Week 3 Flashcards
What are utility function?
A way of analyzing preferences by representing them numerically.
What does a utility function do to a bundle? What are their properties?
They assign a real number to every bundle and have properties that bundles with (strictly) higher utility are (strictly) more preferred.
What Is the notion of utility? and what does it mean?
It is cardinal. The units of utility are irrelevant. They are only informative when compared against bundles.
Show how utility functions are unique up to monotonic functions.
How to visualize a utility function?
Plot its indifference curves
What is an indifference curves
A set of bundles that have the same utility
How do we plot an IC curve? for utility function below.
What is the marginal rate of substitution?
It is the slope of the indifference curve. The derivative x2 with respect to x1 along the indifference curve.
Using u(x1, x2) using differentiation get the MRS.
What does equation show?
MRS = - MU1/MU2
It is the rate a consumer is willing to substitute good 1 for good 2.
How will a higher MU1 affect MRS
It will be steeper
When does a consumer have homothetic preferences?
If they’re MRS only depends on ratio of goods consumed. We say a utility function is homothetic if:
u(ax1,ax2) = au(x1,x2) for all a > 0
What graphical property do homothetic preferences have?
Bundles with same ratio between both goods fall over same straight line that pass through origin.
Curves of homothetic preference have same slop along straight lines that pass through the origin.
What is a Cobb Douglas utility function?
What is a perfect substitute utility function?
What is a perfect complement utility function?
What is a quasilinear utility function?
What is a Constant Elasticity of Substitution function ?
