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PROFESSOR: We're going to start
with an interesting
application of demand curve
analysis, of the kind of
indifference curve and
constrained choice analysis
we've been doing, the
case of food stamps.
And then we're going to move
on and talk about deriving
demand curves.
So let's talk about
food stamps.
It's an interesting case.
This is a policy that's been in
place in the US government
for a very long time, which are
essentially coupons that
individuals can use
to buy food.
It used to literally
be coupons.
It used to literally, you'd
get a stamp, a coupon, and
you'd go to the supermarket and
hand this in instead of
cash to buy your goods.
Now it's actually
a debit card.
And it's given to low-income
individuals as a way of
redistributing income
in society.
So individuals of income below
a certain level, typically,
say, a family with income below
about $25,000 a year,
below what we call the US
poverty line, will be eligible
for food stamps, which is a
debit card they can use to
charge their food purchases.
Now, what I want to talk about
today is how we can use the
kind of analysis we've done so
far to think about the effect
of food stamps.
So let's start with
figure 6-1.
And let's think about someone
with an original budget line.
If someone has a budget line,
they have income of $1,000.
OK, a very poor person, they
have income of $1,000.
And let's talk about them, their
choices between food and
all other goods.
Once again we have
this analysis.
We put everything in
two dimensions.
What we think about is via
mental accounting, as we
talked about last time.
However you want to justify it
to yourself, the way we model
it is thinking about people
having this choice along two
dimensions, food and other
goods, and they
have income of $1000.
Let's say we'll have
two individuals,
individual x and y.
Individual x doesn't care
that much about food.
They really like consuming
other goods.
So they spend $600 of their
income on other
goods and $400 on food.
Individual y cares
a lot about food.
They end up spending $900
of their budget on food.
And that should be 100.
100 on other goods.
So that y-intercept should
be 100 for person y.
So they spend 900 on food
and 100 on other goods.
Now let's say the government
comes in and wants to consider
two options.
The government decides, look,
we want to help poor people.
And particularly we want to give
people like these people
$500 in resources.
Let's think of two different
ways the
government could do that.
One way the government
could do it is it
could give them cash.
It could say, look, we're
going to send
you a check for $500.
What would that do to their
budget constraint?
Well that would shift it out, as
we talked about last time.
It would be an outward shift
of $500 at every point.
So their new budget constraint
would be the line that runs
from $1,500 of all other goods
to $1,500 dollars in food.
So include that.
So both the solid and dashed
portions would be their new
budget constraint.
So the new budget constraint
would run from 1,500 to 1,500.
Person x would choose to
move from x1 to x2.
I'm sorry, they would choose
to move from x1.
It's not labeled as a point.
But they would actually choose
to move from indifference
curve 2 to indifference
curve 3.
OK, that's where they'd choose
to move if they could choose
along this entire line.
Let me sort of, well, I'm not
going to draw it, because I'll
do a bad job.
But basically, if you can think
about the new budget
constraint running from 1,500 to
1,500, person x would move
from indifference curve 2
to indifference curve 3.
They would choose--
Actually, you know what?
Let's put this graph aside.
It's not quite right along
the number of dimensions.
I'm going to draw this, because
there's a number of
problems with that.
So you've got an original budget
line that runs from
1,000 to 1,000.
And we've got person x up here,
and they're choosing to
spend 400 on food and
600 on other goods.
And we've got person
y down here.
This is person x, and they're
in section x1.
And person y intercepts at y1
where they choose to spend 900
on food and 100 on
other goods.
Now, the government first says,
look, we're going to
give people $500 in cash.
That just shifts the budget
constraint out parallel, but
now runs from 1,500 to 1,500.
Let's say that the choices
people make--
Person x would say, great, I'm
going to take that money, I'm
going to spend almost all
of it on other goods.
So I'm going to move to a point
like x2, where I'm going
to consume $1,200 on--
I'm going to consume--
They were consuming--
No, I'm sorry.
15, right.
They're going to move from
spending $600 on other goods
and $400 on food to spending
$1,100 of their dollars on
other goods, and--
let me think for a second.
Let's say they would
go vertically.
So let's say they'd choose
to spend all
of it on other goods.
So they'd take the whole 500,
and they'd go from spending--
they'd continue to spend 400 on
food, but now they'd spend
1,100 on other goods.
So person x, they would
continue to
spend $400 on food.
They'd say I'm going to take
that entire $500, instead of
spending $600 on other goods,
I'm going to spend $1,100 on
other goods.
Let's say person y, they would
say, well I'm going to
sort of split it.
I'm going to spend
some on food.
