## THE MONOTONICITY OF INDIVIDUAL AND MARKET DEMAND

## John K-H Quah

### St Hugh's College, Oxford University

### January 1997

Abstract

This paper studies the interplay between two types of conditions guaranteeing the monotonicity of market demand : conditions on individual preferences and conditions on the distribution of income. We begin with a version of the Mitjuschin-Polterovich condition, which guarantees the monotonicity of the individual demand function. We obtain the striking result that when the indirect utility function is convex, a diminishing marginal utility of income is sufficient to guarantee monotonicty. More generally, monotonicity is guaranteed when the elasticity of marginal utility of income with respect to income is less than two.

When individual demand satisfies monotonicity, so will market demand, provided the income distribution is exogenous. What if the elasticity is greater than two and individual monotonicity does not hold? In that case, we formulate conditions on the income distribution that will guarantee the monotonicity of market demand, in a way that generalizes the result of Hildenbrand. The family of permissible distributions increases as the elasticity approaches two. In short, the paper bridges two basic results in demand aggregation: the results of Mitjuschin and Polterovich, and of Hildenbrand.