Distribution of income and aggregation of demand

Abstract

We show that, under certain regularity conditions, if the distribution of income is price independent and satisfies a condition on the shape of its graph, then total market demand, F(p), is monotone; i.e., given two positive prices, p and q, one has <latex>$(p - q). (F(p) - F(q)) < 0$</latex>. These results allow for density functions increasing on some intervals, like unimodal distributions or even densities with more than one peak. Similar assumptions on the distribution of endowments, yield a restricted monotonicity property on aggregate excess demand, where, now, wealth is determined by market prices. This property guarantees uniqueness and stability of equilibrium of the Walrasian pure exchange economy.