Arbitrage and global cones: Another counterexample

Chichilnisky (1997) claims that another variant of her condition limiting arbitrage is necessary and sufficient for existence of equilibrium and nonemptiness of the core in an economy with short sales allowing half lines in indifference surfaces. Her proof, however, is based on a proposition purporting to relate her notion of "global cone" (see Chichilnisky (1997) for references) to the Page-Wooders "increasing cone." In this paper, we present a counterexample showing that parts (i) and (ii) of Chichilnisky's proposition are false. Thus, Chichilnisky's claimed result is without proof.