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PROFESSOR: All right, so what
we're going to do for the next
few lectures, really through the
end of the course, is turn
away from what we focused on for
most of this course, which
is efficiency, and start
talking about equity.
So most of this course, we've
talked about efficiency and
the principles that lead
to efficient outcomes.
We haven't talked a whole lot
about fairness and equity.
We've mentioned it in passing
for things like why you want a
minimum wage, et cetera, but we
haven't really focused on
how society should consider
efficiency and equity as two
different goals, because
clearly it does.
So for example, a classic
example of the fact that
efficient outcomes may not be
equally equitable is the
perfectly competitive market
versus the perfectly price
discriminating monopolist.
Remember that both outcomes,
both a perfectly competitive
market and a perfectly price
discriminating monopolist,
both lead to
maximum social welfare.
So in the terms we've used in
this course, both provide
equal social welfare.
The difference, of course, being
that in the perfectly
price discriminating monopolist
case, the producer
gets it all, whereas in the
perfectly competitive case,
it's shared between producers
and consumers.
So we actually care.
We actually in the end are going
to care as a society,
not just about social welfare,
but who's getting the shares
of the pie.
In other words, we're not going
to care just about the
size of the pie, but who's
getting what shares.
So first of all, even for a
given size of the pie, we have
to decide who gets
what shares.
Moreover, it gets much more
complicated than that because
the size of the pie
isn't fixed.
And typically, in a society's
efforts to redistribute
shares, they shrink the pie.
That is, societies typically
face the classical equity
efficiency trade off.
Which is that in any effort
to redistribute resources,
inevitably we'll shrink
the total amount
of resources available.
And that's roughly speaking,
because the efficient outcome
is where you start from.
You start from an outcome
where you've
maximized social welfare.
So any intervention that tries
to deviate from that by moving
resources across groups, by
definition will move us away
from that efficient outcome.
We're starting with the
efficient outcome, let's say a
permanently price discriminating
monopolist,
that's efficient.
Any efforts we have to take
some money away from that
monopolist and give it to
other people will end up
causing distortions and reducing
the total size of
total social welfare.
So basically, we're always
going to face this equity
efficiency trade off, and really
the question we want to
ask in this lecture is,
is it worth it?
How do we think about whether
it's worth it to redistribute
from rich to poor, even if along
the way, we shrink the
total size of the pie, even if
we have to deviate from the
welfare maximizing point.
And the best way to think about
this I think is due to
an analogy developed by
a famous economist
named Arthur Okun.
And this is Okun's leaky
bucket analogy.
So Okun's leaky bucket analogy
is the following, he said,
look, let's say as a society,
we agree that we should
redistribute from
rich to poor.
And I'll come later to why we
might agree that, but let's
just say we agree as a society
that we should redistribute
from the richest members to the
poorest members of society.
And let's think of that
redistribution as being
literally the rich people put
money in a bucket, and you
carry that bucket and then dump
it out in front of the
poor people.
Let's say that's the way
redistribution happened.
Well, probably we'd have general
agreement that if Bill
Gates could put $1 in a bucket
and it could be carried and
given to a homeless person,
that's a good thing.
We probably in general agree
that if you distribute from
the richest people to the
poorest people, and $1 from a
rich person becomes $1
for a poor person,
that's a good thing.
However, what if along the
way, some of that dollar
leaked out?
What if Bill Gates put $1 in the
bucket, but by the time it
got to the poor person,
it was only $0.80.
You might say, OK, that's still
fine. $0.80 to a poor
person is a lot.
Bill Gates isn't going
to miss $1, but $0.80
to them might matter.
What if it's only $0.50?
What if Bill Gates put $1 in, by
the time you carry it over,
it leaks out so much so the poor
person only gets $0.50?
What if it's $0.10?
What if literally every dollar
Bill Gates gives up, the poor
person only gets $0.10, then you
might say, gee, it's not
entirely clear it's
worth it anymore.
I mean, yeah, $0.10 is worth
more to a poor person than a
$1 is to Bill Gates, but that's
really wasteful to have
$0.90 just leak out
along the way.
So basically, what we have to
do is ask basically how does
society think about transfers
when some of what happens when
you transfer from rich to poor
is you lose some efficiency
along the way, something leaks
out of the bucket?
And that's basically what we're
going to talk about in
the next two lectures.
We're going to do that
in four steps.
We're first going to ask, how
does society value transfers?
How does society think about the
value of $1 to Bill Gates
versus $1 to a poor person?
How do we think about the value
of those dollars in
different hands, something
we haven't
talked about this semester?
We then are going to talk about
the facts on income
distribution.
How has the distribution of
dollars changed over time in
the US, and how do we compare
it internationally?
Then we're going to talk about
the sources of leakage.
That is, what causes this bucket
to be leaky, in fact,
what causes the equity
efficiency
trade off in practice.
And then finally, we're going to
talk about what governments
do, what government does to
redistribute resources.
