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Unformatted text preview: + ( 0, . . . , , . . . , 0 ) , w ) . A clear conclusion can be drawn when we compare the consumers demand when he faces the budget set B ( p , w ) to his demand when facing B ( p , x ( p , w ) p ) . In this comparison we imagine the price vec-tor changing from p to an arbitrary p and wealth changing in such a way that the consumer has exactly the resources allowing him to consume the same bundle he consumed at ( p , w ) . (See Fg. 5.4.) Claim: Let x be a demand function satisfying Walrass law and WA. If w = p x ( p , w ) , then either x ( p , w ) = x ( p , w ) or [ p p ][ x ( p , w ) x ( p , w ) ] < 0. Proof: Assume that x ( p , w ) 6= x ( p , w ) . Then, [ p p ][ x ( p , w ) x ( p , w ) ] = p x ( p , w ) p x ( p , w ) px ( p , w ) + px ( p , w ) = w w px ( p , w ) + w = w px ( p , w )...
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