In an exchange economy with agents 1 and 2 and goods and , agent 1 lexicographically prefers good (of two bundles she strictly prefers the one with more ; if is equal, the one with more ), while agent 2 lexicographically prefers good . Suppose 1's endowment is and 2's endowment is . The vector is a competitive equilibrium vector of prices if and only if:
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