How does the US government in
particular redistribute
resources from higher to
lower income groups?
So that's what we're
going to talk about
the next two lectures.
So we're going to start with
the question of how does
society value transfers, or
more generally, how do we
think about the socially
optimal
allocation of resources?
The key word here being
allocation.
So we're no longer just going to
talk about the entire size
of the social welfare triangle,
we're now going to
talk about who gets what, and
how do we think about the
socially optimal distribution of
those resources, allocation
or distribution of
those resources.
And to do so, we're going to
have to take an extra somewhat
uncomfortable step we haven't
taken before.
Before, we've just talked about
a purely mathematical
concept of maximizing the
size of a triangle.
Now we've got to actually put
some value judgment on who
gets what within
that triangle.
And the way we make that value
judgment is through the
introduction of what we call
a social welfare function.
A social welfare function,
which is literally the
mathematical representation,
because we're all
about the math here.
It's a mathematical
representation of how society
values different groups.
So social welfare function is
some function of the utility
of individual one, the utility
of individual two, all the way
to the utility of individual
350 million, however many
people we have now in the US.
It's literally a mathematical
representation of how we take
every individual's utility and
come up with a measure of
social welfare.
That's what the social welfare
function's going to be.
So think about that.
Let's look at figure 23-1,
which shows what we call
isowelfare curves.
Think about a society with two
people, Ned and Homer, and
think about the government's
decision,
or think about society--
excuse the word government,
think about
society right now--
society's valuation of the
allocation of resources across
these two individuals.
Each of these curves is meant
to represent a social
indifference curve.
In other words, think
of society as
having a utility function.
Think of this being a social
utility function, and the
utility function has
indifference curves.
So society has some indifference
curves.
So what this depiction says is
society's indifferent between
Homer having u1h and Ned having
u1n, that is, with Ned
having a lot and Homer
having a little.
Or Homer having u2h and Ned
having u2n, that is Homer
having a lot and Ned
having a little.
So I've just made this up.
I've drawn this curve such that
society is indifferent
between those two allocations.
And basically, these isowelfare
curves will look
just like our indifference
curves.
So we've talked in this course
about choosing between goods.
We've talked about choosing
between states of the world,
injured not injured.
We've talked about choosing
between periods of time, today
versus tomorrow.
Now I'm talking about the
hardest one of all, choosing
between people, choosing between
the utility of people.
But it's the same damn
principle, it's the same stuff
we've always done, which is
there's some utility function,
now we call it a social
welfare function.
You maximize it across
its elements--
here it's the utility of Ned
and Homer, and you develop
some indifference curves.
And they have all the properties
indifference curves
always had, further out is
better, that a society is
happier if both Ned and Homer
have more, and along the
curve, you're indifferent.
So these are representations
of how society feels about
transfers across people.
So the big question then
becomes, what does this social
welfare function look like?
Mathematically, how do you
represent this incredibly hard
question of the trade
off across people?
And this is an incredibly deep
question, but the standard
social welfare function that's
used is something due to
Jeremy Bentham, a famous
English philosopher.
You can actually still see his
head if you go to University
College London.
Actually, it's not a
representation of his head,
they actually had him stuffed
and his head on display, but
then apparently, students would
take it at night and use
it for soccer.
So they now just have a
representation of his head
there at UCL.
But Jeremy Bentham developed
what we call utilitarianism,
the utilitarian social
welfare function.
And utilitarianism simply says
that the social welfare of
society is simply the sum of
each individual's utility.
So u1 plus u2 plus dot dot
dot plus u350 million.
That's social welfare.
That is the social welfare of
US society, is the sum of
everyone's utility.
Very straightforward.
So it's a linear social
welfare function.
So what this says is this says
you would maximize social
welfare by transferring from
any one individual to any
other individual, if the first
individual has a higher
utility that the second
individual.
So basically you maximize
social welfare, is that
basically if you--
I'm sorry, let me say
it another way.
If transferring $1 from me to
you makes you better off than
it makes me worse off,
then we should do it.
Now, your first instinct might
be, well, this isn't very
liberal in a sense, this is
just saying everybody's
utility is the same.
That is, we consider Bill Gates
is one of these people,
and I'm one of these people,
and you're one of these
people, and the homeless guy
in Harvard Square is one of
these people.
And they're all just added up.
How is that fair?
In fact, let me ask the
question differently.
Why despite that is utilitarian
wealth, social
welfare function can it be
perceived as fairly liberal,
despite the fact that everyone
just gets added up?
Why in fact is social welfare
function that's utilitarian
call for transfers from Bill
Gates to homeless person?
Yeah?
AUDIENCE: [UNINTELLIGIBLE]
PROFESSOR: Exactly.
If you maximize social welfare,
what it's going to
say is set marginal
utilities equal.