So this is their new
intercept x2.
I'm going to spend some on food,
and I'm going to spend
some on other goods.
So I'm going to go out here.
I'm going to spend now--
instead of spending
$900 on food, I'll
spend $1,200 on food.
I'll take $300 and
spend it on food.
Instead of spending $100 on
other goods, I'll spend $300
on other goods.
OK, so that's person y2.
OK, so that's what they'd do if
we gave them $500 in cash.
Now say the government came in
and said, you know, we're
going to give you $500 but in
the form of a coupon that you
can spend on food.
So the first question is, what
does that do to the budget
constraint?
This is a bit tricky.
We've got to think about this.
Think about their budget
constraint.
What that says is for anyone who
wants to continue to, at
least spend $1,000 on--
anyone who wants to at least
spend $500 on food, it does
not change their opportunities
at all.
So the new budget constraint
looks like this.
It's a solid line to here,
and then it goes down.
This intersects at 500.
It's a solid line to the point
at $500, and then it goes down
and follows the old
budget constraint.
Why does it do that?
Because for anyone to this side,
they are $500 richer
regardless of whether you
give them cash or food.
Either way they're
$500 richer.
Why?
Because as long as you intended
to spend $500 on food
anyway, it doesn't matter the
form in which the government
gives you the money.
Think about that for a second.
It's very important.
If you were going to spend $500
on food anyway, it does
not matter if the government
gives you a check for 500, or
a food card for 500.
Why is that?
That's because your budget
is what we call fungible.
You can always move money around
within your budget.
So let's say you're spending
500 on cash.
Let's take a person like y.
Let's take a person like y.
They were spending 900 on food
and 100 on other goods.
The government comes
in and gives them a
food card for 500.
Well to them that's the same
as $500 in cash because
they're already spending
$900 on food.
They can just take some of the
cash on food, spend it on
other things, and use the card
for the food instead.
So for them, there's no
difference in giving them cash
or giving them the food card.
It has the same effect.
They move to y2 either way.
Now let's take a
person like x.
Well, if you gave them cash,
$500 cash, they'd spend none
of it on food.
So they've been consuming
$1,100 of other
goods and $400 of food.
But they can't do that if you
give them a food card, right,
if you give them food stamps.
That's not a choice.
They are now constrained to
move to a point like x3.
They're now constrained to move
to a point like x3 where
they have to go to this
intersection.
Because this point is
not attainable.
This point is not attainable.
If you give them food stamps,
the new budget
constraint is this.
So x2 is no longer attainable.
They have to move to
a point like x3.
So what do we know about their
level of happiness
at x3 versus x2?
Someone raise their
hand and tell me.
Yeah.
AUDIENCE: It's lower.
PROFESSOR: It's what?
AUDIENCE: Lower.
PROFESSOR: It's lower.
And how do you know that?
AUDIENCE: Because it's kind of
like, if it was on the full
curve, they would
be elsewhere.
PROFESSOR: Well OK, so there's
two different ways to see it.
One is you could say, look
they're at a lower
indifference curve.
You can see what's wrong
with this graph.
The indifference curves cross.
The indifference curves
can never cross.
So that's wrong there.
They're on a lower indifference
curve, OK.
But what's the other way
to think about it?
AUDIENCE: The marginal rate
of substitution and
transformation aren't
the same.
PROFESSOR: The marginal rate
of substitution and
transformation aren't
the same.
That's another way
to think about.
And that's always true
at the optimum.
But what else do we know about
a point like this?
They could have chosen that
point before and didn't.
Right?
When they had the cash, they
had the option of choosing
this point, but they didn't,
they chose a different point.
So we know by something called
revealed preference that
they're worse off.
This is a very important
concept.
If someone makes a choice that
they turned down before, then
by revealed preference they're
less well off.
We've revealed that they're
worse, because they could have
chosen this point before,
but they didn't.
When you gave them the cash,
they chose this point.
So by revealed preference we
revealed they're worse off.
So it's the same
as saying their
indifference curve is lower.
We've revealed they're
worse off.
So what we've learned is for
person y, they don't care if
you give them cash or a food
card, food stamps.
It's called food stamps, but
it's now a debit card.
Person x is made worse off if
you give them the food stamps
instead of the cash.
Why do it?
You're the government.
The US government spends $35
billion every year giving
people food stamps
instead of cash.
Why don't we just take that
$35 billion and give it to
them in cash?
Yeah?
AUDIENCE: Probably because the
government doesn't trust
people to spend it on what
they actually need.
And that will just lead to
more poverty and people
wasting it on things
they don't need.
