Modifying Yield-Goal Based Fertilizer Recommendations to Varying Prices of Grains and Inputs.

University fertilizer recommendations often are based on yield goals and do not explicitly account for crop and fertilizer prices.  With high fertilizer N and low crop prices in 2005/06, producers asked if they should adjust rates.  In response, a mathematical approach was developed that derives a production function (yield response curve) from official K-State yield-goal-based nitrogen recommendations while incorporating long-run crop and N prices.  Analyzing historical N trial data from western and north-central Kansas involving wheat, corn, and grain sorghum, the quadratic plateau (QP) arose as the appropriate functional form.  The QP can be shown to have a yield response to N that is linear for any particular site-year, but where expected yield response becomes curvilinear in the face of random weather across time.  The mathematics of the QP, which is a function of yield goal and price-based optimal fertilizer rates, were incorporated into an Excel spreadsheet and made available on www.agmanager.info.  Shortly after the initial model development, in response to high irrigation pumping costs, our model was expanded to incorporate this second yield factor, irrigation.  Irrigation production functions were based on KSU yield response to irrigation research.  The two factors were assumed to drive yield in a QP limiting factor framework.  In 2008, due to volatile P prices, the model was again expanded, this time to include price-based modifications to KSU P recommendations.  Lacking sufficient trial data to statistically select functional form, a QP yield response was assumed.  As with N (fertilizer and soil test N) and water (irrigation and rainfall), the sub-factors for P (fertilizer and soil test P) had to be integrated.  To mathematically accomplish that we assumed fertilizer P can fully compensate for soil test P.  Since this assumption is sometimes questioned, users of our model to guide P rates should carefully consider this critical assumption.