hello everyone
today we're going to start the real
material of economics 3312
and over the next three chapters we are
going to construct
what we call the theory of the consumer
or the theory of consumer choice
and we're going to use then that theory
of consumer choice
to derive a consumer's demand for goods
and services
and that is you know our
basic building block on the demand side
of the market
the households demand for goods and
services
so this is how we're going to proceed
we're going to do this in three stages
remember you know what we have to deal
with here are the determinants of a
consumer's demand which would be
you know consumer states and preferences
prices of goods and services and income
for the individual consumer
so we're going to begin a little
differently a little backwards we're
going to start off
with a complete representation of a
consumer's taste and preferences that's
our starting point
we put together a a
a a an illustration a picture
of a consumer's taste and preferences
that we can use as the basis on what
your consumer
makes choices and once we have a full
representation of consumer's tastes and
preferences
then we can bring in the idea of income
in prices now our assumption here
is that a consumer's taste and
preferences do not depend
on the consumer's income or prices
but consumers taste and preferences
range
over the entire universe of consumption
possibilities they don't need to be
affordable
because everyone has likes and dislikes
over consumption possibilities away
exceed
their purchasing power so that's not an
issue with tastes and preferences
taste and preferences stand alone and
so that is the material of chapter four
so we're going to deal with in this
lecture in the next lecture
and then in chapter 5 we will introduce
the idea of constraints we will bring in
income and prices and that is what will
determine
what the consumer's feasible consumption
possibilities are that is to say what
can the consumer actually afford
and so we're going to limit the entire
universe of consumption possibilities
to just those consumption possibilities
that are affordable
and we'll represent that through what we
call a budget constraint
and that's what we'll be doing in
chapter five
and then in chapter six
we want to talk about well of
that restricted opportunity of concern
that restricted set
of consumption possibilities which one
will the consumer choose
that is to say what does a consumer's
tastes and preferences
lead the consumer to purchase and
once we are able to identify what the
consumer's
choices will be based on what they can
afford
and their case of preferences then we
essentially are in a position
to derive the consumers demand curve and
discuss the efficiency or the welfare
considerations
that are inherent in that choice
so you know provide an overview in
the language of the authors of your
textbook we're going to assume that
rational consumers follow two basic
decision making principles
in their consumption choice first off
we're going to assume
that they are able to rank
in terms of desirability all possible
consumption opportunities affordable
enough
they are able to look at all possible
consumption
possibilities and they are able to
determine
a ranking of all of those from
say most desirable to least desirable
and there may be some that are ranked
equally in there but overall
the consumer can identify any bundle
which is preferred
to another bundle that's the ranking
principle
and then once the consumer ranks all
possible goods and
all possible consumption bundles from
most desirable to least desirable
then we bring in the choice principle
that is to say the consumer is able to
choose from among the affordable
consumption possibilities
that bundle that is most desirable
now how we're going to do this how we're
going to represent the consumer's tastes
and preferences
is through a construction that we call
indifference curves
so that's what we're going to do today
in this lecture
is we're going to construct
a model of this consumer's tastes and
preferences
using this idea of an indifference curve
and you know what these indifference
curves are going to reveal
to us one of the most important parts of
this
is a consumer's willingness to trade
or to substitute one good for another
because basically you know economic
behavior
is about making trades it's about making
exchanges
and so we're going to focus on how
indifference curves
enable us to characterize the consumer's
willingness
to make these trades these exchanges
and in this chapter two we're going to
use we're going to discuss the notion of
utility we're going to put together a
utility function
where utility is our term for the
satisfaction
or value in consumption that a consumer
gets
from a given consumption choice all
right
so if we think about the principles of
consumer choice here preferences
tell us about a consumer's likes and
dislikes
now it always is
the case that when you ask consumers
about
preferences taste and preferences they
confound it
with income and prices
you know you say well would you prefer
an apple or an orange and they say
things like
well it depends which one is less
expensive
but that's bundling too many variables
together
what we want to talk about in terms of a
