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==Basic setup==
Suppose their [[consumption set]], or the enumeration of all possible consumption bundles that could be selected if there are no budget constraints, has ''L'' commodities and is limited to positive amounts of consumption of each commodity. Let ''x'' be the vector ''x''={''x<sub>i</sub>'';''i''=1,...''L''} containing the
:<math>x \in \textbf R^L_+ \ .</math>
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