We analyze under which conditions a given vector field can be disaggregated as a linear combination of gradients. This problem is typical of aggregation theory, as illustrated by the literature on the characterization of aggregate market demand and excess demand. We argue that exterior...

We are interested in general equilibrium incomplete markets, where the number of consumers is N, the number of goods is L, and the dimension of the space of admissible trades is K (the case of complete markets being then K=(L−1)). We prove that, if N≥K, any non-vanishing analytic function...

The fundamentals of an exchange economy, the preferences of individuals, can be identified from the competitive equilibrium correspondence, which associates equilibrium prices of commodities to allocations of endowments; the argument extends to production economies. The essential step is the...

The paper provides an introduction to exterior differential calculus, and an application to the standard problem of the characterization of aggregate demand in an economy in which the number of agents is smaller than the number of goods.

The competitive equilibrium correspondence, which associates equilibrium prices of commodities and assets with allocations of endowments, identifies the preferences and beliefs of individuals under uncertainty; this is the case even if the asset market is incomplete.