limiting factor framework, economic optimal rates for each of the inputs can be simultaneously determined where they are a function of both the crop price and the price of each of the inputs.