PROFESSOR: Or to put it more
succinctly, what if this axis
was not labeled other goods
but labeled cocaine.
Then we might be sad that you
took the whole $500 and spent
it on cocaine.
We might want you to take that
$500 and spend it on food.
So it's paternalism.
The reason we give the guys food
stamps instead of cash is
we don't trust them
with the cash.
If we trusted people with the
cash, there'd be no reason not
to give them the cash.
We are unambiguously making them
worse off by forcing them
to consume a bundle that's on
a lower utility curve, lower
indifference curve.
But since we don't trust them,
since we're paternalistic, we
are willing to go ahead and
force them to do that.
So then the interesting question
becomes, well, how
much are we costing them?
In fact, it's not obvious.
If everyone in the world looks
like y, then there's no cost
to food stamps.
There's no good done either.
Then it doesn't matter if we
give them cash or food stamps.
But if a lot of people look
like x, then there is a
welfare cost to people.
They are worse off, from
their own perspective,
getting food stamps.
Society may think they're
better off.
So how do we tell?
How do we tell?
Can anyone take a guess?
If you're now an empirical
economist, and you want to
test, how would you tell if
people are like x or like y?
Any ideas?
It's tricky, but let's see if we
have any budding empirical
economists here.
Yeah?
AUDIENCE: You'd see if they're
spending any cash beyond the
$500 that you gave them, because
then you'd basically
[UNINTELLIGIBLE].
PROFESSOR: See if they're buying
food beyond the $500
you gave them.
AUDIENCE: They might spend
$100 cash on food.
PROFESSOR: Excellent.
So that's one way you'd do it.
You could look at people who
get food stamps and see if
they're spending more.
That's a great idea.
The other thing you could
do is you could actually
literally run an experiment
where you take people who are
getting food stamps and replace
them with cash or vice
versa and see what happens
to their behavior.
When we do this, we find
that about 15% of
people are like x.
Or in other words, the
way to say it, is
about $0.15 more precisely.
When you give people food stamps
instead of cash, they
spend 15% more on food than they
would if you just gave
them the cash.
So there's about 15% lower
utility compared to what
they'd want for spending it on
the food instead of the cash.
So the question is,
is it worth it?
We're basically taking people
and making them spend $0.15
more on food than
they'd want to.
That's the right way
to think about it.
If you give them food stamps
instead of cash, they spend
$0.15 more on food than
they would if you
just gave them cash.
Is it worth it?
That's a great question.
It depends on how stupid we
think people are and how
paternalistic we want to be.
If we think people would really
waste the money, then
$0.15 is not much to give up
to make sure they eat.
If we think nobody would waste
the money, then we're just
throwing $0.15 down the toilet
by making them buy food
instead of goods they prefer.
And that's the interesting kind
of public policy question
we have to struggle with.
We think about government policy
and redistribution.
That's exactly the kind
of question we
need to struggle with.
And we'll come back to that
again later in the course when
we talk about efficiency
versus equity.
OK, questions about that?
Yeah?
AUDIENCE: [INAUDIBLE PHRASE].
PROFESSOR: Sure.
I mean, so basically you
make a good point.
We sort of like to know.
Actually that's a
very good point.
You say, when we run these
experiments and replace the
food stamps with cash,
we like to know what
they spend the cash.
We want to know not just what
happens to food consumption.
So if you run the experiment,
and you say, I was giving you
food stamps.
I now cash you out and
give you cash.
And I find you spend
15% less on food.
Well what do you
spend more on?
If it's clothes, maybe
we're not so worried.
If it's cocaine, maybe we are.
So that's a very good point.
That's something we
could look at.
Excellent.
OK, so that's an example of
how we can use the kind of
analysis we did last time to
think about policy making.
Once again, this is
an incredibly
simple framework, right?
Yet I just described to you a
succinct way to think about
the implications for society of
different government policies.
That's the power of this kind
of simplified framework.
Now let's move on, and let's
get to the core of
why we did all this.
The reason we did all this is we
wanted to figure out how we
come up with demand curves,
where demand curves come from.
The stork doesn't bring them.
Demand curves come from
underlying utility
maximization.
And we'll see that now.
And basically the way to do
this is to return to our
example from last time.
Your parents gave you $96.
You could buy movies at $8 a
pop or pizzas at $16 a pop.
So we said last time,
if you turn to the
next page of the handout.
What we said last time is if
given your utility function, u
equals square root of p times
m, you would choose
a point like a.
If the price of pizzas was $16,
the price of movies was
$8, your income was $96, you
would choose a point like a,
where you consumed--
At point a, you're consuming six
movies and three pizzas.
