Topic 3 Utility

Question 1

If a consumer weakly prefers bundle x to bundle y (x1,x2) squiggly greater than or equal to (y1,y2), then what does this imply about utility?

Answer 1

It implies that the utility gained from consuming bundle x is greater than or equal to the utility gained from consuming bundle y:
u(x1,x2) >= u(y1,y2)

Here greater than or equals sign is normal straight lines not squiggly lines

Question 2

What is a utility function?

Answer 2

A tool to represent preferences mathematically

Question 3

If a consumer is indifferent between bundle x and bundle y (x1,x2) squiggly line (y1,y2), then what does this imply about utility?

Answer 3

It implies that the utility gained from consuming bundle x is equal to the utility gained from consuming bundle y:
u(x1,x2) = u(y1,y2)

Question 4

State the utility function for the following preference:

(5,6) squiggly line (indifferent to) (7,2)

(100,100) squiggly line (indifferent to) (50,200)

Answer 4

The above preference relation implies that the consumer is willing to gain 1 unit of good 1 by giving up 2 units of good 2 which suggests that the consumer prefers good 1 over good 2

Thinking in terms of utility, it implies that the utility gained from good 1 is double that of good 2 as you are indifferent between giving up 2 bananas for an apple

… u(x1,x2) = 2x1 + x2

You can simplify this by diving by 2:

… 1/2 u(x1,x2) = u hat (x1,x2) = x1 + 0.5x2
(same 2:1 relationship as first equation just divided by 2)

Question 5

What are the characteristics of utility?

Answer 5

Utility has no unit - it is an ordinal concept (based on ranking order)