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JONATHAN GRUBER:
Today, we're going
to continue our discussion
of consumer choice.
And we're going to
talk now about what
happens when we take that
unconstrained choice we talked
about on Monday and
impose budget constraints.
We'll talk about what
budget constraints are.
We'll then come to talking
about how consumers
make constrained choices.
And then we'll end with
an example of food stamps.
So let's start by talking
about budget constraints.
And we'll start by talking
about their construction,
the construction of
budget constraints.
So, basically, last
time, we talked
about the fundamental
axiom of consumer choice
that more is better.
So what stops people from
just bingeing on everything?
It's their budget constraint.
It's their limited resources.
Now, for most of
this course, we're
going to make a simplifying
assumption that your budget--
that is what you spend--
equals your income.
That is what you earn, OK?
That is there won't be any
savings or borrowing, OK?
Now that is a
simplifying assumption.
And, indeed, we'll
spend a couple lectures
at the end of the semester
talking about what happens
when people can save or borrow.
That said, this is not
a terrible description
of most Americans.
The median American household
has $400 in the bank.
So this is not kind of
a terrible description
of the way most people live
their lives in America,
which is what they
earn each week is
what they spend each week.
So that's what we'll do.
It also might not be sort
of a terrible description
of your life.
I presume, in college, you're
not doing a lot of savings.
You maybe do a little
borrowing, but not
a lot of savings or borrowing.
So what we're going
to do is we're
going to assume that's
true for you as well.
We're going to assume your
parents have given you
some amount of money to spend.
We'll call it Y. Your income
Y is the amount of money
your parents have given
you to spend for say
the semester or the month.
And, once again, let's say
all you spend your money on
is pizza and cookies, OK?
That's all you want to
spend your money on.
We write the budget
constraint as saying
that your resources,
your income Y,
can be spent on either
pizza or cookies.
And the constraint is
that you could spend it--
that budget has to be divided
between pizza, where there's
the price per slice of pizza
times the number of slice
of pizza, or cookies.
We have the price per cookie
times the number of cookies.
So p sub p is the price
per slice of pizza.
p sub c is the price per cookie.
P is the number of pizzas, and
C is the number of cookies.
That's your budget constraint.
You can essentially
devote your income
to some combination
of pizza and cookies,
but you have to consider
how much they actually
cost in doing that.
I find this easier
to see graphically.
So let's turn to figure 3-1.
Figure 3-1 shows a
budget constraint.
So how does the budget
constraint look?
Well, the x-axis is
your income divided
by the price of cookies.
That is, if you decide to devote
all your income to cookies,
then how many
cookies can you have?
Y over pc.
If your income is $100,
and cookies are $10--
that means you're going
to Insomnia Cookies--
then you can only have
10 cookies, et cetera.
Likewise, the
y-intercept is the income
divided by the price of pizza.
That's how many
pizzas you can have.
The budget constraint
represents--
the budget constraint, the
slope of the budget constraint,
is the price ratio, the
negative of the price ratio
because it's a downward-sloping
line, pc over pp.
That is every extra
cookie that you
buy, holding your
income constant,
lowers the amount of pizza
you can have by p sub p, OK?
So let's consider an example.
Suppose that Y is $96,
that the price of pizza--
it's an expensive
pizza place-- is $12,
and the price of a
cookie is $6, OK?
$12 for pizza, this is like
downtown San Francisco or New
York.
$96 income, $12 for a slice
of pizza, $6 for a cookie, OK?
I'm sorry.
Y is-- I wanted to
make Y 72, my bad.
So Y is 72.
Your income is $72, OK?
And you can spend it
on pizza and cookies,
and those are the prices.
Now what that means is,
if you wanted just pizza,
you could get six pizzas.
If you wanted just cookies,
you can get 12 cookies.
And, generally,
the rate at which
you can trade off pizza for
cookies is minus 1/2, OK?
That is every additional
cookie would require giving up
half a slice of pizza, OK?
Every additional cookie requires
giving half a slice of pizza.
That's why the slope
would be negative 1/2, OK?
So, basically, we're going to
call the slope of the budget
constraint--
the slope, we are going
to call the Marginal Rate
of Transformation, the MRT.
Last time, we did the MRS, the
Marginal Rate of Substitution.
Now we're going to have
MRT, the marginal rate
of transformation, which is
equal to minus pc over pp.
Or the slope of the
budget constraint, OK?
That is the marginal
rate of transformation.
Now this class is not alchemy.
We are not literally
transforming pizza
into cookies.
That would be kind of cool,
but we're not doing that.
That's somewhere
else at MIT, OK?
But it's effectively
doing the same thing.
What we're doing is, given that
we have a fixed amount of money
and given that we're
going to spend it all,
the more you spend on pizza,
the less you spend on cookies.