consumer's taste and preferences
are those tastes and preferences that
exist
independent of the consumer's income
and prices you know if you think about
sort of a thought experiment here
suppose that you were
jeff bezos or bill gates or
tiger woods you have more money more
wealth
than you could ever spend in a lifetime
so that
your income and prices are totally
irrelevant
irrelevant all of those people still
have a set of tastes and preferences i
mean they're limited in their
consumption just by time
and in place but they still have
preferences among goods and services and
so i might say
to you well what would you rather have
would you rather have a maserati or a
ferrari
well no i'm not gonna i don't
think anybody in here maybe probably
has the money on hand
or the the the the purchasing power to
get
either a maserati or a ferrari but that
doesn't mean you still can't have
a preference between the two if i ask
you would you rather have a beach house
in malibu
or a ski
uh lodge in jackson hole
wyoming well you know they're both
multi-million dollar properties probably
none of us is going to buy one of those
in our lifetime
but it doesn't matter i still have taste
and preferences
i would rather have the beach house in
malibu
because i don't like cold weather so
it's my tastes and preferences
that enable me to make that choice and
to rank
those two consumption possibilities
right has nothing to do with
affordability
has nothing to do with my income per se
or prices
all right but
our consumer you know able to rank
every possible consumption possibility
is limited by purchasing power and so
what we have to look at then is when we
introduce constraints
or limitations on the consumer's
consumption possibilities
brought about through what is affordable
then the consumer
in our little world here who's able to
rank everything affordable or not
once that universe of consumption
possibilities is restricted to that
which is affordable
we're assuming then our consumer can
identify through the
ranking principle that affordable good
that yields
the highest level of pleasure or
satisfaction and consumption
all right so to put this all in one big
nut
what we have here is a consumer
who is fully informed about their tastes
and preferences but who is constrained
in their consumption choices is able to
identify
the bundle that they most prefer
based on their tastes and preferences
so you know we're going to start chapter
four today this lecture in the next
lecture we're going to deal with chapter
four
 today's lecture will probably be a little
shorter
just because i want to focus simply on
the idea
of indifference curves without confusing it with any other
ideas right now just to build the basic
construction
of an indifference curve and then in the
next lecture
we'll deal with this idea of
substitution
or the consumer's willingness to
substitute one good for another
as implied by the slope
of an indifference curve all right so
we'll start chapter four today
now what we want to do here
in this chapter as i say we'll just do
this first bullet point today
we want to illustrate consumers
preferences for consumption bundles
graphically
through this construction of
indifference curves
and then we want to take these
indifference curves and we want to use
them
to provide us important information
about
the consumer's willingness to exchange
and that all-important
use of an indifference curve this
willingness to trade one good for
another
is captured by a construction that we
refer to
as the marginal rate of substitution
all right the marginal rate of
substitution and i really want to focus
on that hard
because you have to understand
the marginal rate of of substitution you
have to grasp it
in order for our model of consumer
choice
to work okay you have to get that
so let's talk about definitions and
assumptions here
we're going to be dealing with what we
call consumption bundles
all right which is a collection of goods
that the consumer consumes over a given
period of time
now consumption bundle consists of many
different goods and services and there
is a
specific quantity a a given consumption
bundle contains
specific quantities of all possible
goods and services many of them might be
zero but
a consumption bundle contains specific
quantities
of goods and services and different
bundles
differ in their quantities
so that is our basic unit of consumption
a bundle and
you know our consumer is going to be
making choices then
over the universe of affordable
consumption bundles when we finally
introduce those constraints
so our consumer is going to make choices
that reflect then their tastes and
preferences
in terms of the bundles that they prefer
that give them the highest satisfaction
in consumption
so we're stuck here working in two
dimensions
you know there are thousands upon
thousands of possible
consumption goods in this class
we can only draw a world consisting of
two consumption goods because we have to
draw it on a flat surface
so what we're going to use in here from
my lectures at least your textbook's a
little different it uses actual
you know pizza and coke and stuff but in
here i want to just talk about
two consumption goods in this economy
which are x