Once again that should
be p on the y-axis.
You're consuming six movies and
three pizzas at point a.
Now let's say the price
of pizzas rises.
I'm sorry, now let's say the
price of movies rises to $12.
So the price of movies
rises from $8 to $12.
Well what does that do to
the budget constraint?
That steepens the budget
constraint, moves it inward.
Because now think about
your opportunity set.
For the same income of $96 you
can buy the same number of
pizzas you could have before,
but now you're
buying fewer movies.
Same number of pizzas you could
have bought before, but
now you can buy fewer movies.
So your new budget constraint,
you have a new constrained
opportunity set.
With a steeper budget
constraint, the slope, instead
of being minus 1/2,
is minus 3/4.
And given the preference I
wrote, u equals square root of
c times m, you should be able
to show yourself that you'd
now choose a point like b, where
you have three pizzas
but now only four movies.
So you reduce the number of
movies, you keep the number of
pizzas constant.
And you check that we still
spent our total budget.
Well, 4 times 12 plus 3
times 16 is still $96.
So we're still spending
our total budget.
The marginal rate of
substitution you can compute
if you write it down from that
utility function, will be
minus 3/4, which is the same
as the marginal rate of
transformation with
this new price.
So you will choose a
point like point b.
Now let's say instead
the price of movies
fell from $8 to $6.
Well in that case, your budget
constraint would flatten.
It would move outwards.
Your opportunity set would
expand in that case, because
effectively you're richer.
Your opportunity set expands.
You move to bc little 3.
You move to bc little 3.
And given those preferences I
wrote down, u equals square
root of p times m.
u equals square root
of p times m.
You end up choosing point c,
with the same three pizzas but
now eight movies.
Once again, how do we
know that's right?
Well first of all the marginal
rate of substitution, you can
compute, will equal the
new marginal rate of
transformation.
And also you can see you spend
your entire $96 income.
You're still roughly splitting
it with $48 on movies and $48
on pizza, exactly
splitting it.
So all we've done here--
Forget the bottom diagram
for a second.
All we're doing in this top
diagram is saying, given your
utility is u equals square root
of p times m and given
your income and the prices,
these are the choices you
would make as prices change.
Are there questions
about that?
Now armed with that, we can
draw a demand curve.
Because what have we done?
We've just given you three
different prices for movies
and three different quantities
of movies you choose.
We know when the price
of movies was $8,
you chose six movies.
That's point b.
I'm sorry, that's point a.
The points are mislabeled
too on this.
I'm sorry.
If you go to this bottom
graph, these points are
mislabeled.
So it should go b, a, c.
It should go b, a, c.
So when the price of movies is
$8, that's point a in the
middle, you choose 6 movies.
When the price of movies
rises to $12, your
demand for movies falls.
You only choose 4 movies.
When the price of movies falls
to $6, you choose 8 movies.
Thus the demand curve.
And we're done.
That's where demand
curves come from.
They just come from utility,
constrained utility
maximization.
You just take your utility
function, you maximize it,
given the constraint the budget
constraint places on
you, and boom, you have
a demand curve.
Now note that this a particular
case we did.
And it's a particular case
that's interesting.
In this case as we change the
price of movies, what happened
to demand for pizzas?
AUDIENCE: Stayed the same.
PROFESSOR: Stayed the same.
That is a particular case.
It's basically the case that
will happen with utility
function of this form.
It's a case of what we call
no cross-price elasticity.
This example has no cross-price
elasticity.
What that means is that in this
particular case we chose,
as the price of one good
changes, it does not change
your demand for the
other good.
That's a special case that will
not in general be true.
You can imagine if your income
was only $96, and the price of
movies was swinging around, that
might affect your taste
for pizzas.
That might affect your demand
for pizzas as well, because
you're only have
a fixed budget.
That's a more general case.
We've chosen a particular case
here with no cross-price
elasticity.
But don't think that's
general.
This is not a general lesson.
There's the price of one good
changes the other goods
unaffected.
In fact, in general, both goods
will be affected when
any one price changes.
That's a more general result.
You should be able to check at
home that you can do this
exact same exercise for pizzas
and draw the demand curve for
pizzas the exact same way.
You'll still get a flat--
you'll still get no
cross-price elasticity.
You'll still get this flat
curve-- well now it will be
vertical curve with respect
to movie purchases.
But you can see as you change
the price of pizzas, you'll
find a well-defined pizza
demand curve as well.
OK?
So that's where demand
curves come from.
We basically maximize utility at
different prices given your
income, and we end up with a
demand curve that shows us the
relationship between how many
movies you choose and the
price of movies.
