We define and study in this chapter the characteristics of an individual consumer. In particular, we introduce the concepts of preference relation, utility function, and demand function.

For a considerable part of this book it would suffice to accept the notion of demand function as the definitional characteristic of consumers. It should be emphasized, however, that demand functions are a poor conceptual foundation for economic theory and that the grounding of the latter on preferences goes beyond an aesthetic convenience. Demand functions are good devices for the study of price equilibrium theory but are inadequate for the analysis of welfare issues (see Chapter 4) or theoretical problems that do not emphasize prices (see, for example, Chapter 7).

Our aim in this chapter is not merely to get the existence of demand functions. We want them to be smooth. Mathematically speaking, a demand function exhibits nothing but the parametric dependence of a maximizer element.