and y now uppercase x reflects the good
itself
uppercase y reflects that good itself
and specific quantities then of good x
and y are denoted with
lowercase variables x and y
so that a specific consumption bundle
is a point on this graph where i have x
on the horizontal axis and y on the
vertical axis
and so i take this one point here that
contains and this is how i would show it
you know that there there are nine units
of x
and 10 units of y then is that point
in consumption space where our
consumption space
is the x y space here
so that is a consumption bundle for us
in this class
now we have to make some assumptions
about a consumer's taste and preferences
in order to begin our construction so
what we say is that a consumer faced
with any two consumption bundles a and b
that contain a different quantity of at
least one of the two goods
the consumer can always say whether the
consumer prefers bundle a to bundle b
or bundle b the bundle a
or the consumer can say and this is key
that the consumer is indifferent between
the two bundles so if a consumer prefers
a to b
it's because the consumer derives more
satisfaction from that particular
set of consumption goods those
quantities of consumption goods
than the consumer does from the
quantities that are in bundle b
and vice versa of course but if bundles
a
and b contain different amounts of the
two consumption goods
it doesn't mean that one necessarily has
to be better than another
a consumer could say well actually
those two different bundles yield the
same level of satisfaction
to me so i am actually indifferent
between those two bundles that's an
application the ranking principle
we also assume though that more of any
good
is better more is better the consumer
will always prefer
a bundle that has more of at least one
of the two goods
and not less of the other good
this is sometimes referred to as
non-satiation
more is always better now if you
go on an economics and you do a little
bit more sophisticated treatment of this
theory of the consumer
you might look at bundles where in fact
the consumer
is satiated and i could think of this in
terms of
you know putting sugar in your iced tea
you know one teaspoon of sugar in your
iced tea may be
very good if you you prefer the
sweetness of that teaspoon of sugar in
your iced tea to no sugar
and a second teaspoon might even make it
a little bit better
and if you really like sweet iced tea a
third teaspoon might you know
work for you but a fourth teaspoon
probably start making you sick and you
wouldn't want a fourth teaspoon in fact
it might make you worse off
and so that would violate this notion of
more is better
we are for now just to get up and
running disallowing
that possibility you are never satiated
you always be happier with a little bit
more of a good
if you don't have to give up any other
good
okay in this case more x and same y is
always better more y and same x
is always better more x and more y
is always better we also assume that a
consumer has
transitive preferences okay this is for
rationality so if a consumer prefers
bundle a to bundle b and the consumer
prefers bundle b
to bundle c then in order for our
consumers
tastes and preferences to be transitive
the consumer would have to prefer a to b
to c  so a preferred to b and
b preferred to c means that a must
necessarily
be preferred to c now
let me think about my consumption space
here
in terms of the preferences that i've
made
i've got bundle a here which contains 9
units of x
and 10 units of y
well if more is better
then bundle b contains more x and more y
than a so b must be preferred
to bundle a since it has more
of at least one of the two goods and no
less of the other
in point of fact any bundle that contain
nine units of x
but more than 10 units of y
must necessarily be preferred to bundle
a
and equivalently any bundle that
contains 10 units of
x excuse me 10 units of y
and more x the 9 must be also preferred
to a
and then all of the bundles in here that
contain more of both x and y
than a must be referred to a so it's
pretty straightforward just based on my
more is better assumption
that everything in this
rectangular area drawn here that is pink
must be bundles that are referred to a
and by the same logic then i can say
this
i can say any bundle that contains
10 units of y but less
than 9 units of x
must be inferior to the consumer
than bundle a and any bundle that
contains 9 units of x
and less than 10 units of y must also be
inferior
and then all the bundles in this area
here which contain less of both x and y
must be inferior in the consumer's mind
to bundle a
so you know i've i've taken this
consumption space here
and i have eliminated
uncertainty about a consumer's choice
over a pretty large area i know that any
bundle up here
compared to a will be preferred
any bundle down here preferred compared
to a
will be inferior so a would be preferred
to any bundle
in this rectangle here including along
the lines all right so that's
you know already a lot of work in terms
of thinking about how a consumer will
make choices
consumer will choose b over a
a consumer would choose a over c and by
transitivity the consumer
would necessarily choose b over c
now the problem here is
that we still have these
