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 α ∈ [ 0, 1 ] , p [ α x + ( 1 − α) y ] = α px + ( 1 − α) py ≤ w and α x k + ( 1 − α) y k ≥ 0 for all k , that is, α x + ( 1 − α) y ∈ B ( p , w ) . We will refer to the problem of Fnding the %-best bundle in B ( p , w ) as the consumer’s 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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This note was uploaded on 12/29/2011 for the course ECO 443 taught by Professor Aswa during the Fall '10 term at SUNY Stony Brook.
- Fall '10