Yield Risk in a Dynamic Model of the Agricultural Household

A dynamic model of the agricultural household is posited in which the household chooses goods, leisure, and land and labor to maximize expected utility over multiple periods. The effect of yield risk and household preferences on its production and consu­ mption desicions are derived from the relationship between the household's direct utility function and a dynamic version of its indirect expected utility function. Similarities between the results derived from the standard agricultural household model 'and this model are shown. The model is, in general, nonseparable due to the absence of a contigent claims market. A special case is shown where a type of separability exists, although parameters and prices appearing in the indirect utility function determine the "risk parameter" in the supply and factor demand functions. In this special case, household demand is shown to depend on certainty-equivalent income. A numerical illustration of the model is also pro~ided. YDU, n• IN A BDWIIC _,EL CF TIIB . l&IICULTUUL . PHOCD by Terry Roe and Theodore Grahaa-Toauil 1. Iatrodutioa Huaerous studies have found that far11ers in developina countries prefer lower but certain levels of incoae to aarainally higher uncertain incoae levels (Koscardi and de 1anvry. 1977; Dillon and Scandizzo, 1978; and Binswanger. 1980). nese studies have obtained estiaates of faraers' aversion to risk ranaing fro• a aoasureaent of absolute risk aversion of . 9 for Northeastern Brazil to partial risk aversion estiaates of . 316 to 1.74 for farmers in India. Since continaency aarkets are surely iaperfect in developing economies, risk averse faraers tend, in an effort to reduce income uncertainty. to allocate resources to activities with lower expected ■ arainal value products than they would in the absence of uncertainty2. ne relationship between depressed income due to risk, and household consuaption has not b.een studied in aodels of the agricultural household. An obvious implication of a11uaing the absence of risk when risk ia present is that inferences dra,rn fro ■ these aodels ■ ay be aisleacling. ne proble ■ is to determine the nature of the aisleading inferences that ■ iJht othenrise be drawn. Moreover, failure to consider the affect of risk on household choices li■ ita the in1i1hts that can be obtained into the welfare effects of aarket iaperfections, such as those which inhibit households fro ■ allocating resources to off-farm activities, crop insurance or i ■perfectiona which provide liaited access to production technoloaies and other risk reducing inputs. -2In this chapter, we seek to incorporate production risk into a dynamic version of the agricultural household model. We investigate.a fairly simple aodel in an effort to determine the impact of yield risk and the household's riak preferences on its production and consumption decision,. Our 110del yields the familiar result that conslllllption and production occurs along the locus of points formed by the tangency of marginal utilities and marginal products to their respective price ratios. An analogue of Roy's Identity is also found to hold which relates conaUJDption and input demands to the derivatives of a dyn! lmic version of the household's indirect utility function. At this point, the results depart from those of the traditional aodel. In general, separability between production and consumption decisions does not hold, although a special case is demonstrated where a type of separability exists. While relationships between the household's choices and increasing risk can be derived for this special case, parameters of the household's direct utility function and prices of the argUJDents appearing in this function are found to determine the •risk aversion parameter• appearing in the product supply and input demand functions. Also, for this special caae, demand is found to be a function of certainty equivalent income. Bence, our findings suggest that parameter restrictions on estimating equations derived from models of the agricultural household which assume an absence of risk aay be inappropriate if risk and risk aversion are important. The paper ia oraanized as follows. To provide perspective, a brief background on how the issues faced in this paper contrast to other models of UD.certainty appears in the next section. Then, the basic model is specified and the dynamic progruuning approach to its solution is presented. A solution to the model is characterized in the fourth section. A specific problem is specified in the fifth section for which reduced form equations