If you differentiate this with
respect to everybody's
utility, you're going to get
that the rule that you get
from maximizing, the first order
condition mathematically
is going to be that everyone's
margin utility should be equal
with utilitarian social welfare
function, which is
very radical.
That says that we should
redistribute until Bill Gates
has the same marginal utility
as the homeless person.
Thought of that way, that's
incredibly radical
redistribution.
It's not weighting Bill Gates
equally to the homeless
person, it's weighting his
utility equal, but it's saying
we should have massive
transfers.
In fact, basically we should
equalize income in society,
effectively.
That basically, what
we should do is--
in fact, let me be
more precise.
If individuals are identical,
which they're not, but if
individuals had identical
tastes, the utilitarian social
welfare function would say
that social welfare is
maximized with an equal
distribution of income.
Pretty radical.
If individuals are identical,
social welfare is maximized
with the equal distribution of
income, despite the fact we
started with this pretty
un-obnoxious looking function,
we're simply going to weight
everybody equally.
We're not even saying we care
more about poor people than
rich people, we're saying weight
everybody equally.
That fairly innocuous looking
function delivers the radical
implication that if everyone is
identical, we should have
an equal distribution of
income in society.
And that's a typical social
welfare function
that we look at.
But that actually is not
considered really a
particularly lefty social
welfare function.
In fact, if you talk to the left
side of the philosophical
distribution, they'll
say this is not an
appropriate measure to use.
They much prefer something like
the Rawlsian criteria,
named for the philosopher
John Rawls.
The Rawlsian social welfare
function is that the role that
society's goal should be to
maximize the well-being of its
worst off member.
That a fair and just society
is one which maximizes the
well-being of the worst
off person in society.
So that says social welfare is
equal to the min of u1, u2,
dot dot dot dot.
So it's a max-a-min criteria.
You want to maximize the min,
maximize the minimum utility
in society is the Rawlsian
social welfare function.
Now, in some situations,
this can deliver--
in fact, if everyone's
identical, this would deliver
in many cases the same outcome
as utilitarianism.
But in some cases, it's much
more radically lefty.
Think about it this way.
Suppose we had a situation where
everybody but me and
you, but me and this guy
have equal incomes.
Everybody in the world's equal
income is at $40,000.
But my income is $1 million,
and his income is $39,999,
he's got $1 less income
than the rest of you.
And let's say that a new
government is running for
office that proposes to take
away all of my money, so I'm
down to $40,000, and
give him $1 and
bring him up to $40,000.
Now in utilitarianism, that
would not be an appropriate
thing to do, because clearly
my utility is going to fall
more from going from 1 million
to 40,000 than his is going to
go from going 39,999
to 40,000.
So under utilitarianism this
would be a bad thing to do.
But in Rawlsianism, it'd be a
good thing to do, because he's
the worst off member.
So it doesn't matter what
happens to me, it only matters
what happens to him.
So Rawlsiansim is an incredibly
radical theory,
which posits that we only care
what happens to the poorest
guy, even if we have to like
take all the money away from
the richest guys,
we don't care.
We only care about what happens
to the poorest guy.
So that's a very radical sort of
lefty view of how we should
think about distribution.
On the other hand, we have
a very radical--
well, some would say a more
radical view on the right,
which is a Nozickian social
welfare function, named for
the philosopher Robert Nozick,
also at Harvard.
Rawls and Nozick were
both at Harvard.
Nozick said this is just
way too radical.
He said utilitarianism is
way too radical, way
too far to the left.
Forget Rawlsianiasm,
that's just nutty.
Even utilitarianism is way too
far to the left, because he
says, basically what should
matter in society is an equal
distribution of resources--
I'm sorry, an equal distribution
of opportunities.
And conditional on equal
distribution of opportunities,
if individuals take those
opportunities and choose to do
outcomes which give them
different incomes, that's
their problem.
So for example, let's say that
we started with everyone in
the world started with an equal
distribution of income.
But let's say that MIT students
loved to hear me
lecture, and were willing to pay
$100 to hear me lecture.
And so at the end of the year,
every MIT student ended up
$100 poorer and I ended
up a ton richer.
Well, under both utilitarianism,
and certainly
under Rawlsiansim, that is an
outcome which is not social
welfare maximizing, because I
don't care about that last
$100 whereas you guys care
a little bit about
giving up the $100.
So clearly social welfare would
be maximized if I gave
some of that money
back to you.
Under Rawlsianism, clearly I
should give it all back to
you, because all we care about
is you guys being $100 poorer.
Nozick says this is crazy.
This is a voluntary
transaction.
You guys voluntarily paid me
$100, making me richer.
Why should there be any
redistribution?
Why should social welfare
be any lower from that
transaction?
How could a voluntary
transaction
lower social welfare?
And this is sort of a right
wing approach to thinking
about social welfare, which is
look, everybody should have
equal opportunities.
It's not fair to have some
person not have access to
education and things.
