Separability and Risk in the Static Household Production Model

The household production model highlights the possible interdependence of consumption and production decisions in the farm household. The structure of this interdependence significantly affects the analytics both theoretical and econometric of farm households. Singh, Squire and Straus 20 have an excellent discussion of this interdependence and its methodological implications. A particular type of interdependence called interchangeably recursiveness or allows production decisions to be made independently of consumption decisions although the latter depends on the former through the budget constraint. This separability is of interest because it justifies a large number of well-developed methodological approaches in farm household studies among these being the various duality theory approaches. Sasaki and Maruyama 19 and Jorgenson and Lau 10 both and independently found the existence of perfectly competitive goods and factor markets to be sufficient for the existence of separability under deterministic conditions. While there are a large number of things that can upset this result even in the deterministic setting, e.g., nonhomogeneity of labor as in Kuroda and Yotopoulos 13 and Lopez 14, the recognition of the role of risk appears especially threatening to separability even in a competitive setting as pointed out by Barnum and Squire 1. If contingent claims markets exist or if households are risk neutral, separability exists under risk situations. But insurance markets may not exist and, for many risks faced by the farming households could not, unless heavily subsidized, exist. Furthermore, households have been variously shown to be risk averse 15; 7; 4. Roe and Graham-Tomasi 18 utilizing a multiplicative yield risk in the context of a dynamic model concluded that on the whole, independence does not hold and estimating equations from certainty theory are not appropriate. Thus with respect to risk one can say that the die is loaded against separability. This paper aims to show that there are risk specifications which allow separability for the household production model even in the absence of the contingent claims market. In section II, we introduce the standard model of the household with commercial production. It involves a household that produces an output which it partly consumes and partly sells in the market. Risk enters the revenue function either additively or multiplicatively. We then introduce two definitions of separability: in the sense of efficiency and in the sense of elasticity. We show in section II that additive risk whether on yield or on monetary revenue allows sepa-