3. Assume that the set of alternatives is X= R2. Consider the family of budget sets B = {B(1,1),2, B(3,4), B(4,2).:}, and suppose that the choice rule C() is such that C(B(1,1),2)= {(1,1)}. (Remember that the budget set B(1), has associated prices (P1, P2) and in- come w) (a) If the choice rule C(-) is such that the consumer demands more than 1 unit of good 1 under B(3,4)., show that the choice structure (B, C(-)) does not satisfy WARP.

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3. Assume that the set of alternatives is X = R2. Consider the family of budget
sets
B = {B(1,1),2, B3,4), B(4,2).}
and suppose that the choice rule C(-) is such that C(B(1,1),2)= {(1, 1)}.
(Remember that the budget set B(pipa).w has associated prices (P1, P2) and in-
come w)
(a) If the choice rule C() is such that the consumer demands more than 1 unit.
of good 1 under B(3,4)., show that the choice structure (B, C(-)) does not
satisfy WARP.
(b) If the choice rule C() is such that the consumer demands less than 1 unit
of good I under B(3,4), and more than 1 unit of good 1 under B(2).
show that the choice structure (B, C(-)) satisfies WARP.
Transcribed Image Text:3. Assume that the set of alternatives is X = R2. Consider the family of budget sets B = {B(1,1),2, B3,4), B(4,2).} and suppose that the choice rule C(-) is such that C(B(1,1),2)= {(1, 1)}. (Remember that the budget set B(pipa).w has associated prices (P1, P2) and in- come w) (a) If the choice rule C() is such that the consumer demands more than 1 unit. of good 1 under B(3,4)., show that the choice structure (B, C(-)) does not satisfy WARP. (b) If the choice rule C() is such that the consumer demands less than 1 unit of good I under B(3,4), and more than 1 unit of good 1 under B(2). show that the choice structure (B, C(-)) satisfies WARP.
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