Arbitrage and global cones: Another counterexample

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