Texas Coastal Bend grain sorghum producers' fertilizer decisions under uncertainty

Abstract

Optimal (profit and utility maximizing) fertilizer levels are computed based on normative decision guides developed from experimental data on grain sorghum yield/fertilizer levels over an eight year (1977-1984) period, as well as subjective data elicited from several producers regarding their expectations of prices and yields and their utility for income (i.e., risk measures). Both a discrete approach based on stochastic dominance decision analysis and a continuous fertilizer decision model are used to analyze the subjective data. The impact of several weather variables on grain sorghum yield and response to fertilizer are studied. The risk characteristic of fertilizer input is considered based on the variance of yield relative to different nitrogen levels. Grain sorghum producers in the Texas Coastal Bend are generally risk averse, but to varying degrees. Using the Modified Ramsey elicitation method, most surveyed producers' utility for income is well represented by an exponential utility form. Exponential risk measures also exhibit inter-temporal stability of ordinal rankings of producers and are significantly related to a few measured farm and farm operator characteristics. Contrary to the common characterization of inputs as either risk increasing or risk reducing, the effects of applied fertilizer on yield variability do not appear to be consistent throughout the entire range of nitrogen levels considered. Based on experimental results, nitrogen fertilizers in Texas Coastal Bend grain sorghum production are risk (i.e., variance) increasing within the range of most producers' fertilizer use. Relative to individual producers' perceptions (i.e., conditional subjective yield distributions), however, nitrogen fertilizers are risk reducing or increasing (and in a few cases, risk neutral). Present TAEX fertilizer guidelines are inconsistent with both the experimental results and subjective production relationships of grain sorghum producers in the region. Actual fertilizer use, on the average, is higher than the present TAEX guidelines. Results based on experimental plot data suggest somewhat lower optimal fertilizer levels than those from discrete as well as continuous optimization procedures using subjective producer information. Using minimum values of Mean Absolute Percentage Errors, expected utility maximization represents producers' actual fertilizer decisions under uncertainty better than does expected profit maximization.