Economic Optimization Using Input Response Data.

We needed a way to incorporate the results from a large number of N response trials within a state or region into N rate guidelines for corn, and to make these guidelines sensitive to price changes for corn and N. To do this, data from each trial were fitted to an appropriate function, chosen from among quadratic, linear, no response, and, most commonly, quadratic + plateau functions. The coefficients of each fitted function were used to calculate yield and net return to N (yield increase above the yield at N=0 × corn price − cost of N) at discrete N rates up to 240 lb N per acre. Net return to N (RTN) values at each N rate were averaged across trials to produce an RTN response as a function of N rate. A quadratic function was fit to the points surrounding the apex of this RTN function, and the maximum point was designated as the N rate that provides the maximum return to N (MRTN). In addition, the function fitted to the apex of the RTN curve was used to calculate endpoints of the range over which the RTN is within a set amount (default is $1.00 per acre) of the RTN at the MRTN N rate. At typical price levels, this range is about 35 to 40 lb of N, with the MRTN in the center of the range. This range allows the user to adjust N rate decisions based on experience and approach to risk. User choices include previous crop (corn or soybean), inclusion of non-responsive trials, and prices of corn and N. Additional information is available on the website that runs this calculator: http://extension.agron.iastate.edu/soilfertility/nrate.aspx.