But once everybody's got equal
opportunities, there's no
reason why if you make voluntary
choices that lead to
unequal distribution of
income we should care.
Now this is actually
very compelling.
It has a lot of merit, and
really should make us think
about our emphasis should be on
opportunities rather than outcomes.
But it has one flaw, which is
that in fact, most of the
differences in society aren't
due to choices, but rather due
to outcomes outside people's
control, often just luck.
So basically, if it was true
that we all started equal and
that any differences in income
came through our choices, then
this would be a very powerful
way of looking at the world.
But in fact, if you look at
most differences in income
across people, they're not due
to their choices, or to
effort, or to other things you
can actually figure out how to
measure, they're due to
unmeasured things.
Often it looks like luck.
And in that case, you would care
about the fact that I end
up richer than you.
So if I end up richer than you
because you're willing to pay
me, that's one thing.
But if I'm richer than you just
because I won the lottery
and you didn't, that's a
different thing altogether.
And so basically, whether how we
feel about the equality of
opportunities view versus the
equality of outcomes view
depends very much on what we
think is the source of
difference in incomes.
If we think it has to do with
effort and choices, then
people can often favor this
view, that if people by their
effort and choices made more
money, let them keep it.
But if people made more money
through luck and things beyond
their control, then people tend
towards more this view,
saying look, if you got your
money through luck and things,
there's no reason why we should
have such an unequal
distribution of income.
And that's sort of another
tension in thinking about
these social welfare
functions.
There are no right
answers here.
I don't mean through my tone
or word choice to imply
there's any right answer.
I'm just trying to lay out the
arguments for these different
ways of thinking about it.
Then finally, the last way we
could think about it, and to
many people, really the most
compelling, is through what we
call commodity egalitarianism.
Commodity egalitarianism, which
is a fancy name for
saying look, it doesn't
matter who has what.
It just matters that everybody
can survive.
This is kind of like a
reinterpretation of Rawls.
It's almost a mix of Rawls
and Nozick in a way.
It's saying look, what matters
is that people aren't
starving, that they have decent
shelter, decent health
care, et cetera, you can
define your minimum.
But once you've defined a
minimum, we shouldn't care
about how rich people get
beyond that minimum.
So basically, the key thing is
that we should not care--
what commodity egalitarianism
focuses on, the insight it
brings, which is an important
one, is it's not clear why
relative should matter.
What should matter
is absolute.
It's not clear why I should
care how much
richer I am than you.
We should just care that you
have enough to live a decent,
socially acceptable life.
And then if I want to get
rich, God bless me.
So it's kind of like saying we
care about the minimum, but
it's not all we care about.
We care about making sure
there's a minimum decent
standard of living, defined
however you want to do it.
Different people choose choose
different things.
For some people, it's just
food and shelter.
Other people could include
health care, or clothing, or
other things.
I'm not saying what the
right minimum is.
Let's define some minimum, and
then say beyond that if guys
get rich, God bless them.
That's their prerogative, as
long as the poor people have
enough to survive.
And this is an incredibly
interesting, compelling view,
because it's a radically
different view, which says
relatives don't matter,
absolutes are all that matter.
All they're making sure is that
the absolutely people at
the bottom have a decent
standard of living.
And that's a very different
view as well.
So basically, social welfare,
when we talked about utility
functions, I didn't really talk
much, I just said, you
write down a utility function,
we often use
square root of c, whatever.
I didn't really talk much about
the form, I just said it
should have diminishing
marginal utility, and
otherwise I said sort
of all bets are off.
With social welfare functions,
it's a lot more open-ended and
a lot harder, and we don't
even really know what the
right standards are.
But it's just saying that we
can't get away from asking
this awkward question.
Because ultimately society does
end up with an unequal
distribution of resources, and
given that, we can't get away
from asking the question of
how do we feel about that?
Economics is about asking
uncomfortable questions.
And this is an uncomfortable
question we have to answer,
which is how do we feel
about different
distribution of income.
And the reason this
is an issue--
Yeah?
AUDIENCE: [UNINTELLIGIBLE]
PROFESSOR: That's a
great question.
I don't know.
I wouldn't ask you
to write it down.
I mean, it's a much more
complicated-- there's not a
simple mathematical function
with your Nozick
or commodity egal.
Commodity egalitarianism,
I guess the
function would be that--
the social welfare function
would be that there's some
minimum u bar.
Below u bar, we have an infinite
weight on you in our
social welfare function.
But once you get to u bar, we
only care about you the same
as everybody else.
That would be sort of commodity
egalitarianism.
Nozick, I don't know how you
write it down mathematically.
Why does this matter?
This matters because it turns
out in society we do have a
very unequal distribution
of resources.
So to see that, let's go to the
next page, figure 23-2,
this is from my textbook
that I use for my
course on public policy.
And this shows the income
received by
quintile in the US.
Let me explain what
this table means.
Each row is a fifth
of the population.