areas here that aren't cut and dried
there's nothing to say what a consumer's
choice would be
between a and some bundle that's out in
either this area here
or this area here we don't know
because these bundles out here like here
contain more x
but less y so there's a trade off there
and you can see where i'm going i'm
going to a trade-off
and up in this area here these are all
bundles
that contain less x but more y
so the question really is you know
if i look at a bundle up in these areas
where i have the question marks
the question is would the bundle be
preferred to a
or would a be preferred to that bundle
really depends
on the trade-off between the
new bundle and a and
the consumer's taste and preferences are
what are going to determine
whether that trade-off is favorable or
unfavorable
so you know if i come to this bundle d
this bundle d contains two fewer
units of y but three
additional units of x and so if i ask
you the question would the consumer
prefer bundle d to bundle a
or a to d you say well i don't know
it all depends whether the consumer
would be willing to trade away
two units of y
in exchange for three additional units
of x
so is that a good trade or a bad trade
and this is getting to the stuff of
economics here
we're talking about a consumer trading
making exchanges
would the consumer trade two wise
away in exchange for three x's
well what's that going to depend on it's
going to depend on the consumer states
and preferences
and the relative valuation that the
consumer is placing
on y and x
so what we need to look at is a way
to determine whether the consumer is
willing to make that tradeoff
and that's where our indifference curve
comes in
so what i need to do is i need to ask
the consumer
would you prefer d to a or a to d
and the consumer tells me well i prefer
d to a
well okay then if the consumer prefers d
to a
the consumer would be willing and happy
to trade away two y's for three x's
but i may ask somebody else that same
question that person would tell me well
actually i prefer a
to d so if i were to offer a trade to
this individual well
if you give me two y's you can have
three x's
my consumer would say no i'm not going
to do that because
i prefer bundle a to bundle d
so i prefer to keep my two y's and not
get those three x's in exchange
but there's a third possibility here and
that
is that when i ask my consumer if you
give up two y's
in exchange for three x's are you better
off or worse off
my consumer says you know i don't sense
a difference
i don't really care i'm indifferent
between a bundle with nine x's and ten
y's
and a bundle with 12 x's and 8 y's
i'm indifferent so those are my three
possibilities
the consumer prefers d to a would make
the trade
the consumer who prefers a to d would
not make that trade
and the consumer who is indifferent
between a and d would either make the
trade or not make the trade
and be neither better nor worse off in
either case
so i use what i call an indifference
curve and what the indifference curve is
is it is a depiction of all possible
consumption bundles
that yield exactly the same level
of satisfaction to my consumer as
bundle a so this indifference curve goes
through
bundle a and it represents
trade-offs between bundle a and any
other
bundle on that indifference curve
that would neither make the consumer
better off nor worse off
the consumer would be indifferent
so my indifference curve essentially
divides the entire consumption space
into three areas everything on that
difference curve
is equally good as a but everything
above that indifference curve to the
northeast
would be preferred to bundle a
and everything below that indifference
curve that is to say everything to the
southwest
would be inferior or worse than a
to this consumer now this indifference
curve arises based on our consumer space
and preferences
it's our consumer states of preferences
and enabled our consumer to rank
all these goods and then identify those
goods that are equally
satisfying in consumption
so what do i have i have all this xy
area
above that's preferred to a i have
everything below that indifference curve
that is worse than a
and then i have all of the in the uh
bundles of
potential consumption bundles that are
considered conceived and you know deemed
to be by our consumer
equally good as a now
this helps me solve my problem my
question was would my consumer prefer
a to d d to a or b indifferent
well if i draw an indifference curve the
indifference curve
that goes through bundle a my question
is answered
you can see that d lies above the
indifference curve through a
so my consumer would be very happy
to make that trade of two y's in
exchange for three x's
because that would move my consumer
into that area of consumption space that
is preferred to a
so yes my consumer would trade
two y's for three x's my consumer would
happily go from
a to d all right
now that's important you know this
picture right here is very important
because
it tells us what choice our consumer
would make
when confronted with this exchange
so we use this notion of a difference
curve
that you know that represents all
bundles
that a consumer likes equally well
and i drew one indifference curve that
went through that point a
