A note on the decomposition (at a point) of aggregate excess demand on the Grassmannian
The authors analyze the properties of aggregate excess demand functions for economics with an arbitrary finite set of \(N\) commodities where agents face trading restrictions of the ``missing markets'' type. Their budget set is defined by \(K\)-dimensional planes in \(\mathbb{R}^n\). It is shown that, if there are at least \(K\) agents in the economy, the only general property satisfied by the value of the aggregate excess demand and its derivatives, at any arbitrary point, is Walras law. They do this by considering a collection of agents whose preferences are of the ``generalized Leontief'' type, as they defined effectively, on an affine subspace of \(\mathbb{R}^n\) of dimension N-K. This the solution of the linearization at a point problem in the context of the general Grassmannian problem.
scientific article; zbMATH DE number 1455524