If we had an equal distribution
of income, then
each of these numbers
would be 20%.
Each fifth of the population
would have a
fifth of the income.
But that's not true.
So if you look at 1967, the
poorest 20% of people only
earned 4% of the income.
And the richest 20% of people
earned 44% of the income, or
11 times as much, 43.8, about
11 times as much.
That's an unequal distribution
of income.
What's interesting is
you can see over
time how it's changed.
From 1967 to 1980, things
actually got
a little more equal.
The poorest share actually grew,
and the richest share
fell a bit.
Then this since 1980, things
have gotten a lot more
unequal, to the point where in
2007, the poorest 20% of
people only controlled 3.4%
of our resources.
That is, 1/33 of all resources
in society go to the bottom
20% of the income distribution,
whereas 1/2 go
to the top 20% of the
income distribution.
So the richest 20% of people
get half the income that's
earned in the US.
The poorest 20% of people get
1/33 of the income that's
earned in the US.
So this is why this stuff
matters, because there is
inequality in practice.
In fact, it matters a lot in the
US in particular because
the next table shows how
we do relative to
the rest of the world.
So this compares us to what's
called the OECD countries.
OECD is the organization for
economically something
something, it's a
French acronym.
And basically, it's sort of
close to developed countries.
It's a first and second
world if you will.
It's different years because
the data is collected at
different frequencies.
But the rough facts are
constant over time.
This shows the share of income
in each of the quintiles
across all this list
of countries.
And the bottom next to last
row shows the unweighted
average across these developed
countries compared to the US.
What you see is we are the
second most unequal nation on
this list other than Mexico.
We are more unequal than any
other nation on this list. On
average, the poorest 20% of
society has more than twice as
much in other countries, whereas
the richest 20% has
about 20% less, 40% of the
resources instead of 50% of
the resources.
And so what you see is we
have a much more unequal
distribution of income than any
other major economy except
for Mexico.
So basically, this says we have
an incredibly unequal
distribution in American society
by some absolute
standard, just if you look at
the numbers, it seems unequal,
and relative to the
rest of the world.
No country in history has ever
had all these numbers be 20%.
Societies are always
unequal, the
question is just how unequal.
And compared to the rest of the
world at least, we seem
pretty unequal.
So that says that under a
utilitarian function, or
especially in a Rawlsian
function, we should worry that
we're not maximizing
social welfare.
Under a utilitarian social
welfare function, at least,
it's going to be hard to think
whether it maximizes social
welfare when there's
such an unequal
distribution of resources.
Certainly in a Rawlsian
function we're not.
Nozick, who the hell knows.
That depends on where we start
with opportunities, how much
is due to choice and how
much is due to luck.
But of course, this doesn't
speak at all to the last view,
which is a commodity
egalitarianism view, which
says none of this matters.
All that matters is the
measure of absolute
deprivation.
And we have such a measure in
the US, it's called the
poverty line.
The poverty line is a concept
that was actually thought up
by the mid-level government
bureaucrat in the 1960s.
What this woman, Molly
Orshansky, did is she said
look, the typical family in the
US spends about a third of
their income on food.
Let's figure out what a
minimally nutritionally
adequate diet costs.
That is, how much do you have
to spend on food to have at
least a minimally
adequate diet.
No Starbucks, no Outback
Steakhouse, just enough to
actually have a nutritionally
adequate diet, and then let's
multiply it by three, and we'll
call that what a family
needs to live in the US.
Food's typically a third of
consumption, let's figure out
a minimally adequate diet,
multiply it by three, call it
the poverty line.
And basically, we've taken
this exercise and
used it ever since.
We simply update it by inflation
to see how the
poverty line changes
over time.
So basically, we've just taken
this concept and updated it by
inflation over time.
The result of what you get
is in figure 23-4.
This shows the US poverty
line in 2006.
Actually, this is mislabeled,
it's 2009 actually.
It's a typo in my book.
What this says is that for a
family of one, the minimum
standard that you need
to live is $10,830.
And it goes up with family size
because more people need
more to eat.
Now, if you are from Mississippi
or maybe North
Dakota, this might look like
kind of a reasonably large
number to you.
If you're from Boston, this
looks like insane, like how
could someone live on $10,830 a
year in Boston, New York, or
DC, or San Francisco,
or any major city?
And the answer is they can't.
The answer is that the poverty
line has not been kept up
appropriately, because we've
simply taken this number and
inflated it by inflation over
time, but it hasn't accounted
for the fact that people's
consumption
bundles have changed.
In particular, food is no longer
a third of the typical
person's consumption bundle,
it's now 1/6.
So in fact, the poverty line
should be much, much higher
than it is, but it hasn't been
updated over time in a
meaningful way.
So you can think this is a very
low minimum standard for
what people need to live, and
certainly below what anyone
needs to live in any major
metropolitan area.
That said, we can look at what's
happened to the share
of population in poverty, and
that's in figure 23-5.