that showed all bundles that our
consumer
likes equally well as a
right here's pizza and frozen yogurts
and so this indifference curve
divides our consumption space then into
these three areas preferred to
equivalent to a and worse than a
now what are properties of different
squares
they have to be thin they're only one
point wide
they're infinitely thin and as you can
see it has to be that way because if
they were thick
then we would have two consumption
bundles
on this indifference curve that would
say well they're on the same
indifference curve so they must be
equally
valued by the consumer but clearly b has
more of both goods than a
which violates our
more is better assumption so if b
has more of both goods than a it must be
preferred to a
so they couldn't be on the same
indifference curve so we can eliminate
fat indifference curves they have to be
thin
and
in fact infinitely thin one point
wide they cannot slope upwards
and they have to always be downward
sloping because
as you can see if i were to go from
point d to point e
they're both on the same indifference
curve although this is an upward sloping
portion of the indifference curve
e clearly would have to be referred to d
again
by our non-satiation or more is better
assumption
and so if e has more of both goods than
d then it has to be preferred to d
it can't be on the same indifference
curve
all right so e and d cannot be equally
valued by the consumer since e has more
of both goods
and the indifference curve that runs
through the consumption bundle a
separates this is a repeat here all the
better than a
from the worse than a bundles but also
from the
equal to or equivalent to a in
consumption
now every point
in consumption space is on an
indifference curve
every point has to be on an indifference
curve
and a full set of preferences
then is what we call an indifference map
so that i might have point a on this
bundle
you know point g on this bundle point l
on this bundle and point z on this
bundle
and for all those points as i'm going in
this direction as i'm going toward the
northeast
i'm moving to new indifference curves
but those indifference curves contain
bundles that are to the northeast
of the lower end difference curves
therefore must consist of bundles
that are preferred to bundles on lower
indifference curves
so every bundle on this indifference
curve is of equal value to our consumer
consumption but every bundle on this
indifference curve
is deemed to be better preferred to
every bundle on this indifference curve
which is to say i can take this bundle
up here
say bundle a up here
and tell you right off the bat is better
than bundle b
down here simply because the bundle on
this indifference curve
and all bundles on this indifference
curve is strictly preferred
to all bundles on this lower
indifference curve
and the same is true for all the
indifference curves so when i think
about every possible bundle being on an
indifference curve
a full representation of preferences is
this
preference map and
this preference map then enables me
to always determine what choice a
consumer would make
when offered alternatives now
indifference curves from the same family
you know from the from uh the same
preference map
cannot cross so if i had two
indifference curves across
well as you can see i've got a problem
here
because d and a are equally good
and a and b are equally good so
by transitivity if d is equal to a and a
is equal to b
in consumption then d must be equal to b
but clearly b is inferior to d because d
contains more of both consumption goods
so my transitivity assumption my
rationality assumption my transitivity
assumption
means that indifference curves cannot
cross
right being on the same indifference
curve the consumer would be indifferent
between
d and b by virtue of transitivity
and that violates our basic consumption
all right
consumer prefers bundles on the
indifference curve
furthest from the origin okay again
since the area above an indifference
curve
consists of bundles that are preferred
to the bundles on the indifference curve
that must mean that as i go to higher
and higher indifference curves
i'm moving to bundles that are valued
higher and higher in consumption by my
consumer
now what would an algebraic expression
of a difference curve look like
well here for example
is a a an algebraic representation
of an indifference curve and i'm going
to call this
an indifference curve that is associated
with a given level of satisfaction
we'll just call that u right it's really
going to be utility for us but we
haven't talked about utility yet so
we'll just call this the level of
satisfaction
u and if i'm looking at an indifference
curve then
all of the different bundles on that
indifference curve must
yield the same value u
all right that's what we mean by being
equal in consumption
that the product of the quantities of
the two goods
is constant and so even though we change
quantities their
product stays constant or these two
goods
yield the same level of satisfaction and
consumption
so in this sense if we think about this
utility
equal to c times f a bundle consisting
of
two x's and ten y's would give the
consumer
or two c's and 10 f's would generate
a benefit or a measure of satisfaction
of 20.
