This paper presents a formal model in which differential satiation dynamics of various consumer needs translate into long-run changes of consumer behavior when income rises. In the model individuals allocate their income to the consumption categories proportional to need deprivation states corresponding to the consumption categories, a decision making process called matching. The paper compares the Engel curves obtained from matching with the Engel curves obtained from traditional constrained maximization. The latter allocation is used as a normative benchmark of the behavior that leads to the highest utility. While superficially both ways to allocate income generate similar results, matching allows to explain some empirical regularities that maximization cannot account for. For example, only by using matching one can reconstruct that income elasticities for food tend to decrease with rising income. Moreover, the comparison of both ways to allocate income shows that the deviations from rational behavior are greater for relatively poor individuals than for richer individuals so that the inequality in terms of welfare can be stronger than the inequality in terms of income. Innovations influencing the satiation patterns can strengthen this effect.
Consumer theory Engel curves Engel's law Structural change