Unformatted text preview: x ( p , w ) is called the demand func-tion . The domain of the demand function is ³ K + 1 ++ whereas its range is ³ K + . Example: Consider a consumer in a world with two commodities having the following lexicographic preference relation, attaching the ﬁrst prior-ity to the sum of the quantities of the goods and the second priority to the quantity of commodity 1: x ± y if x 1 + x 2 > y 1 + y 2 or both x 1 + x 2 = y 1 + y 2 and x 1 ≥ y 1 . This preference relation is strictly convex but not continuous. It induces the following noncontinuous demand function: x (( p 1 , p 2 ) , w ) = ² ( 0, w / p 2 ) if p 2 < p 1 ( w / p 1 , 0 ) if p 2 ≥ p 1 . We now turn to studying some properties of the demand function....
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- Fall '10
- Binary relation, Convex function, Convex preferences