Demand curves themselves
can also shift.
We talked about that in
the second lecture.
We talked about demand
curve shifting.
And one reason demand
curves can shift is
because you get richer.
So let's talk about how
that can happen.
Let's now turn to figure 6-3,
which is really tiny.
My bifocals are in
at the mall.
I just haven't picked
them up yet.
So let's take the glasses
off for this one.
Now let's take a case.
Once again, originally you're
at point a, where you're
choosing six movies
and three pizzas.
Now let's say your
income rises.
Your parents are feeling
generous.
And instead of giving
you $96, they're
going to give you $128.
Once again, on that y-axis it
should be labeled p, not c.
You can now afford up to 8
movies and up to 16 pizzas
with your $128 income.
So your budget constraint
has shifted
outwards from bc1 to bc2.
At that new higher budget
constraint, you're going to
choose, instead of choosing a,
which is six movies and three
pizzas, you'll choose
b, which is eight
movies and four pizzas.
You're richer so you choose
more of both.
Likewise if your parents cut
your income to $64, you're
budget constraint will
shift inwards.
Your opportunity set will
be constricted.
You move to budget
constraint three.
And you choose fewer of both
pizzas and movies.
So you can see as your budget
constraint shifts, how you
choose different amounts of
both pizza and movies.
We can translate that
to shifting
demand curves for movies.
So if you draw that down to
the next diagram, you say,
look, I can now graph that at
a given price of movies--
prices have not changed
in the example.
The slope of the budget
constraint is the same.
Only your income has changed.
At a given price of movies of
$8, as my income changes, I am
on different demand curves.
You can see the demand curve for
movies shifting out and in
as my income changes.
So as my income went up, the
demand curve for movies went
out and moved from point
a to point b.
As my income fell, the demand
curve for movies went up,
shifted in, moved from
point a to point c.
We can then drop that down one
more level, just to make life
especially interesting, and draw
the relationship between
your income and your
demand for movies.
And that's the third figure.
Here we graph the relationship
of your income and your demand
for movies.
This is not a demand curve.
Demand curves only relate
price to quantity.
This is what we call
an Engel curve.
Those of you who studied your
socialism theory will remember
Engels worked with Marx.
It's not him.
It's Engel not Engels.
Different guy.
So basically this is
an Engel curve.
And basically it shows the
relationship between your
income and your demand
for a good.
And this turns out to be a
very important concept.
Because an important thing that
we'll focus on now is
what we call the income
elasticity of demand.
We've talked about price
elasticities.
What's the price elasticity
of demand?
Someone quickly, someone raise
their hand and tell me, what's
the price elasticity
of demand?
Get some other folks
involved here.
Yeah?
AUDIENCE: How demand changes
with the price of the item?
PROFESSOR: Right, so as price
changes, how demand changes.
The income elasticity
is the same concept.
It's a change in demand as
your income changes.
In the book it's this
fancy letter.
I can't write, so I'm going
to call it gamma.
But it's some c thing that
I can't draw in the book.
Which is delta Q over Q
over delta y over y.
So just like the price
elasticity is the percentage
change of quantity, percentage
change in price, the income
elasticity is the percent
change in quantity with
percent change in income.
Once again, just like price
elasticities are locals.
You talked about
it in section.
You talked about, sort of,
local versus global price
elasticities and how it's really
local to that segment
of the curve.
Income elasticities
are local too.
Your income elasticity will
obviously change along an
Engel, could change along
an Engel curve.
But the key point is that for
most goods the Engel curve is
upward sloping.
That is for most goods, this
is greater than zero.
Just like we talked about the
price elasticity being less
than zero in general, this is
less general, but for most
goods, the income elasticity
is greater than zero.
We call these normal goods.
Normal goods are goods for which
the income elasticity is
greater than zero.
As you have more income,
you buy more of them.
On the other hand, if the income
elasticity was less
than zero, we would call
those inferior goods.
Inferior goods, goods where as
your income goes up, you buy
less of them.
Yeah.
AUDIENCE: Is there any term
for when income elasticity
equals zero?
PROFESSOR: If it equals zero,
you're just income inelastic.
It's in between normal
and inferior.
I don't think there's
a precise term.
You're just income inelastic.
So can someone tell me how you
could get an inferior good?
Does anyone have a good
idea of an example
of an inferior good?
How could a good be inferior?
Yeah.
AUDIENCE: Canned food, because
if you have a low income, you
buy canned food because
it's cheaper.
But [INAUDIBLE].
