The Value of Soil Testing for Potassium Fertilizer in Tennessee Cotton Production

This thesis presents two separate studies focusing on the value of soil test information for potassium (K) fertilization of upland cotton. The objective of the first study was to determine the value of soil test information for available K in upland cotton production using the linear response plateau (LRP) and linear response stochastic plateau (LRSP) functions. This study uses dynamic programming to solve for optimal K fertilizer rates that maximize NPV when K carryover was and was not considered by a producer. This study extends the existing literature by comparing the value of soil testing information using a stochastic and deterministic yield response plateau functional form. Including carryover decreased the optimal K application rate and the K carryover level, while yield was optimal regardless of whether the producer considered carryover. The LRSP model Using K carryover information for K application decisions increased net present value and helped maintain steady levels of soil K. The LRSP function fit the data better than the LRP, and the value of soil testing was $11 per acre lower over ten years using the LRSP.

The objective of the second study was to determine the K fertilizer application rate and temporal frequency for obtaining K soil test information that maximizes NPV to K fertilizer in cotton production in the southeastern US. This study used a dynamic programming model to determine the optimal K application rates over time. Monte Carlo simulation was used to determine NPV for cotton production using five soil test schedules ranging from soil testing annually to every fifth year. On average, optimal K application rates for all temporal frequencies varied slightly. The range of optimal K application rates increased as the producer waited longer periods of time to update their soil test information. As the temporal frequency increased, the lower bounds of their carryover levels and yields decreased due to yield limiting levels of K. NPV of returns to K was maximized at $7,580 per acre when producers updated soil testing information every two years, which was $2 per acre per year greater than annual soil testing.