So here's the sort of commodity
egalitarianism thing
to look at, which is what's
happened to poverty.
And what you see is there was
a massive decline in poverty
for everyone in the 1960s
to early '70s.
We call this the War On Poverty
under the Kennedy and
Johnson administrations, a huge
reduction in poverty.
What you see is that since about
1970, that reduction has
continued for one group, for
the elderly, their poverty
rates continued to fall.
So in 1959, 35% of elderly
people lived in poverty.
Then through massive expanses of
a program we'll learn about
in a couple of lectures called
Social Security, that fell, so
that today, only about
10% of elderly
people live in poverty.
On the other hand, for everyone
else, and especially
for kids, it's basically
flattened out or increased
since 1970.
So basically, overall poverty
rate hit about 13% in 1970,
and it's been pretty
flat since.
For kids, it fell to about
15%, and it's been
bounced up and down.
It's now back up to about 20%.
So from a commodity
egalitarianism view, even if
we take the poverty line as a
minimum acceptable level,
there are currently about 40
million families in the US
living below poverty.
40 million people, I'm sorry,
living below the poverty line.
So even at this minimum
standard, we've got a failure
of redistribution.
We're not maximizing social
welfare given that we've got
40 million people living
below this standard.
So based on whatever standard
you want to use, except the
hard to evaluate Nozickian
standard, we're clearly not
maximizing social welfare
at the current
distribution of income.
We've got an incredibly unequal
distribution of
income, and even if all we
care about is making sure
people have a decent standard of
living, we're also failing
on that standard for upwards
of 40 million people.
For a more realistic poverty
line, it might be more like 60
or 70 million people.
So clearly there is an argument
here for some income
redistribution, whatever your
social welfare function is.
So we can write down--
I'm not going to ask you to
write down mathematically
social welfare function and
maximize it and solve for
outcomes and stuff like that,
but what I want to leave you
with here is simply
two points.
First of all, there are lots of
reasons why we might want
income redistribution in society
under any of these
alternatives.
That's point one.
Point 2 is our current
distribution of resources
seems sufficiently unequal that
we likely do want some
redistribution of resources
in society.
For most social welfare
functions you can write down,
given the facts I've shown
you, we would not be
maximizing social welfare at
the current distribution of
income in society.
I'm trying to couch this in
a way that doesn't make me
particularly lefty or righty.
I'm just trying to couch this
in a way which just draws on
the uncomfortable fact that we
have to talk about this.
We have to talk about income
redistribution.
The only way to do so is
to have some framework.
I've given you four frameworks
and said under all of them, or
at least most of them, we would
be uncomfortable with
the existing distribution
of income in society.
Questions about that?
So what do we do about that?
What do we do about the fact
that we have unequal
distribution of resources
in society?
Well, we redistribute.
We say look, let's get out
Okun's bucket and start
carrying some money around.
We don't like the fact that
there's people living in
poverty who can't eat.
We don't like the fact that
the poor have so much less
than the rich.
Let's start redistributing.
Once you do that is you
have to recognize
the leak in the bucket.
And recognize there's a trade
off, that it's not so simple
as saying, fine, let's take from
the rich and give to the
poor, because there's a
leak in the bucket.
And so that as we take from the
rich and give to the poor,
we shrink the total size
of social welfare.
And that gives a trade off.
And in particular, there's two
sources of leakage that we
have to think about.
The first source of leakage is
that when you tax a rich
person to take their money away,
they work less hard.
And when they work less hard,
there's less goods produced in
society, and that
shrinks the pie.
The other source of leakage
you have to think about is
that when you give money to
poor people, they may
themselves quit their jobs to
qualify as poor so they can
get the money, and that further
shrinks the pie.
So both the taxing the rich and
the giving to the poor are
sources of leakage
in the bucket.
And that's a trade off with
dealing with these enormous
distributional problems
that I laid out.
So let's just go through one
example, general example to
make this point.
Let's say we have a society
where everyone is equal, and
everyone earns a wage
of $20 an hour.
Equal society, everyone's
equal in terms of their
underlying preferences, and
everyone earns $20 an hour.
But people work different
amounts of hours.
Now they could work these
different amount of hours
because they're lazy,
Nozick might say.
They could work these different
amount of hours
because they just can't find
a job, or because they're
disabled, or because they're not
skilled enough to work a
full-time job.
Whatever the reason is, we're
going to stay away from what
that reason is.
Although obviously, what the
reason is matters for these
social welfare functions.
Let's just say we have a society
where everyone earns
$20 an hour, but we have a
distribution on how many hours
people work.
And let's say that we want
to start with a commodity
egalitarianism view, and say
we want to make sure that
everyone has enough to eat.
We want to make sure that
everyone has at least $10,000.
So we come in and we say look,
we're worried about this
distribution of resources
in society.
We want to make sure everyone
has at least $10,000.
