Question

2. Lyuba has preferences over peonies (p) and tulips (t). The following list shows all feasible bundles that Lyuba can consume in a month:

   A = (pA,tA) = (1,3), B = (pB,tB) = (3,1), C = (pB,tB) = (2,2).
   If Lyubas preferences are given by: A is indifferent to B, C is strictly preferred to A

   and C is strictly preferred to B, then:

   1. (a) A function that represents Lyuba’s preferences is U(p,t)=3p+t.

   2. (b) A function that represents Lyuba’s preferences is U(p,t)=p+t.

   3. (c) There exists a utility function different from the ones mentioned above that rep- resents Lyuba’s preferences.

   4. (d) None of the above.

Answer 1

Given Lyuba's preferences over peonies(p) and tulips(t) with feasible bundles over a month.

The preferences are listed as:

A= (pt, tA) = (1,3)

B= (pB, tB) = (3,1)

C = (pC, tC) = (2,2)

Given, Lyubas's preferences are ordered as:

She is indifferent between A and B, so utility from A is equal to utility from B, u(A) = u(B) ;

C is strictly preferred to A, so utility from C is greater than utility from A, u(C) > u(A) ;

and C is strictly preferred to B, so utility from C is greater than utility from B, u(C) > u(B).

(a) Utility represented as U(p,t) = 3p + t cannot be Lyuba's utility function because in this case, A= (pt, tA) = (1,3), putting values of p=1 and t =3 so u(A) = 3(1) + 3 = 6; B= (pB, tB) = (3,1); putting values of p = 3 and t = 1 so u(B) = 3(3) + 1 = 10.

This option is incorrect because in this case u(A) < u(B).

(b) Utility represented as U(p,t) = p + t cannot be Lyuba's utility function because in this case, A= (pt, tA) = (1,3), putting values of p=1 and t =3 so u(A) = 1 + 3 = 4; B= (pB, tB) = (3,1); putting values of p = 3 and t = 1 so u(B) = 3 + 1 = 4 ; C = (pC, tC) = (2,2), putting values of p = 2 and t = 2 so u(C) = 2 + 2 =4.

This option is incorrect because in this case u(A) = u(B) = u(C).

(c) This option is correct because there exists a utility function different from above that represents Lyuba's preferences.

For instances u(pA, tB) = pt represents her utility function.

In this case: utility from A = 1 * 3 = 3 , where p=1 and t=3;

utility from B = 3 * 1 = 3, where p=3 and t=1;

and utility from C = 2 * 2 = 4, where p =2 and t =2;

Here u(A) =u(B), u(C) > u(A) and u(C) > u(B).

(d) This is an incorrect option as option C is correct.