Suppose you are given the following preference information: a: (0, 1, 0: 3000, 2000, 1000)is indifferent to b: (3/4, 0, 1/4: 3000, 2000, 1000). If U(3000)= 1 and U(1000)= 0, what is U(2000)?
A)depends on the specific person involved
B)0.25
C)0.75
D)0.50

Question

Quizplus · Accepted Answer

Since a is indifferent between having all 3000 and all 1000 with a weight of 1 towards 3000, we know that they value each dollar between 0 and 1 as worth 1 U. Therefore, the value of b's 2000 is 3/4 of 1 U and the value of b's 1000 is 1/4 of 1 U. This means that b's overall value is (3/4)U + (1/4)(0)U = (3/4)U. Since a is indifferent between b and having all 2000 with a weight of 1 towards 3000, this means that a values all 2000 as (3/4)U. Therefore, U(2000) = (3/4)U/(2000/3000) = 0.75.

Suppose You Are Given the Following Preference Information: A: (0