So what we're going to
do is we're going to
give everyone a transfer.
And that transfer function is
going to be equal to the max
of 0 and $10,000 minus
your income.
In other words, if your
income is 0, we're
going to give you $10,000.
If your income's $5,000, we're
going to give you $5,000.
If you income is $9,999, we're
going to give you $1.
Once your income is $10,000,
we give you nothing.
So this is very much like a
commodity egalitarianism view.
We're going to bring
you up to 10,000.
We're going to bring you up to
10,000, but once you're above
10,000, we don't
care about you.
So this is much less radical
than the utilitarian solution.
This is just saying,
we're just going to
bring the poor up.
We're just going to
deal with that.
However, if we're going to have
this program, we've got
to pay for it.
We've got to give money
to poor people,
where's that come from?
Let's say we finance the program
by taxing higher
income people.
What we're going to say in
particular is we're going to
have a tax rate tau--
so regular t is transfers,
tau is taxes--
which is 0 if your income is
less than $20,000, and 20% if
your income is greater than
$20,000, greater than or equal
to $20,000.
So we're going to have
a tax schedule.
We're not going to tax you if
you're less than $20,000.
But once you earn more than
$20,000, we're going to tax
you at 20%.
So this is our redistributive
scheme in society.
This is our Okun's bucket.
The rich put the money in.
We tax them to get the money
to put in the bucket.
We bring it over and give it
to the poor in the form of
bringing everybody
up to $10,000.
That's our redistributive
scheme, the simplest possible
redistributive scheme.
What does this do?
Let's now go to figure 23-6.
Pretty complicated figure,
so let's walk
through this slowly.
We initially have a budget
constraint that runs from the
intercept at 40,000 on the
y-axis to the intercept of
2,000 on the x-axis.
So the initial budget constraint
is the outer budget
constraint here running from
40,000 on the y-axis all the
way down to 2,000
on the x-axis.
That's because we have a
$20 hour an hour wage--
I'm sorry, let me go back.
This is a consumption leisure
trade off, like we do whatever
we do in labor supply.
When we do labor supply, we do
consumption leisure trade off,
so you're deciding
how hard to work.
How do you decide how
hard to work?
You can do it by trading off
consumption and leisure.
You can either take
2,000 hours of
leisure and consume nothing.
Or you could take zero leisure,
work 2,000 hours to
consume $40,000.
That's your trade-off, or
combinations in between.
And we have three individuals,
A, B, and C. A is someone who
works very little.
They take a lot of leisure and
have very low consumption.
C is someone who works a lot.
They have low leisure and
high consumption.
And B's in the middle.
Basic labor leisure trade off,
questions about that?
Now, how does this new
government policy affect the
budget constraint?
Well, it affects
it in two ways.
First of all, for those
above $20,000, we
now lower their wage.
Instead of taking home $20 hours
an hour, they're only
going to take home $16 an hour,
because we're taxing
them at 20%.
So for everyone above $20,000,
we shifted the budget
constraint in.
We have lowered the
price of leisure.
We've lowered the price of
leisure by taxing them.
So we've shifted that budget
constraint in.
It's the same budget constraint
up to 20,000, but
now it pivots, and at
20,000, you're now
on the lower segment.
With a slope, you can write
there, the slope is $20 at the
higher segment, it's only $16
for that lower segment.
That's the first change you've
made to the budget constraint.
That's the tax part.
The second change is that for
anyone with income below
$10,000, we've now said no
matter how hard you work,
we're going to give
you $10,000.
So now we've said, once your
leisure is 1,500 hours, or
your work is 500 hours, anywhere
to the right of that,
your income is always $10,000
no matter how hard you work.
If you earn $5,000, your
income is $10,000.
If you earn $1, your
income is $10,000.
If you earn $9,999, your
income is $10,000.
So the new budget constraint is
a flat segment starting at
the intersection of 10,000 and
1,500 and moving all the way
to the right.
That is, no matter how much
leisure you take, above 1,500
hours of leisure, your
consumption is always $10,000,
so it's flat.
So the new budget constraint
is the inner segment above,
then the old budget constraint
from $20,000 to $10,000, and
then a flat from point B to
point D. I'm sorry, not from B
to D. Kill that last comment.
From the intersection of 10,000
and 1,500 all the way
to the right, that's the
new budget constraint.
Questions about that?
This is very important.
This is just an application to
understand how these things
affect budget constraints.
What does this do to
people's choices?
Well, for a person like
C, they are now
taxed on their labor.
Person C doesn't care about the
welfare program, they're
rich, they don't care about
this $10,000 thing.
But they do care about the
fact they're now taxed.
Assuming substitution effects
dominate, the price of leisure
has fallen, so they choose more
leisure and less labor.
So person C, who was at C moves
to point E, working less
assuming substitution effects
dominate, more
leisure, less labor.
Person A, for them, this
is a no-brainer.