So you're effectively
transforming pizza
into cookies and vice
versa because you're
going to spend all your money.
You've got to spend
it on something.
So, the more you spend on one,
the less you get of another.
So, through the
budget constraint,
we are effectively transforming
one good to the other.
By having more of one, we're
getting less of the other.
So that's the sense
in which we call
it the marginal rate
of transportation--
of transformation.
So, basically, this comes
back to the key concept
we talked about in the very
first lecture, opportunity
cost.
The opportunity cost of a
slice of pizza is two cookies.
Remember, opportunity
cost is the value
of the next best
alternative, OK?
The opportunity cost is
the next best alternative.
Well, here you only have
two alternatives, pizza
and cookies.
So the opportunity cost of a
slice of pizza is two cookies.
And that's the sense
in which you're
transforming pizza into cookies
or cookies into pizza, OK?
Now this seems kind of
abstract, but let's actually
think of an organization
which has taken this principle
to heart to develop the
best method of weight loss
in America, which is Weight
Watchers, OK, Weight Watchers.
Now it turns out that
dieting is super hard
and basically doesn't work, OK?
There's a large
literature, which
says that people go
on diets all the time.
Then they stop them, and
they gain the weight back.
OK, dieting is incredibly hard
and basically doesn't work, OK?
But a much more
successful approach
has been established
by Weight Watchers.
It's not the only
approach, but it's
been proven much
more successful, OK?
And, essentially, what
does Weight Watchers do?
They set up a budget constraint
and ask you to follow it.
So, for example,
they essentially
assign point values to every
good you might consume.
You go on the website,
and everything
in the world you might want
to eat has a point value.
They then ask, well, what
weight are you today?
What's your age and gender?
That stuff matters
for weight loss.
And what weight do
you want achieve?
And they say, if you
want to achieve a weight
loss of x over y
days, then you've
got to limit
yourself to z points.
So, essentially, your
goal is to lose weight.
So we're going to give
you the budget constraint.
We're not going to
tell you what to eat.
That's why it's
better than dieting
because, once again,
Adam Smith was right.
People like to have choices.
They like to let
choice drive things.
But we are going to
tell you a total budget.
So, for example, vegetables
are like zero points.
Snickers bars are like
six points, et cetera.
They have various
point systems, OK?
So, for example, suppose your
budget is 30 points, which
would be pretty typical, OK?
Suppose you go to
McDonald's for lunch,
and you get a number one.
The number one at
McDonald's is a Big Mac,
which has 14 points, fries,
which have 10 points,
and a Coke, which
has six points.
That's 30 points, and
it's only lunch, OK?
You've blown your whole
budget for the day on lunch.
Now you could just get
depressed and say screw it.
I'll just be fat.
But, clearly, looking
around the room,
you guys have not
made that choice.
Or you could look at
the budget constraint
and say, well, what
else can I get.
Well, it turns out you can
get a 10-piece nugget, which
is 12 points, apple
slices, which is one point,
and a Diet Coke,
which is zero points,
for a total of only 13 points.
Now you have 13 points and
plenty of room for dinner.
Now, to be honest,
anyone who tells you
that second lunch is as good as
that first lunch is a liar, OK?
I'd much rather a Big Mac and
fries and a Coke than nuggets
and apple slice and Diet Coke.
Give me a break.
But I'd also much
rather have dinner, OK?
So, basically, this lets
you make the trade-off
by imposing a budget
constraint, by setting
relative prices across goods.
The points are like utils.
They're not meaningful.
They're only
meaningful relatively.
It lets you set relative
prices across goods
and then it lets
you, essentially,
optimize across those various--
across those various goods.
So budget constraints,
essentially,
by setting up this marginal
rate of transformation,
can help with a lot of
kind of decisions in life.
OK, questions about that?
OK, now what happens if we
shock the budget constraint?
So we talked about
constructing them.
What about shocking
the budget constraint?
We're going to do a lot
in this class of what
we call comparative statics,
which is, essentially,
making changes in
one thing or another
and seeing what it
does to the system.
So let's talk about shocking
the budget constraint.
Let's start first with
a change in prices.
Suppose the price of pizza
goes from $12 up to $18.
This is a really good
slice of pizza, OK?
Well, what happens to
the budget constraint?
Let's look at figure 3-2.
Figure 3-2 shows what happens.
You have your original
budget constraint BC1.
The equation of that line is
12P plus 6C equals 72, OK?
The price of pizza and the
number of slices of pizza
plus the price of cookies
times the number of cookies
equals 72.
Now the price of
pizza has gone up.
What that's done is that has
pivoted inward your budget
constraint to BC2.