PROFESSOR: Exactly, so canned
food versus fresh food.
As your income goes up, you'll
substitute away from canned
food to fresh food.
So actually as you get
richer, you'll
consume less canned food.
So canned food is an
inferior good.
Excellent.
The classic example
uses potatoes.
Potatoes is a good
cost-effective, cheap source
of nutrition.
But, you know, no one wants to
eat potatoes all the time if
they don't have to.
So when the income goes up, we
substitute away from potatoes
towards arugula or whatever.
So basically, essentially
we could think of
inferior goods as goods--
Once again, more is
always better.
There's no goods
we don't like.
More is always better.
But there are goods we'd like
to substitute away from.
We'd like to have
others instead.
And goods you substitute away
from as you get richer are
inferior goods.
Goods you move towards as you
get richer are normal goods.
Moreover, we can break
this down further.
Within the class of normal goods
we can talk about gamma
less than one and gamma
greater than one.
Any guess as to what terms
I'll use for gamma?
Any examples in, sort of, the
class of goods where it would
be less than one versus
greater than one?
What's an example of a good that
would be less than one?
Think about what that means.
Yeah.
AUDIENCE: Perhaps food,
because if your income
[INAUDIBLE PHRASE].
PROFESSOR: Right.
AUDIENCE: [INAUDIBLE]
if your income increases.
PROFESSOR: Excellent.
So we call these necessities.
And we call these luxuries.
Goods where the income
elasticity is less than one
are necessities.
You want more of them
as you get richer.
But you don't want as much
more as you get richer.
So you've got the food as
the classic example.
As your income doubles, you're
going to eat more food but not
twice as much food.
Likewise luxuries are things
where as your income doubles,
you'll buy more than
twice as much.
So you think about fancy cars.
You might buy one with your
first million but three with
your next million.
So those are luxuries.
They'll increase more than
proportionally as
your income goes up.
Necessities will increase less
than proportionally as your
income goes up.
Now, of course, it's a very
hard distinction to draw.
And of course it varies
by person.
So take clothing.
Is clothing a necessity
or a luxury?
Well, some clothing is probably
a necessity, and some
clothing is probably a luxury.
You know, Dolce and Gabbana
is a luxury.
You know, Keds is a necessity.
Or whatever, I don't know, what,
The Gap is a necessity.
So basically we could think
about, it's actually a subtle
distinction what makes
luxury and what's--
Normal versus inferior
is kind of stark.
Luxury versus necessity, that's
a little bit trickier.
That's going to depend on
the person and depend
on the type of goods.
But it's important to understand
that concept.
OK, questions about that.
Yeah.
AUDIENCE: I have a question
in general.
Is there a way to relate income
elasticity to, like,
own-price elasticity?
PROFESSOR: Actually that's
a great question.
That's a great segue to what
we're going to do next.
It's actually a fundamental
determinant of own-price
elasticity, and we'll
talk about why next.
Other questions about
this concept?
Yeah.
AUDIENCE: [INAUDIBLE PHRASE]?
PROFESSOR: Yes, income
elasticity is, once again,
just like price elasticities are
not necessarily constant.
You could have a constant income
elasticity curve or a
non-constant income
elasticity curve.
It can absolutely change.
In general it will.
But it might not.
Good questions.
But that other question in the
back, gee, how does this
relate to own-price
elasticity?
Great segue.
In fact the income effect is
going to be one of two key
determinants of own-price
elasticity.
Now what we're going to do is
we're going to go even further
behind the demand curve.
We talked about the demand
curve comes from.
We talked before about how the
slope of the demand curve is
the price elasticity.
Remember, the price elasticity
was the slope.
Now we're going to talk
about where does
the slope come from.
Where do price elasticities
come from?
So I've shown you where the
demand curve comes from.
Now let's talk about what
determines the underlying
slope of the demand curve.
What determines the
price elasticity.
And what's going to determine
it is two different effects
which work generally together
but sometimes in opposition.
There are two effects that
determine price elasticity.
The first is the substitution
effect.
The Substitution Effect is the
change in quantity demanded
when price increases holding
utility constant.
So the Substitution Effect
is delta p--
it's in percentage terms-- delta
p over p, over delta q
over q, holding utility
constant at a
fixed level u bar.
So given that your utility has
not changed, how does your
demand for the good shift?
We're now getting
kind of deep.
Think of this as, as a good gets
relatively expensive, how
do you shift away
from that good?
Think of this as the
shift away from the
good as it gets expensive.
But at the same time, there's a
second effect which we just
introduced, which is
the Income Effect.
