Asymptotically Well-behaved Demand Functions for Normal Goods

The well-behaved (downward sloping and consistent to the consumer surplus) Marshallian demand function forms a basis of the partial equilibrium analysis both in positive and normative perspectives, since the downward slopness and some other regularity conditions imply that there exists a competitive equilibrium uniquely in the partial equilibrium market and the consistency to the consumer surplus enable us to evaluate alternative policies in the market by means of the consumer surplus measure. It is well-known that Marshallian demand functions are well-behaved only if they are defined for neutral goods, i.e., the case of quasi-linear preferences. This paper considers a possibility that Marshallian demand functions for normal goods become well behaved when the initial incomes are sufficiently large. As a main result, this paper provides necessary and sufficient conditions for a standard preference ordering under which the derived Marshallian demand function becomes well-behaved when the initial income is sufficiently large. Moreover, if a preference ordering is represented by a smooth utility function, a formula is provided to compute the well-behaved demand function directly from the utility function.