Utily Functions

Question 1

What is a utility function U(x)?

Answer 1

A utility function assigns a utility level to every possible bundle Of goods

Question 2

What is the purpose of a utility function?

Answer 2

The comparison of bundles.

U(x) > U(y) is x >(curled)y
U(x) = U(y) is x ~ y

Question 3

What are the two types of utility functions?

Answer 3

Ordinal and Cardinal

Question 4

What are ordinal utility functions?

Answer 4

Ordinal utility functions only describe the RANKING of bundles, not utility levels.

If U(c) = 2*U(y) it DOES NOT imply that Lisa likes x twice as much as y

Different utility functions can represent the same preferences

It doesn’t allow interpersonal comparisons of utility functions

Question 5

What are cardinal utility functions?

Answer 5

Cardinal utility functions assign exact utility levels to bundles.

U(x) = 2*U(y) implies Lisa likes x twice as much as y

Question 6

Which utility functions do we use the most ?

Answer 6

Ordinal utility functions as people can usually only rank bundles and not assign exact utility levels to them.

Question 7

How can utility functions summarise the information?

Answer 7

Using indifference maps.

Question 8

If a consumer’s utility if u(q1, q2) then what is one of the corresponding indifference curves?

Answer 8

Ū = U(q1, q2)

Question 9

Utility functions allow what of indifference curves?

Answer 9

Utility functions allow a reinterpretation of the slope of indifference curves

Question 10

What does a slope of an indifference curve mean?

Answer 10

It measures the marginal rate or substitution between goods

Question 11

How do you work out MRS?

Answer 11

Slope: dq2/dq1 (Dy/dx)

Question 12

What is the marginal utility of a good?

Answer 12

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

Question 13

What is marginal utility mathematically?

Answer 13

U₁ = (∂U(q₁,q₂))/∂q₁

U₂ = (∂U(q₁,q₂))/∂q₂

Question 14

The slope of an indifference curve = negative ratio..

Answer 14

The negative ratio of marginal utilies

Question 15

If indifference curves are convex?

Answer 15

MRS is diminishing

Question 16

What happens if MRS is diminishing (curve is convex)

Answer 16

U1/U2 get smaller as we move down the curve.

As we get more q1, each additional unit is worth less to us. So U1 goes down.

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

Question 17

What are perfect substitutes?

Answer 17

Goods a consumer is indifferent about

U(q1,q2) = iq1 + jq2

MRS = -i/j

Question 18

What are perfect complements?

Answer 18

Goods that are consumed in fixed proportions

U(q1,q2) = min(iq1, jq2)

MRS is not defined (u1 = 0, U2 = 0) unwilling to substitute goods for each other !

Question 19

What are imperfect substitutes?

Answer 19

Between perfect subs and perfect complements

2 examples of imperfect substitutes

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

Quasi linear: U(q1,q2) = u(q1) + q2

Question 20

Draw me a cobb Douglas curve

Answer 20

Question 21

Draw me a Quasilinear curve

Answer 21