It has flattened the
budget constraint
because the slope,
remember, is the ratio
of the price of cookies to
the price of pizza, right?
That's a ratio.
Well, that ratio
has just fallen.
It used to be a 1/2.
Now it's a 1/3.
Negative 1/2-- well,
it used to be a half.
Now it's a 1/3.
So the slope has fallen from
negative 1/2 to negative 1/3.
So what's happened is you can
still have as many cookies
as you had before.
The y-intercept has
not changed, but you
can have fewer slices of pizza.
That's why it's a pivot
because one price has not
changed, only the other price.
So it's a pivot inward.
The other thing
here, you'll notice
we have all these funny
dots and stuff, OK?
That represents
what has happened
to what we call your opportunity
set, your opportunity
set, which is an
important concept, OK?
Your opportunity set is the
set of choices available to you
given your income
and market prices,
the set of choices available
to you given your income
and market prices.
So your opportunity
set initially
was the black dots
plus the red dots.
Now your opportunity
set has shrunk.
Your opportunity set is
now just the black dots.
Given your income,
you can now get
less stuff, same amount of
cookies, but less pizza.
And you are worse off.
Your opportunity set has shrunk.
Your opportunity set-- even
though your parents are still
sending you the same check, you
are worse off because you can
now buy less pizza with it, OK?
So that's what happens
to the opportunity set
when a price changes.
And, likewise, you
should show to yourself
the same thing will happen when
the price of cookies change.
In that case, you'll
get an increase
in the steepness of the
budget constraint, OK?
But your opportunity
set will still--
your opportunity set
will still shrink, OK?
Now what about-- yeah?
AUDIENCE: Don't we not
care about all the dots
below the line, though,
because we're assuming
we're spending all the money?
JONATHAN GRUBER: Well,
that's a good point,
and we're going to
come back to that.
We haven't-- we assume they're
spending all their money,
but it's just a way
of representing.
You could think of the line
being lower as the same thing.
We care about-- we just
care about the area
because it represents the
set, but you're right.
You could just focus
on the line and say
the line is everywhere lower.
So they're worse off.
That's another
way to look at it.
But we like to think
about as a set.
It comes in handy later
for various reasons, OK?
But that's a good question.
Now let's ask about
a second thing.
What if your income goes up?
What if prices are
back to 12 and 6,
but your parents decide
to send you more money?
Suppose your parents--
or send you less money.
It turns out you haven't
been paying enough attention
in 14.01.
You're parents are mad.
They're monitoring you.
That's why we have
the camera here.
This goes directly to
all your parents, OK?
I'm sort of joking.
And so let's say parents cut
your allowance to $60, OK?
Well, what does that do?
That's in figure 3-3.
OK, in figure 3-3, the
old budget constraint
was that you get
pizzas and cookies
at a price of $6 and $12,
and you could get them
until you spend $72.
Now you can only get
them until you spend $60.
Now what we see is not a pivot
in the budget constraint,
but an inward shift in
the budget constraint,
because the relative
price of pizza and cookies
has not changed.
Therefore, the slope
hasn't changed.
OK, the slope is
dictated solely--
you don't do anything
to control the slope.
The market controls
the slope, OK?
But you and your family
control the level,
and the level has shrunk.
So you're pivoting inwards, OK?
And, once again,
now, instead of being
able to buy say 12
cookies and six pizzas,
now you can only buy say
10 cookies and five pizzas.
That's the most you can get, OK?
So, once again, your opportunity
set has been restricted,
but in a different kind of way
through this pivot inward, OK?
So that's how we
sort of manipulate
these budget constraints.
And we're going to come
back to that next lecture.
That'll be important.
Yeah?
AUDIENCE: So, in looking
at the differences,
can like an increase
in the price of pizza
or like a decrease
in your budget--
is it more showing that
like the change in slopes
doesn't really
affect you if you're
like say buying more
cookies than pizza?
But like, in terms of if
your budget as a whole
decreases, then it
affects you overall.
JONATHAN GRUBER: That's
a great question,
and we're going to actually
answer that question
next lecture very explicitly.
So hold on to that
question, and we'll
talk about we're going
to compare explicitly
why income changes
differ from price changes
and what are the
underlying mechanisms.
Yeah?
AUDIENCE: How do you
determine your marginal rate
of transformation?
How do determine your--
like say it wasn't just
pizza and cookies.
Like say it was more products.
How would you
determine that value?
JONATHAN GRUBER:
Great, great question.
So, as I said, we
always are going
to start with simplifying
assumptions to make life easy.
There's no reason
that this couldn't
be written in three dimensions.
And you'd have
relative marginal rates
of transformation, rates at
which you're willing to trade
off various things.
So you could just extend
the math in all dimensions.
It wouldn't add any
richness, and it'd just
make your head spin.