The Income Effect is the
complement of the Substitution
Effect, which is the change in
quantity demanded because of a
change in income holding
prices constant.
So this is the Income Effect
we just introduced.
So it's delta Q over Q
over delta y over y.
But this is holding
prices constant.
And these two put together
determine your
own elasticity demand.
Think of it intuitively.
We'll do it intuitively,
and graphically, and
mathematically.
Intuitively, it's when a price
goes up, two things happen.
On the one hand, you're like,
gee, at that different price
ratio, I might want
to substitute
my consumption bundle.
The second is, gee, the
price just went up,
I'm effectively poorer.
And that's also going
to affect my demand.
So to see that let's
go to the graphical
analysis and figure 6-4.
And we're going to actually
decompose income and
substitution effects.
This is one of the things that's
sort of hard to do it
intuitively.
The graphics kind of makes
it the most clear.
We're going to start
at a point like a.
Point a is our initial
equilibrium at our budget
constraint one, where
we're choosing six
movies and three pizzas.
Once again, this is
pizzas not CDs.
We're choosing six movies
and three pizzas.
That's at point a.
Now we're going to say imagine
the price of movies
has risen to $12.
Well we know that ultimately
you'll end up at
a point like c.
We demonstrated that before.
That was when we derived the
demand curve for movies.
We know that if the price of
movies rises from $8 to $12,
your demand for movies
will shrink from six
movies to four movies.
We already established that.
But now what we can see is
that that's actually a
composition of two effects.
The first effect is the
Substitution Effect.
And the Substitution Effect is
the change in prices holding
utility constant.
How do we hold utility
constant?
You have to be on the same
indifference curve.
So the way to measure the
Substitution Effect is we
effectively draw an imaginary
budget constraint.
We say, look, imagine you're
on the same indifference
curve, but prices changed.
So we draw budget constraint--
you're originally on budget
constraint one.
Now we draw a new budget
constraint,
budget constraint three.
Budget constraint three, it's
sort of hard to see.
Budget constraint three is drawn
so that it has the new
price ratio.
That is, it's parallel to the
final budget constraint bc2,
but it's tangent to the original
indifference curve.
This is hard, so let me just
walk this through again.
You've got your original budget
constraint, bc 1.
You chose your point a.
Now the price of movies has just
increased, so you move to
bc2 in reality.
And at bc2, you choose
point c.
But for the Substitution Effect
we're going to say,
let's hold utility constant
and ask what package you'd
choose at these new price
holding utility constant?
Well the way to do that is to
draw an imaginary bc3--
bc3 never existed in reality--
that is parallel to the new
budget constraint, that is the
new set of prices, but it's
tangent to your old
indifference curve, that
is utility is constant.
If that were the case,
you'd choose point b.
You'd choose 4.89 movies.
Therefore we say that the
Substitution Effect is 1.11.
We reduce your movies by 1.11
through the Substitution
Effect only.
The price change only, holding
your income, holding utility
constant, is 1.11.
Then we say, well, what's
the Income Effect?
The income effect is given
prices are fixed, what's the
effect of just being poorer,
because movies
are now more expensive.
We know how to make
someone poorer, we
just lower their income.
So we shift from bc3 to bc2 and
from point b to point c,
and we're done.
We get the total effect
of the price.
So we have to shift from a to
c is all that you see in the
real world.
But behind that is the
Substitution Effect which
shifts you from a to b and the
Income Effect, which is this
parallel shift inwards of the
budget constraint, which
shifts you from b to c.
I'm going to go through that
again in a minute.
But let me first answer these
questions, then I want to show
you some of the math of this.
Are there questions about
what's going on here?
Yeah.
AUDIENCE: The income effect can
have either sign, right?
PROFESSOR: The income effect
can have either sign.
Excellent point.
What have I illustrated here?
What kind of good is this?
This is a normal good.
Excellent point.
This is a normal good.
I've assumed a normal good.
And this should actually say
in the title income and
substitution effects
for normal good.
So I've assumed a normal good.
And we know this student aptly
pointed out the normal good,
because we know that as your
income fell, moving from point
b to c, you consumed
less of it.
This comes to the question that
was in the back, which is
as the price changes, whether
we consume more or less is
related to the Income Effect but
doesn't tell you precisely
what the Income Effect is.
But as your income changes, if
you consume more or less,
that's directly Income Effect.
So we see it's a normal good.
So the Substitution Effect
moves us from a to b.
The Income Effect,
from b to c.
What I want to do is one more
thing before we stop.
And then I'm going to come back
next time and go back
over this and then talk about
some applications.
