Incorporating Subsistence into Hedonic Price and Nutrient Demand Equations

The characteristics model of consumer choice explicitly introduces food nutrients into the decision-making process (Eastwood, Brooker, and Terry 1986; Hager 1985; Ladd and Suvannunt 1976; LaFrance 1985). Solution of the model leads to hedonic price and nutrient demand equations. The former can be thought of as relating the market price of a food to its nutritional composition. The latter refers to the amount of a nutrient consumed as a function of socioeconomic variables. Habit persistence was introduced into traditional demand analyses via the Klein-Rubin utility function, which led to its use in the linear expenditure system, the extended linear expenditure system, and most recently the almost ideal demand system. The interpretation, given originally by Samuelson (1947-1948), is that a consumer needs minimum amounts of goods, so utility is derived from the consumption of goods over and above these subsistence levels. To date none of the characteristics models, and especially those for food, has incorporated the concept of subsistence. This omission appears to be a serious limitation. Consumers need minimum amounts of nutrients in order to survive, let alone have healthier lives, ceteris paribus. These subsistence levels are primarily attained through the regular consumption of food. Utility arises from the consumption of nutrients in excess of the subsistence levels. A direct consequence is that the arguments of the utility function ought to accommodate subsistence levels of nutrients. To the extent that this formulation is a better approximation of consumer decision-making, three implications follow directly. First, the characteristics model needs to be revised. Second, the hedonic price and nutrient demand equations should be estimated with adjusted measures of nutrient consumption. Third, public policies directed toward enhancing dietary status may need to be reevaluated in light of the revised model. These considerations are particularly important given current interest in new standards for nutritional labeling of foods; current food policy emphases on understanding relationships among consumers' dietary attitudes, knowledge, behaviors, and food consumption; and the introduction of many new foods in response to dietary awareness.(1) This paper introduces subsistence into the characteristics framework. The utility function is written in terms of nutrients consumed above the subsistence level. Solving the model leads to empirical hedonic price equations and nutrient demand equations that reflect nutrition levels associated with minimum dietary standards. The approach yields hedonic price equations that can be consistent with declining marginal utilities of nutrients. Estimates of the equations are presented, and the results are discussed. INCORPORATING SUBSISTENCE INTO THE CHARACTERISTICS MODEL Assume the utility derived from food nutrients is separable from the other arguments of the utility function. Let |x.sub.i,j~ be the amount of the jth nutrient in the ith food, n is the number of food items, and m equals the number of nutrients. The amount of a nutrient that is consumed, |X.sub.j~, is derived from the quantities of foods (|q.sub.i~) and their exogenous nutrient compositions, shown as equation (1). |X.sub.j~ = |X.sub.j~(|X.sub.1,j~, . . . , |X.sub.n,j~, |q.sub.1~, . . . , |q.sub.n~) Let |S.sub.j~ denote the subsistence amount of the jth nutrient for the consumer and |D.sub.j~ be the excess amount. |S.sub.j~ is considered to be based on dietary needs exogenous to the consumer. |X.sub.j~ = |D.sub.j~ + |S.sub.j~. The utility function is equation (2). U = u|(|X.sub.1~ - |S.sub.1~), . . . , (|X.sub.m~ - |S.sub.m~)~ = u(|D.sub.1~, . . . , |D.sub.m~) Because the consumer must purchase market goods in order to obtain the characteristics, an important relationship is the marginal utility of each good. Recalling equations (1) and (2), a change in |q.sub. …