Lecture 6 - Utility Functions

Question 1

What is a utility function?

Answer 1

A utility function U(x) assigns a utility level to every possible bundle of goods

Question 2

What are the two types of utility function?

Answer 2

There are two types of utility functions: Ordinal and Cardinal

Question 3

What are the features of an ordinal utility function?

Answer 3

• They only describe rankings of bundles, not utility levels
• If U(x) = 2*U(y), this does not imply that Lisa likes x twice as much as y
• Different utility functions can represent the same preferences

Question 4

What are the features of cardinal utility functions?

Answer 4

• Cardinal utility functions assign exact utility levels to bundles
• If U(x) is cardinal, U(x) = 2*U(y) does not imply that Lisa likes x twice as much as y

Question 5

Which utility function is used most often and why?

Answer 5

We mostly use ordinal utility functions as:
1- People can usually only rank bundles, not assign exact utility levels to them
2- Interpersonal comparisons of utility generally thought of as impossible

Question 6

What is the link between utility functions and indifference maps?

Answer 6

Utility functions can summarise the information in indifference maps

Question 7

Define the marginal utility of a good

Answer 7

The marginal utility of a good is the change in total utility from consuming an extra unit of a good

Question 8

How does utility change along an indifference curve?

Answer 8

Along an indifference curve, utility is constant

Question 9

What is the slope an indifference curve also equal to as well as the MRS?

Answer 9

The slope of an indifference curve is also equal to the negative of the ratio of marginal utilities between the two goods (-U1/U2)

Question 10

If indifference curves are convex so that the MRS is diminishing…

Answer 10

1- U1/U2 becomes smaller as we move down the curve

2- As we get more q1 (good 1) each additional unit is worth less to us so U1 goes down

3- As we get less q2 each additional unit is worth more to us so U2 goes up

Question 11

Describe the shape of the indifference curve for two goods that are perfect substitutes

Answer 11

It is a downwards sloping straight line

Question 12

Describe the shape of the indifference curve for two goods that are perfect complements

Answer 12

The indifference curve is made up a vertical and horizontal line that meet at a right angle

Question 13

Describe the shape of the indifference curve for two goods that are imperfect subtitutes

Answer 13

The indifference curve has the general downwards sloping shape of a regular indifference curve

Question 14

What are the two most common type of utility function framework?

Answer 14

Cobb-Douglas: U(q1,q2) = q1^aq2^1-a
Quasilinear: U(q1,q2) = u(q1) + q2