Offer curves and uniqueness of competitive equilibrium

We establish sufficient conditions to guarantee the uniqueness of competitive equilibrium by properly restricting the distribution of endowments and preference profiles in a two-commodity, two-agent exchange economy. If agents’ offer curves share a common directional monotonicity property –i.e., at least one commodity is always normal for all agents–, then competitive equilibrium is unique. If not, we can provide testable geometric conditions for uniqueness by restricting the support of the distributions of individuals’ preferences and endowments that characterize the agents’ offer curves. The conditions are checked in well-known utility representations of preferences commonly used in the literature to illustrate the failure of uniqueness of equilibrium.