Date of Graduation


Document Type


Degree Name

Master of Science in Agricultural Economics (MS)

Degree Level



Agricultural Economics and Agribusiness


Michael P. Popp

Committee Member

Di Fang

Second Committee Member

John D. Anderson


Corn potassium fertilizer, Cotton potassium fertilizer, Current agronomic recommendations, Potash fertilizer recommendations, Profit-maximizing potassium, Rice/soybean rotation potassium fertilizer


This thesis is comprised of two studies that estimate profit-maximizing potassium (K) fertilizer application rates for various crops across different time periods. Estimation of profit-maximizing fertilizer-K rate (K*) for both studies considered the initial soil test level of K (STK) and yield response information, as traditional recommendations do, and added crop price and the cost of fertilizer. Profit maximum occurs where the marginal revenue from additional yield is equal to the marginal cost of applying an additional unit of fertilizer-K. The first study calculated K* for corn (Zea mays) and cotton (Gossypium hirsutum) and compared results to previous studies on rice (Oryza sativa L.) and soybean [Glycine max (L.) Merr.] without consideration of impact on STK over time. Corn results showed that current extension fertilizer-K rate recommendations could be profitably curtailed with cost savings from reduced fertilizer-K application greater than yield loss. Contrastingly, cotton results proved that K* was greater than the current recommendations with estimated yield increases that were more than sufficient to afford additional fertilizer-K costs even in years when crop price was relatively low and fertilizer cost was relatively high. This was attributed to both greater yield response to fertilizer-K and crop value in cotton compared to soybean, rice, and corn. Hence, paying attention to both agronomic and economic factors for making fertilizer-K rate recommendations is important. Decision support software was developed to quantify effects of STK, yield response by crop, and user-specified crop price and fertilizer cost on fertilizer-K rate recommendations. The second study adds estimation of changes in STK using long-term K-rate trial information for fields in a rice/soybean rotation. Results proved that previous analyses, where tracking STK was not possible, had more moderate yield response to K and higher average yield in comparison to the crop-rotation study where STK changes were tracked. Hence yields, K*, and producer profit were lower when simulating profit-maximizing fertilizer-K rates in the rotation. However, because the short-run field tests were conducted across more sites, the results using the crop rotation yield response to K were deemed less representative of average Arkansas conditions. Using either yield response estimation method, regardless of initial STK, STK converged to the same final STK by the end of an 11-yr simulation period. With the more moderate, short-term K response the final STK was 80 ppm, 86 ppm when using the greater long-term K response, and 85 ppm when applying K at uniform extension rate recommendations (KE) with the short-term yield response curves. Using either of the two yield response curve estimates led to different K* across years and resulted in final STK values considered low by agronomic standards. Hence, using K* from the short-term trials vs. KE, or the long-term K*, is likely to lead to less K runoff and leads to lesser STK reserves in the soil at minimal yield loss and the potential for minable K reserves to last longer. A philosophy of building STK to ensure higher yield and/or to rely on STK should fertilizer-K cost spike, was considered second best.