Week 2

Question 1

What do we use to represent preferences when there are many outcomes?

Answer 1

Utility Functions

Question 2

What do we use to represent preferences when there are many outcomes?

Answer 2

Utility Functions

Question 3

What is a utility function?

Answer 3

A mathematical expression that translates the full range of possible outcomes into a person’s valuation of the outcome – their payoffs.

Question 4

What is a utility function?

Answer 4

A mathematical expression that translates the full range of possible outcomes into a person’s valuation of the outcome – their payoffs.

Question 5

How does a utility function works?

Answer 5

It assigns a number
U
(
x
,
y
)
U(x,y) to every bundle
x
,
y
x,y, representing a person’s valuation of that bundle.

Question 6

What are the two ways to measure how much a person values various outcomes?

Answer 6

1. By indicating how valuable each is on some absolute scale.
2. By simply ranking them in order.

Question 7

What type of utility functions do we consider?

Answer 7

Ordinal utility functions.

Question 8

What type of utility functions do we consider?

Answer 8

Ordinal utility functions.

Question 9

What type of utility functions do we consider?

Answer 9

Ordinal utility functions.

Question 10

What matters in ordinal utility functions?

Answer 10

Whether
U
(
A
)
U(A) is bigger than or smaller than
U
(
B
)
U(B).

Question 11

What is meaningless in ordinal utility functions?

Answer 11

The difference
U
(
A
)
−
U
(
B
)
U(A)−U(B) is meaningless, and we cannot make interpersonal comparisons.

Question 12

What does cardinal utility attach significance to?

Answer 12

The magnitude of utility and the size of the utility difference between two bundles.

Question 13

What does 𝐴≻𝐵 imply in terms of a utility function
𝑈?

Answer 13

U(A)>U(B)

Question 14

What does 𝐴∼𝐵 imply in terms of a utility function
𝑈 ?

Answer 14

U(A)=U(B)

Question 15

Define “utility function.”

Answer 15

A numerical score representing the satisfaction that a consumer derives from a given consumption basket.

Question 16

What is a positive monotonic transformation in the context of a utility function?

Answer 16

A transformation of a utility function that preserves the order of preferences.

Question 17

Why must the order be the same in a positive monotonic transformation?

Answer 17

To ensure that the preference rankings of consumption bundles remain unchanged.

Question 18

Draw the positive monotonic transformation

Answer 18

Refer to powerpoint

Question 19

Why are positive monotonic transformations important in utility theory?

Answer 19

They allow for different numerical representations of the same preference ordering without altering the underlying preferences.

Question 20

How can a utility function
𝑈(𝑥,𝑦) be constructed?

Answer 20

Indifference curves

Question 21

What does monotonic preferences imply about bundles on higher indifference curves?

Answer 21

All bundles on a higher indifference curve have to have bigger labels (higher utility values).

Question 22

What is the general form of the utility function for goods that are perfect substitutes (IDC is straight lines)?

Answer 22

U=ax+by

Question 23

What is the general form of the utility function for goods that are perfect complements ( IDC is L-shaped)?

Answer 23

U(x,y)=min(ax,by).