Welfare Evaluation and Household Production with Non-Constant Returns to Scale

Abstract

A recent body of literature examining energy-consuming durables investment [2; 3; 4] has fused the household production and utility maximization models to estimate demand functions for end-use products such as heated water and air. All of these studies have made the seemingly necessary simplifying assumption that the household production functions exhibit constant returns to scale (CRS). This assumption provides for a linear budget constraint, a necessary condition for deriving demand functions. However, since it is unlikely that all the household production functions in fact closely approximate CRS, serious measurement error may occur. It is the purpose of this paper to prove that the CRS assumption is unnecessary. A marginal benefit function for end-use products, which is analogous to a Marshallian demand function, can be derived and estimated under a non-linear budget constraint. These demand functions for end-use products are useful in measuring the welfare effects of government programs, for example, rebates for purchases of high efficiency appliances.' It will be shown that measures of consumer's surplus, both Marshallian and exact, can also be estimated under non-linear budget constraints. In sections II and III, we formally derive a marginal benefit function and explain how it and consumer's surplus can be observed. In section IV, Shephard's lemma and Roy's identity are modified to account for the non-linear budget constraint and a method of deriving exact consumer's surplus is shown. Section V is an illustrative example of the described process and section VI concludes the paper.