Utily Functions Flashcards
What is a utility function U(x)?
A utility function assigns a utility level to every possible bundle Of goods
What is the purpose of a utility function?
The comparison of bundles.
U(x) > U(y) is x >(curled)y
U(x) = U(y) is x ~ y
What are the two types of utility functions?
Ordinal and Cardinal
What are ordinal utility functions?
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
What are cardinal utility functions?
Cardinal utility functions assign exact utility levels to bundles.
U(x) = 2*U(y) implies Lisa likes x twice as much as y
Which utility functions do we use the most ?
Ordinal utility functions as people can usually only rank bundles and not assign exact utility levels to them.
How can utility functions summarise the information?
Using indifference maps.
If a consumer’s utility if u(q1, q2) then what is one of the corresponding indifference curves?
Ū = U(q1, q2)
Utility functions allow what of indifference curves?
Utility functions allow a reinterpretation of the slope of indifference curves
What does a slope of an indifference curve mean?
It measures the marginal rate or substitution between goods
How do you work out MRS?
Slope: dq2/dq1 (Dy/dx)
What is the marginal utility of a good?
The change in total utility from consuming an extra unit of a good
What is marginal utility mathematically?
U₁ = (∂U(q₁,q₂))/∂q₁
U₂ = (∂U(q₁,q₂))/∂q₂
The slope of an indifference curve = negative ratio..
The negative ratio of marginal utilies
If indifference curves are convex?
MRS is diminishing
What happens if MRS is diminishing (curve is convex)
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.
What are perfect substitutes?
Goods a consumer is indifferent about
U(q1,q2) = iq1 + jq2
MRS = -i/j
What are perfect complements?
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 !
What are imperfect substitutes?
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
Draw me a cobb Douglas curve
Draw me a Quasilinear curve
