A Topological Invariant for Competitive Markets

I summarize and extend my results establishing that limited arbitrage is necessary and sufficient for the existence of a competitive equilibrium and for the compactness of the Pareto frontier [11] (announced in [14] and [8]). In response to a comment [36], I show that the authors misunderstood my results by focussing on brief announcements [14] and [8] which did not detail the hypothesis, rather than on the publication which contains the proofs [11]. The original results are extended here to encompass "mixed economies" based on [16]. They are used to define a topological invariant for a competitive market, which encodes exact information on its equilibria and on its social diversity, and predicts a failure of 'effective' demand.