Question

Part 1: Suppose Kim is at Chipotle and she can buy tacos (T) or burritos (B) and they are perfect substitutes. If she is indifferent between (T,B) = (2,2) and (0,3) which of the following utility functions rationalizes her preferences?
a) u = T + B
b) u = 3T + 2B
c) u = T + 2B <-- answer
d) none of the above

Part 2: Now Suppose Kim wants to order chips (C) and guacamole (G) and they are perfect complements. If she is indifferent between (C,G) = (3,8) and (4,2) which of the following utility rationalizes her preferences:
a) u = min(1C,2G)
b) u = min (6C, 9G) <-- answer
c) u = min (3C, 2G)
d) none of the above

Can someone help me explain why these are the answers and how are these two preferences connected to each other?

Answer 1

Part 1. Perfect substitutes.

It has straight Indifference curve

she is indifferent between (T,B) = (2,2) and (0,3)

This means she gets same utility from both the options.

Now we have the utility functions in the option.

Put these values in all the utility function to see in which one the value of U is same.

For example a) u = T + B

(T,B) = (2,2) , U= 2+2=4

(T,B)= (0,3) , U=0+3=3

U is not same 4≠3, hence this is not the answer.

c) u = T + 2B

(T,B) = (2,2) , U= 2+2*2=6

(T,B)= (0,3) , U=0+2*3=6

U is same 6=6, hence this is the answer.

Perfect substitutes means she gets same utility when they substitue taco with one unit of burrito.

Part 2. Perfect complements

It has L-shaped Indifference curve.

she is indifferent between (C,G) = (3,8) and (4,2)

This means she gets same utility from both the options.

Now we have the utility functions in the option.

Put these values in all the utility function to see in which one the value of U is same.

b) u = min (6C, 9G)

(C,G) = (3,8) ,u = min (6*3, 9*8)= min(18,72)=18

Utility is the minimum value is 18 as 18<72.

(C,G)= (4,2) ,u = min (6*4, 9*2)= min(24,18)=18

Utility is the minimum value is 18 as 18<24.

since utility is same in both the case. This is the answer.

For doubts comment below