Preferences and utility functions

Question 1

Assumptions about preferences

Answer 1

Completeness
Transitivity
Non satiation

Question 2

Completeness

Answer 2

When facing a choice between two goods the consumer can rank them

Question 3

Transitivity

Answer 3

Consumers rankings are logically consistent in the sense that if a>b and b>c then a>c

Question 4

Non satiation

Answer 4

All else equal, more of a good is better than less

Question 5

Do people actually become satiated?

Answer 5

• mixed results in studies of whether richer people are on average happier than poorer people (Helliwell et al 2012, Easterlin 2014)
• a survey found that no matter how rich people are they will say they need slightly more money to live comfortably

Question 6

Indifference curves

Answer 6

A way of graphically and mathematically expressing preference

Question 7

Properties of indifference curves

Answer 7

1. Bundles on indifference curves farther from the origin are preferred to those closer to the origin
2. Every bundle lies on an indifference curve
3. Indifference curves can’t cross
4. Indifference curves can’t slope upwards
5. Indifference curves can’t be thick

Question 8

What does the slope measure on an indifference curve?

Answer 8

Marginal rate of substitution (MRS)

Question 9

What does the total differential tell us?

Answer 9

By how much does a function’s value change if we change all variables by a small amount

Question 10

Equation for total differential of f(x,y)?

Answer 10

df(x,y)=pdx x dx + pdy x dy

Question 11

Utility function

Answer 11

A utility function assigns a utility level to every possible bundle of goods. This allows comparison of bundles

Question 12

Ordinal utility functions

Answer 12

• only describe rankings of bundles not utility levels
• in an ordinal utility function if U(x)=2 x U(y) it doesn’t necessarily mean the person likes x twice as much as y
• do not allow interpersonal comparison of utility

Question 13

Cardinal utility function

Answer 13

• cardinal utility functions assign exact utility levels to bundles
• if U(x) =2 x U(y) then this does imply that the person likes good x twice as much as y

Question 14

Which type of utility function is most commonly used and why?

Answer 14

We mostly use ordinal utility functions since people can only rank bundles and not assign them levels

Question 15

How do you find the marginal utility of good one in the utility function?

Answer 15

Differentiate the utility function with respect to q1 and hold q2 constant

Question 16

What is MRS equal to?

Answer 16

MRS=change in q2/change in q1= -u1/u2

Question 17

Perfect substitutes

Answer 17

Goods that a consumer is indifferent about, shown by straight diagonal downward sloping lines in a utility function

Question 18

Perfect compliments

Answer 18

Goods that are consumed in fixed proportions, shown as L shaped utility functions where MRS is undefined

Question 19

Imperfect substitutes

Answer 19

Most goods are imperfect substitutes, can be shown as cobb Douglas or Quasilinear

Question 20

Why are indifference curves downward sloping?

Answer 20

Because of the assumption that more is better

Question 21

Andrea enjoys burritos (B) and hot sauce (H) in a 1:3 ratio. Which of the following statements is true?
A) B and H are perfect substitutes
B) the MRS between B and H is 1/3
C) B and H are perfect compliments and the utility function is U= min{B,1/3H}
D) B and H are perfect compliments and the utility function is U= min{B,3H}

Answer 21

C) B and H are perfect compliments and the utility function is U= min{B,1/3H}