Research on World Agricultural Economy

Economically Optimal Soil Sampling Density and Application Technology for Potassium Fertilizer for Soybean in the Mid-Southern US

Michael Popp

Department of Agricultural Economics and Agribusiness, University of Arkansas Division of Agriculture, Fayetteville, AR 72701, USA

Bayarbat Badarch

Department of Agricultural Economics and Agribusiness, University of Arkansas Division of Agriculture, Fayetteville, AR 72701, USA

Aurelie Poncet

Department of Crop, Soil, and Environmental Sciences, University of Arkansas Division of Agriculture, Fayetteville, AR 72701, USA

Shelby Rider

Department of Agricultural Economics and Agribusiness, University of Arkansas Division of Agriculture, Fayetteville, AR 72701, USA

Nathan Slaton

Department of Crop, Soil, and Environmental Sciences, University of Arkansas Division of Agriculture, Fayetteville, AR 72701, USA

DOI: https://doi.org/10.36956/rwae.v6i4.1789

Received: 27 February 2025 | Revised: 14 April 2025 | Accepted: 19 May 2025 | Published Online: 26 November 2025

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Abstract

To maximize beneficial potassium (K) fertilizer use in irrigated soybean (Glycine max. (L.) Merr.) fields with spatially varying soil-test K (STK), the value of added information from more precise STK maps must be greater than the associated information collection costs. In eleven fields, we modeled the impact of soil sampling densities (SD) ranging from 2.2 samples ha^-1 in the largest field (41.2 ha) to 13.59 samples ha^-1 in the smallest field (7.4 ha) on STK maps with 0.4 ha grid size. The accuracy of profit-maximizing fertilizer rate prescription maps varied by SD and subsequent yield estimates using either uniform rate technology (URT) or variable rate technology (VRT). Fertilizer rate recommendations also depended on: i) the expected field yield; ii) the crop price; and iii) the fertilizer cost, costs for fertilizer application, and information collection charges that varied by application technology. Relative profitability comparisons across SD and fields revealed that collecting more than 1.1 samples ha^-1 was not viable. URT was more profitable than VRT (ranging from $2.29 ha^-1 to $7.62 ha^-1) at both relatively low and high field-level average STK and spatial variation in STK. At the mid-range level of STK, where adding K-fertilizer was on the verge of being profitable in light of nearly adequate STK, VRT outperformed URT in two of eleven fields by $11.50 to $21.35 ha^-1. Regardless of soybean price and fertilizer cost, a smaller upcharge for VRT compared to URT fertilizer application than the $5 ha^-1 modeled herein is necessary to increase VRT viability.

Keywords: Soybean; Potassium Fertilizer; Soil Sampling Density; Variable Rate Technology

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