Question

Consider a person choosing among four options

{A,B,C,D}

. We observe her making the following choices.

i) She prefers C to A in a direct comparison.

ii) She is indifferent between A and B.

iii) She prefers B to D.

Answer the following questions:

a) (5 points) Assuming she is rational, what would she choose if offered C or D?

b) (5 points) What is her best option among the four in her choice set?

c) (10 points) Is the following utility assignment representative of her preferences? u(A)=10, u(B)=10,

u(C)=14, u(D)=10? Why or why not?

Answer 1

Answer

(a)

It is given that She prefers C over A and she is indifferent between A and B. This implies that she prefers C over B. Also according to (iii) She prefers B to D. Thus she prefers C over B and B over D. So according to transitivity She prefers C over D. Hence, If she is rational she will choose C.

(b)

As discussed above She Prefers C over A , B and C(all of them). Hence, her best option among the four in her choice set is Option C.

(c)

As discussed above her best option among the four in her choice set is Option C. Hence, Her utility from all of the option is highest for option C. We can see from above that u(C) = 14 is the highest. It is also given that She is indifferent between A and B. Thus, u(A) must equals u(B). Here u(A) = 10 = u(B). Thus this statement is also true. Finally we left with (iii) She prefers B over D. Assuming that she weakly prefers B to D, then u(B) should be greater than or equal to u(D). Here u(B) = u(D). Thus it also satisfies.

Hence Assuming she weakly prefers prefers B to D, then this utility assignment is a representative of her preferences.

Note :

If he strongly prefers B over D then u(B) should be greater than u(D) and this utility assignment is not a representative of her preferences.