Question

Pick an arbitrary consumption bundle (x, y) ∈ R2+ (meaning x ≥ 0, y ≥ 0). Draw or describe the better than set (upper contour set), the worse than set (lower contour set) and the indifference set in a graph for the following situations:

• I like consuming x, and the more the better. I am completely indifferent to the amount of y that I consume.

• As long as my consumption of x is less than x∗, the more the better. After x∗ the less the better. I am completely indifferent to the amount of y that I consume.

• I like both x and y, but a unit of x must be paired with a unit of y in order for me to enjoy it (like left and right shoes).

• I prefer the bundle (x*, y*) to all other bundles. If I have any other bundle, then I am indifferent between having this bundle and having nothing (0, 0).

Answer 1

a). I like consuming x, the more the better it is and completely indifferent to the amount of y I am consuming.

We can take the utility function: - x^(1/2) + y = 4

Here, We can't consume x=0 as it is undefined,

MUx = 1/2x^(1/2). , x can't be 0.

c). I like both x and y but a unit of x is must paired with a uniy of y. i.e. This is complementary good U (x,y) = min (ax,by).

Example: - if a =2 and y =1

Then bundle can be (2,1),(4,2),(6,3) etc.

If AB is y- axis and BC is x-axis then the left is utility curve.

d). In this graph blue line is budget line with income=4. and and red one is utility function x*y = 4

In this graph I can only consume (2,2)

If i will given any other bundle I will not be able to achieve it So, I will be indifferent betwenn (0,0) and any other bundle rather than (2,2).