Consumer Choice: Utility Function

Question 1

Utility function

Answer 1

U (x,y)

Question 2

Ordinal vs cardinal utility

Answer 2

Ordinal unity functions - whether utility A is bigger/smaller than B. Difference is meaningless, just ordinal.

Cardinal attaches significance to the magnitude of utility, the difference in utility has some significance.

(We only use ordinal)

Question 3

Utility function must have positive monotonic transformation, what does this mean.

Answer 3

The order must be same as initially (represents the same preferences throughout)

Learn what it looks like graphically. (One graph shows it, one graph shows example of it not working)

Question 4

What would a utility function U₁(x,y) = x²y² indifference curve look like and why?

Answer 4

Indifference curves look the same.

As
U₁(x,y) = x²y²=(xy)²=U²(x,y)

So U₁=U² (represent the same preferences)

Question 5

Algebraic expressions of utility functions for:
Perfect substitutes
Perfect complements
Neutral good
Bad good

Answer 5

Perfect subs
U = ax + by

Perfect complements
U = min(ax,by)

If second good Y is neutral:
U = ax (as Y gives 0 utility)

If second good Y is a bad good:
U = ax - by (as gives disutility)

Question 6

Marginal utility equation: to see rate of change in utility following a change in good 1.

Answer 6

MUx = dU/dX
Or
ΔU=MUx x Δx

Differentiate utility with respect to good 1.

(Vice versa if we are looking at good 2)

Question 7

Recall MRS formula

Answer 7

Δy/Δx

Question 8

How to link MRS to marginal utility?

Answer 8

Assume there is a change in both amounts of goods where utility stays the same (ΔU=0)
MUxΔx + MUyΔy = ΔU = 0

Then rearrange to get
Δy/Δx = -MUx/MUy

Question 9

So what is MRS formula in terms of marginal utility

Answer 9

MRS = Δy/Δx in standard

MRS = MUx/MUy in terms of marginal utility