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Unformatted text preview: Fned by weak inequalities, and bounded since for any x B ( p , w ) and for all k , 0 x k w / p k ). It is also convex since if x , y B ( p , w ) , then px w , py w , x k 0, and y k 0 for all k . Thus, for all [ 0, 1 ] , p [ x + ( 1 ) y ] = px + ( 1 ) py w and x k + ( 1 ) y k 0 for all k , that is, x + ( 1 ) y B ( p , w ) . We will refer to the problem of Fnding the %-best bundle in B ( p , w ) as the consumers problem . Claim: If % is a continuous relation, then all consumer problems have a solution. Proof: If % is continuous, then it can be represented by a continuous utility function u . By the deFnition of the term utility representation,...
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- Fall '10