so the units of the benefit measure
themselves
are meaningless in other words
you know the the the you has no real
interpretation
except higher values of you imply
higher values of satisfaction
consumption and lower values of you
lower values
and any set of consumption goods
that yields the same value for you
using this expression c times f or x
times y
means that they are indifferent between
those two consumption
bundles so here we are if a bundle was
referred to 210
then the consumer's benefit or utility
that would be associated
with a higher number so for any bundle
where the product is greater than 20
would imply a bundle that yields more
satisfaction to the consumer
again i make no other interpretation of
this except higher u
better and of course
if the product of these two quantities
was less than 20
it would be a bundle that yields
less satisfaction in consumption than
any bundle that yields 20.
so in a difference curve through that
point
two x's and ten y's would be all the
bundles that yield a benefit to a
consumer of exactly 20.
all right so we can express the equation
of the indifference curve
that goes through that bundle 210 we can
express the equation it's a little
confusing this would be x times y equals
20.
we can express the equation of the
indifference curve then
as c is equal to 20 over
f just by rearranging all right so i
so i've got c times f equals 20 so c
must be equal to f
over 20. and so this gives us the
relationship
which is to say all of the bundles
that yield exactly 20
the value of the utility function of
that value of u of 20.
so let me back up here i've got c is
equal to
u over f now if i look at this bundle
right here
let's say this bundle
1 and 10 every bundle on this
indifference curve
then yields a level of u or utility
equal to 1 times 10 or 10.
so the equation of this indifference
curve
would be c which is cheese piece on the
vertical axis
is equal to 10 divided by frozen yogurt
on the horizontal axis
and if i look at this particular point
this contains two f's
and ten c's
2 times 10 is 20 so all the bundles on
this indifference curve
yield 20
u u equal to 20. so the relationship
between c
and f for all the bundles that yield
u equal to 20 that relationship is
described by c
equals 20 f well so here we've got
you know uh 10 is equal to 20 over 2
at this point on that same indifference
curve i've got what
i've got 5 is equal to 20 over 4
and at this point on the difference
curve i have 4
is equal to 20 over 5.
so all of these points on this
indifference curve
are values of c and f whose
product is equal to 20.
all of the bundles on this indifference
curve are values of c
and f whose product equals 30.
and of course on this one product equals
10.
but what i want to do is put this in
standard algebraic
form so i have the variable on the
vertical axis
on the left hand side and then the
variable on the vertical axis
on the horizontal axis on the right hand
side
so this is my in this is my dependent
variable this is my independent variable
you might say
if you learned that in your algebra
classes
but this relationship expresses my whole
u constant
it expresses the relationship between
the two consumption goods
that are on the same indifference curve
now key here as long as the consumer's
taste and preferences do not change
their indifference map does not change i
have graduate students
who try and shift indifference curves
you can't shift indifference groups
you have to tell me that there's been
some material change in the individual's
tastes and preferences
whether you know i don't know they got
hit by a
rock or you know something you know
altruism
someone clobbered him over the head and
it caused a personality change
but the preference map is fixed
it doesn't move and that's gonna be very
important when we get to other variables
that do move if you keep in mind this
indifference map does not move
and the only way that a difference curve
would shift
is if the consumer's taste and
preferences change and there's no reason
to expect our consumer states and
preferences to change it in the short
run
you know at least i'm certain
you know as you
go from being a child to an adolescent
to
a young adult your taste and purposes
are going to change but
over the course of this
semester no one's taste and preferences
are going to change
and when moving from one bundle another
then
we either are moving to different
indifference curves
because the indifference curves are there
when we go from bundle a to bundle b
for example we are simply either going
to a new indifference curve
or along the same indifference curve
and when any other variable changes such
as prices or income
remember that comes later price is an
income but when those things
change it doesn't have any effect on our
consumers tastes and preferences they
exist independent of those
variables there's no change in the
consumer's
tastes and preferences all right so the
next lecture we're going to introduce
this idea of marginal rate of
substitution
and
the notion of utility functions which
 i basically already breached
but we're going to make it more explicit
and we'll talk about
the algebra of indifference curves a
little further and then use that
as a means to
operationalize our use of this
indifference man
so the next lecture will cover the
material on chapter four that is intended to
as i say make our indifference model
operational all right
so i'll see you next time