What I want to do right
now is I want to--
The Income Effect, say the
following, the sign is
ambiguous, because it depends
on if it's a normal or an
inferior good.
The Substitution Effect
is unambiguous.
Substitution Effects are
always negative.
Holding utility constant, a
price increase of a good
always shifts you away
from that good.
Negative or less than or equal
to zero could have no effect.
But once again, I always talk
in inequalities even though
they're typically inexact.
The key is the Substitution
Effect is always negative.
We can think about this in two
different ways depending on
how you want to think
about it.
Graphically we could
show this by the
fact that if the price--
think about it graphically.
If you're on the same
indifference
curve as you were before--
that's the definition of
Substitution Effect where I
keep the same indifference
curve--
but you're tangent to a steeper
budget constraint,
which is what happened when
prices go up, you must be
choosing less of the good.
Think of it graphically.
Just look at the graph.
I'm in the same indifference
curve.
But to be tangent to a steeper
curve, it's going to have to
be to the left.
So graphically it's going to
have to be that I'll choose
fewer movies when the price
of movies goes up.
That's graphically.
Mathematically we can just say,
look, what do we know is
our rule for utility
maximization?
We know our rule for utility
maximization is that the
marginal utility of movies over
the marginal utility of
prices equals the price of
movies over the price--
marginal utility of pizza.
I'm sorry.
Marginal utility of pizza.
So the price of movies,
so the price of pizza.
Or the MRS equals the MRT.
We know that mathematically.
That's our maximization
condition right?
Well if the price of movies goes
up, holding the price of
pizza constant, then the right
hand side has risen.
If the right hand side rises,
then the left hand side has to
rise to get this equality.
How does the left
hand side rise?
The left hand side rises by
either the marginal utility of
movies going up or the marginal
utility of pizzas falling.
And how do you do that?
By shifting away from movies
towards pizza.
How do you make the marginal
utility of movies go up?
Consume fewer movies.
How do you make the marginal
utility of pizza go down?
Consume more pizza.
Now in this case, pizza
doesn't change in this
particular case, but
in general it can.
But the key point is you are
going to see this Substitution
Effect is going to shift
you towards fewer
movies to try to get--
basically because given utility
constant, to try to
equilibrate this, you're going
to have to move to a higher
marginal utility of movies.
Given that the price of movies
has gone up, you're going to
have to move to worlds where you
care about movies more, or
you're not in equilibrium.
Think about it this way.
If the price of movies goes to
$100 a movie, and you're going
to be indifferent to where you
were before, on the same
utilities you were before, it
can't possibly be true that
you consume the same
number of movies.
You'd have to be sadder if you
consumed the same movies.
You're going to have to
move away from movies.
And that's why the Substitution
Effect is always negative.
You're always going to move away
from the good where the
price increases, holding
utility constant.
But then we have the second
effect with the Income Effect,
which then basically, if the
good is normal, reinforces
that Substitution Effect.
It says not only do you not want
movies because they've
gotten more expensive, you also
don't want movies because
you're poorer.
Your opportunity set's
restricted.
And when your opportunity set's
restricted, you buy less
of everything including
movies.
So there's two reasons.
We only saw one own-price
elasticity demand, one shift.
But there's two reasons
behind that.
The first reason is because the
relative prices have changed.
And the other is because you're
effectively poorer.
You add those up, and you
get the final effect.
Now the first, as I said,
is unambiguous.
That Substitution Effect will
always move you to the left.
You're always going to want less
of a good if its price
goes up from Substitution
Effect.
The second is ambiguous.
That depends on whether the good
is normal or inferior.
Next time we'll talk
about what happens
with inferior goods.
With inferior goods, we can see
that we can actually get
what we call a Giffen good.
A Giffen Good is a good where
it's inferior, so the income
effect goes the other way.
And you can actually technically
get a good where
when the price goes up, you
actually want more of it.
When the price goes down
you want less of it.
That is, you can get
a wrong sign, wrong
slope demand curve.
I say demand curves
always slope down.
I might even refer to it
as the law of demand.
That's not technically true.
Technically there exist goods,
we'll talk about the next
time, called Giffen Goods where
you can actually get the
demand curve sloping
the wrong way.
The price increase can actually
cause you to want
more of it.
In fact, these are based--
I like the name Giffen because
it's close to griffin.
And griffins are imaginary
and so are Giffens.
In fact, there's no evidence
such goods exist, but it's a
nice theoretical concept to
build your understanding of
Income versus Substitution
Effects.
So for next time think a bit
about how that could be.
And we'll come and show you
graphically how you can get
Giffen goods depending on the
sign of the Income Effect.
