Chapter 3 - Preferences and Utility

3 basic properties of preferenec

(1) completeness

(2) transitivity

(3) continuity

completeness

if there are 2 goods, a person will never be indecisve and there are only 3 situations

• A>B

• A<B

• A=B

transitvity

if there are 3 options, A, B, C and

A>B and B>C, then A>C

continuity

if A>B, then anything close enough or similar enough to A is > B

how do we use utility functions to compare?

we can use them to compare rankings for different goods for one person but you can’t use it compare rankings between people i.e. good a between two diff people

ceteris paribus assumption

even though utility is affected by a ton of different htings, we assume they’re all constant and that utility is only affected by consumptino of goods and services

do we assume that more of a good is better or worse?

we assume that more of a good is always better

indifference curve

shows different combinations of 2 goods that an individual would rank equally

marginal rate of substitution

how much someone would give up of good y to get more of good x

**typically diminishing bc when you have a otn of y and not a lot of x, you’re willing to give up more y to get 1 x but later, when you have a lot of x, you’ll give up less y to get one x

negative because you have to give up some of good y in order to get more of good x

steeper MRS

more willing to give up good y for good x

ex. ratio of 4 y for 1 x

flatter MRS

less willing to give up y for x

i.e. ratio of 0.25 y for 1 x

can any two of an individual’s utility curves intersect?

no

convex

a set of two points is said to be convex if they can be connected by a straight line and still be contained w/in the function

**when MRS is diminishing, this is always true

what does notion of convexity help w?

if a function is convex, it means they can get more utility out of the average of two points instead of just picking one of those two and they’ll prefer a balance

does the MRS depend on units?

no because it’s a ratio

MRS = -dx/dy = U_x/U_y

do we somenow already know people’s preferences?

no, we get them from watching how they repsond to changes in income, prices, etc.

cobb douglas utility

typical utility function, curved

perfect substitutes

straight line bc U(x,y) = ax+by

this means MRS is constant and equal to a/b along the entire indifference curve and that no matter how much someone has of one of the things, they’ll trade the same amt of good x for good y

perfect complements

CES utility