They can have both more leisure
and more consumption
by moving from point A to point
D. Under this new budget
constraint, they used to have
about-- it's not labeled
there-- but have about 1,700
hours of leisure and consume
maybe $5,000.
Now they can have more leisure,
they can have 2,000
hours of leisure and
consume $10,000.
So they move to point D. They
work less hard as well.
Person B, the way I've drawn
this, this is critical.
The way I've drawn this, their
indifference curve cuts
through the horizontal segment
running from the old budget
constraint to point D. Why
is that important?
Because that means that
there'll be a higher
difference curve out at point D,
because indifference curves
can't cross.
So if their old indifference
curve cuts through that
horizontal segment, it must
mean that they would be
happier out at point D.
They're giving up some
consumption.
This isn't a no-brainer like
for A, but they get so much
leisure it's worth it.
So you could have drawn B, if
I'd drawn B higher up, their
indifference curve wouldn't have
crossed this horizontal
segment, and then they wouldn't
have wanted to move
out to point D.
So for A, it's a no-brainer.
they move to D. For B
it depends on their
indifference curve.
Yeah?
AUDIENCE: For C, doesn't he
change to working harder and
consuming less?
Because he moves [INAUDIBLE],
so his leisure [INAUDIBLE].
PROFESSOR: Yeah, you're right.
This is drawn wrong.
You're right, we draw it so
that income effect is
dominating.
Good point.
I'm sorry, that should
have been--
good catch.
Point E should be to the
right of point C,
that's a mistake here.
We should have drawn it with
substitution effects
dominating.
That would have been more
leisure and less consumption.
He get less consumption,
but he works more
because of the tax.
But you're right, that should
have been to the right of
point C. Please correct that.
They should have been to the
right of point C. Substitution
effect should lead
him to earn less.
So he earns less, although once
again, it's ambiguous.
A clearly works less,
that's unambiguous.
And B, it depends on their
difference curves.
But the way we've drawn it here,
B works less-- in fact,
B works a ton less.
B goes from taking maybe 1,400
hours of leisure to taking
2,000 hours of leisure.
This is a huge change for B.
What this means is this tax
and transfer system has
massively reduced the amount of
labor supplied in society.
Why do we care?
Go to figure 23-7.
We care because we
initially were in
equilibrium at point e1.
But when people work less hard,
that's a shift inward in
the labor supply curve that
reduces the total amount of
labor supplied and causes
a dead weight loss.
We've distorted the economy by
people working less hard.
Trades that would've
made both parties
better off are not happening.
Trades that would have made both
parties better off are
not happening.
We've distorted the economy and
caused a dead weight loss.
And that is the equity
efficiency
trade off in a nutshell.
The equity efficiency trade off
is we knew we wanted this
tax and transfer system.
We were very upset about
the number of
people living in poverty.
But by putting this in, we've
caused a dead weight loss,
because it caused the rich
people to work less hard and
the poor people to
work less hard.
There's leaks in the bucket
on both sides.
This dead weight loss triangle
is the leak in the bucket, the
social waste that comes from
this redistribution system.
Questions about that?
So that leads us to mask,
was it worth it?
Is a transfer system
like this worth it?
Well, there's a simple answer.
You solve the social
welfare function.
Once again putting
Nozick aside, we
can't write that down.
But if you're utilitarian, you
just solve it, because, in
other words, what you say
is look, two things
are going on here.
Everyone's utility is
falling because
there's a social waste.
So each of those u's goes down,
but the rich u's go down
a little bit, and the poor
u's go up a lot.
And you have to basically
ask which of
those effects are bigger.
In other words, if the dead
weight loss triangle is very
small, then clearly--
or if there's a small
leak in the bucket--
then clearly, total utilitarian
social welfare
will go up with a scheme like
this, because the poor people
will be made so much happier,
and the other
people won't care much.
But if that dead weight loss
triangle is huge, let's
imagine half of society's output
disappears for this
transfer system, well, then
probably social welfare will
fall, because so many people are
made sadder that the fact
a few poor people are made
happier isn't worth it.
Remember, 40 million people are
in poverty, that means 300
million people aren't.
So if 300 million people, if
they see their incomes cut in
half so that 40 million people
can see their incomes raised
some, for most utilitarian
social welfare functions, that
won't be a good deal.
So basically, we can literally
mathematically represent
whether this transfer was a
good thing or not by using
this social welfare function
to evaluate it.
Under a Rawlsian function,
we know the answer.
We know this is a good thing,
because Rawls doesn't care if
we destroy all of society,
as long as that bottom
guy gets pulled up.
So basically, Rawls we know that
this is a good answer.
Utilitarian, we don't know.
That's going to depend on the
loss to the rest of us from a
smaller pie versus the
gain to the poor from
getting more resources.
Questions about that?
All right, what we'll do is
we'll come back next time, and
we'll talk about what is the
government actually do to
actually affect redistribution
in society,
and how does it look?
