The Concept of Weak Complementarity

Abstract

The previous chapter presents the model for welfare measurement of price changes. This model relies on the result that a change in the price of a good is related to quantity demanded of that good by way of the envelope theorem. The same link naturally holds for factors (such as labor) sold at parametric prices. But many problems in the allocation of resources and the protection of the environment involve services that enter directly into a consumer’s utility function or a firm’s production function. For example, a household living in an industrial city will enjoy air quality determined not by their own consumption decisions but by the city’s level and composition of transportation and manufacturing. A household may purchase the quantity of its drinking water, but the quality of the water will be determined by public water supply policies. In these cases, environmental quality is a direct determinant of utility, and government actions or exogenous events affect the level of the environmental good or service entering the individual’s preference function. In such cases one cannot rely on the conceptual basis developed for price and income changes for measuring the welfare effects of changes in public goods. In this chapter we begin to develop the basic theory and extensions that support a more general set of welfare measures dealing with changes in the level of goods and services that enter preference functions exogenously.