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  (announced in  and ). In response to a comment , I show that the authors misunderstood my results by focusing on brief announcements  and  which did not detail the hypothesis, rather than on the publication which contains the proofs . The original results are extended here to encompass "mixed economies" based on . 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.
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