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

individual utility is affected by what

the consumption of physical commoditiespsychological attitudes

peer group

personal experiences

general environment

can we compare utility across individuals?

no

what do we assume about goods?

we assume that more is better than less

utility and indifference curve

each utility function has a set of indifference curves that describes it

for each set of indifference curvers, there’s a particular utility functino that corresponds to it

sometimes instead of using utility functionwe use indifference curves

indifference curve

shows a set of consumption bundles among which an individual is indifferent

**any point on the curve = same utility

marginal rate of susbtitution

the negative slope of the indifference curve at any point = the marginal rate of substitution

measures an individual’s willingness to substitute y for x

**changes as x and y change for the most part

convexity

a set of points is convex if any two points can be connectd by a straight line and the data is contained w/in the set

**necessary condition

if the indifference curve is convex - what does this mean?

it means (x1+x2)/2, (y1+y2)/2 will be preferred to either (x1,x2) or (y1,y2)

**well balanced bundles are preferred to bundles that are heavily weighted toward one commodity

homothetic preference

preferences are homothetic if the MRS depends only on the ratio of the amount consumed of the two goods

consumptino of the two goods doesn’t affect the MRS in any other way

with homothetic preferences all indifference curves have the same shape

multigood indifference surfaces

indifference surface = set of consumption bundles that satisfy the equation where U1 is a constant level of utility