WEED CONTROL DECISION RULES UNDER UNCERTAINTY William Deen, Alfons Weersink, Calum G. Turvey, and Susan Weaver A model of weed control, which took into account the stochastic nature of crop price, yield, and weed density, was developed to assistfarmers in determining weed densities that justify herbicide application and the optimal rate of application. In an application of cockleburcontrol in soybeans, it was found that the value of following the "if-then-else" treatment strategy versus a fixed application rate regardless of weed density was approxi- mately $25 per acre at low weed numbers. Profits of the marginal treatmentstrategy are higher than the "if-then-else" strategy, but may not be sufficient to cover the additional informational costs. Under both strategies, the total amount of herbicide applied decreaseswith increases in uncertainty under the assumption of risk neutrality. The result is due to the convex relationship between weed density and yield loss. Under the assumption of maximizing expected utility, there are instances in which herbicide use increases with risk aversion as per conventional wisdom. Introduction Consumers, as well as farmers, are concerned about environmental and human health impacts associated with pesticides, food contaminationfrom herbicideresidues,ground- water contamination resulting from leaching of herbicides, and surface water contamination through surface run-off from herbicide treated fields. In addition, farmers are concerned with potential operator exposure to herbicides, increasingpest resistance, changingpest domin- ance, removal of existing herbicidesdue to poli- tical pressure exerted by consumers, and finally, overall returns to their farming enterprise. The authors are a Research Leader, the George Morris Center, Guelph, Ontario, Assistant Professors, Department of Agricultural Economicsand Business, Univer- sity of Guelph, and a Research Scientist, Agriculture Canada, Harrow, Ontario. Financial Assistance for the project was provided in part by the Ontario Ministry of Agriculture and Food's Food System 2002 program and the Agriculture Canada/NSERCresearch partnership program. The authors wish to acknowledge the helpful comments of Glenn Fox, Scott Swinton, and two anonymous journal reviewers. Total amount of pesticide applied is a function of: (1) the number of applications; and (2) the rate of application. A reductionin either would result in reduced overall pesticide usage and would also assist in alleviating the concerns consumers and farmers have regarding the safety and profitability of pesticide usage. Reducing total applied herbicide while maintaining profit- ability would represent a Pareto improvement; consumers would be better off since potential environmental and human health concernsasso- ciated with the use of a pesticide would potentially be reduced. Economic threshold concepts are management tools designed to promote more efficient pesticide use in pest control. Biologists tend to focus on reducing the number of pesti- cide applications through the use of discrete choice threshold concepts. The suggested treat- ment strategies involve applying a fixed pesticide dosage if pest population density exceeds a minimum: otherwise, the recommendation is not to treat (Norton). The concept, often called the "if-then-else" approach, has been applied to control weeds in rice (Smith), barley (Blackshaw), winter wheat (Doyle et al.), white potatoes (Marra et al.), corn (Zanin et al.), and soybeans(Weaver). In contrast, economists have tended to focus on continuous choice threshold concepts in determining the optimal application rate for a given pest density. The resulting marginal treatment strategy ensures profit maximization, but considerable information is required for the strategy to be implemented. Studies using the marginal approach have examined such aspects as increasing pest resistance (Hueth and Regev), multiple-species in a dynamic setting (Wetzstein et al.) and risk (Tisdell). Reichelderfer and Wetzstein both claim that risk reduction is the major reason for producers to apply pesticides. However, in a recent review of risk in decision-making for agricultural pest control, Pannell (1991) concluded that risk may not necessarily lead