Question

1. Consider an agent with preferences represented by the utility function: u(x,y) = xy (a) For each pair of bundles, indicate which is preferred or if they are indifferent between the two. Show your work. (4 points) A (3,9) B(2,8) ------------ C(4,7) D(8,8) E (5,20) F(10,10) G(5,9) H(12,4) (b) Using the bundles in (a), make a list that orders the bundles according to the agent's preferences. Start the descending list with the most preferred bundle and end with the least preferred bundle. (3 points)

Answer 1

a)

i)

Utility at A (3,9)=U(A)=3*9=27

Utility at B (2,8)=U(B)=2*8=16

Utility is higher for bundle A. So, Bundle A is preferred.

ii)

Utility at C (4.7)=U(C)=4*7=28

Utility at D (8,8)=U(D)=8*8=64

Utility is higher for bundle D. So, Bundle D is preferred.

iii)

Utility at E (5.20)=U(E)=5*20=100

Utility at F (10,10)=U(F)=10*10=100

Utility is equal at both bundles. So, consumer is indifferent to bundle E and bundle F

iv)

Utility at G (5.9)=U(G)=5*9=45

Utility at F (12,4)=U(F)=12*4=48

Utility is higher for bundle F. So, Bundle F is preferred.

b)

Point with highest utility will be most preferred. Following is the list in order of preference

EFD > H > G >CAB

E, F	100
D	64
H	48
G	45
C	28
A	27
B	16