Conditional Demand Functions and the Implications of Separable Utility

Abstract

Most contributions to demand theory can be divided into two distinct categories. One consists of studies of the foundations of the theory; these are usually concerned with weakening the fundamental axioms to obtain greater generality. The other consists of studies which impose strong restrictions on either preferences or demand functions and investigate the implied restrictions on the other; these sacrifice generality to obtain specific results. In the former category are investigations of the conditions under which preferences can be represented by real valued, continuous utility functions and of the conditions under which demand functions can be defined in the absence of such representability. Examples include Chipman [1], Rader [14], Debreu [2], Sonnenschein [17] and Richter [15]. The latter category includes investigations of the demand functions arising from specific utility functions (e.g., Wegge, 22), of self-dual preference orderings [Houthakker, 7] and, perhaps most prominently, of separable utility functions [Strotz, 19; 20; Gorman, 5; Frisch, 3; Houthakker, 6; Sono, 18; Pearce, 10; 11; Goldman and Uzawa, 4]. The purpose of this paper is to derive and explain the implications for consumer behavior of the three principal separability hypotheses: the utility tree, block additivity and additivity.l Although most of the results