The Demand For Goods Under Mixture Aversion

Abstract

We analyse the demand for goods which the consumer has an aversion to consuming in mixtures. Examples are presented. It is suggested that the axiom of non-satiation should be relaxed in order for the model to be internally consistent. The indi¡erence map with mixture aversion and satiation is constructed and is shown to have very unusual properties. It is then demonstrated that constrained maximization of the underlying utility function can result in both goods being consumed. It is also demonstrated that the type of goods analysed here can exhibit the rare characteristic of Gi¡enity. " IntroductionThe simplest model of consumer theory assumes that only two goods are available to the consumer, and that the consumer prefers mixtures of the two goods to extreme quantities of either one of the two goods. It is easily demonstrated that, under the assumption that more is preferred to less, this preference for mixtures gives rise to indi¡erence curves which are convex to the origin. Preference for mixtures is, in fact, embodied in one of the axioms of consumer theory, namely the axiom of convexity.An interesting variation on the simple model is concerned with the situation in which the consumer has an aversion to consuming mixtures of the two goods. The most popular example concerns two di¡erent types of alcoholic beverage: most of us have su¡ered the consequences of mixing grape and grain '. Sproul (1984, p. 25) reports that`I enjoy drinking beer and wine but I prefer not to mix them. I would be just as happy with a bottle of either, or with three-quarters of a bottle of each.' The alcohol example is also tackled by Clements and Selvanathan (1991) and in more humorous spirit by Covicks (1974). In deciding on the level of consumption of beer and wine during a single drinking session, the consumer is in£uenced by the prospect of the undesirable consequences of alcohol consumption, which tend to be worse when a mixture has been consumed than when the same total quantity of a single beverage-type has been

A Convenient Utility Function with Giffen Behaviour

“…Also Spiegel [20] provides a utility function of which the Giffen property is discovered by way of a numerical exercise. Sörenson [21] proposes a modified Leontief utility function, which eliminates the substitution effect at the kink of the indifference curve and offers some economic justification for such a functional form (see also, [22]). As a classroom example, however, the function is less suitable, because the nondifferentiability at the kinks prevents the use of the relative price rule (Gossen's Second Law) for the derivation of the demand curves.…”