But the basic-- so
all the basic ideas
can come across with
two goods, but it'd
be the same mechanics
with more goods, OK?
You essentially, when we get to
the constrained optimization,
you'll essentially have
more first-order conditions
in your constrained
optimization.
That's the way to
think about it.
OK, so let's-- actually,
that's a great segue.
Let's turn to the
second part, which
is how we use budget
constraints and the utility
function we learned about
last time to actually describe
how consumers make choices.
So we're going to take utility.
Remember, I said
last time consumers
are going to maximize their
utility subject to a budget
constraint.
Well, now we've taught
you about utility.
We've taught you about
budget constraints.
Let's put them together, OK?
How to consume-- how do
consumers put them together?
Well, graphically, the
representation of preferences
was our indifference curves.
That represented
people's indifference
with further out
indifference curves
made people happy, right?
That was last time.
So, essentially, what we're
going to ask graphically
is what is the
highest indifference
curve you can achieve
given your budget, right?
We know you want to be that
highest indifference curve
possible by more is better.
So we're simply
going to ask what
is the highest
indifference curve you can
reach given your budget, OK?
So let's consider the same
utility from last time.
Utility is square
root of P times C, OK?
And let's consider the same
budget we wrote down up here--
$72 income, $12 price of
pizza, $6 price of cookies.
And now let's ask where
can you go with that.
So let's turn to figure
3-4 and do it graphically.
We'll do it mathematically
in a minute, OK?
So, in figure 3-4, you
have our budget constraint,
which runs from 6
pizzas to 12 cookies.
That's the original
budget constraint.
And you have a series
of indifference curves.
And these indifference
curves, I1, I2, I3, I4,
they all come directly
from this utility function.
So, simply, I've solved
this utility function.
I'll talk about the
math in a little bit,
and you'll do more math
in section on Friday, OK?
But, essentially,
you can solve--
we'll show you--
you'll drive on Friday
how you take this
utility function
and literally can draw the
indifference curves from it,
OK?
But, for now, take my word
that these indifference curves
represent this utility function.
And what we see is that
point D is the furthest out
indifference curve you
can achieve while still
meeting your budget, while still
meeting your budget constraint.
And, therefore, we say that
the optimum, graphically,
is the tangency between
your indifference curve
and your budget constraint is
the optimal constrained bundle.
You see how we brought--
last time, we talked about
further out indifference curves
make you happier.
Today, we talked about
the fact that you're
limited by your budget.
So we have the furthest
indifference curve
you can get to is going
to be, definitionally,
at the tangent of the
indifference curve
and the budget constraint.
And, once again,
that gives you--
we realize we don't want
to measure utils, but, just
for mathematical, for
mathematical purpose, that
gives utility at the tangency
of square root of 18, OK?
At that point, you are choosing
six cookies and three pizzas.
That is the choice
you are making.
That is the best off you
can get given your budget.
And, to see this, let's
talk about some other points
and why they're not better, OK?
Let's talk about point A.
Why isn't point A better?
Why isn't it better
to have two-- maybe
you just-- maybe you
like cookies a lot
and don't like--
or like pizza a lot
and don't like
cookies that much.
How can we say that point
D is better than point A?
Yeah?
AUDIENCE: Because point D is
on a higher indifference curve.
JONATHAN GRUBER: It's on a
higher indifference curve.
So point D dominates
point A because it's
a higher indifference curve.
Well, fine.
Same person, by that logic,
why not choose point E?
AUDIENCE: It's above the budget.
JONATHAN GRUBER: Yeah,
you can't afford it.
So the bottom line is
you can see graphically
why the tangency is
the best you're going--
is the best you're going to do.
OK, likewise, point C
you wouldn't choose.
Point C has the same slope.
It has the same
slope as point D.
In other words, the slope
is minus 1/2 at point C.
You've drew a line tangent
to point C. The slope will
be minus 1/2, just
like it is at point D,
but you wouldn't be
spending all your money.
So you wouldn't choose
that point either.
Yeah?
AUDIENCE: What if you have
just three indifference
curves so there is none
that hit the tangent?
Do you just go for one that's
like the most tangent I guess?
JONATHAN GRUBER: We're going
to come to-- we're going to--
well, first of all,
we're not going
to have discrete indifference.
We could have lines, and
the lines could end up--
you could end up lying along.
You could end up lying along a
budget constraint for example.
Or you could have--
you could even have
utility functions,
which just touch a
budget constraint
at one extreme or another.
And we'll talk
about those cases.
Yeah?
AUDIENCE: So [INAUDIBLE]
utility function
go through lines and the
budget constraint, right?
JONATHAN GRUBER: Yeah.
AUDIENCE: Isn't this just
Lagrange [INAUDIBLE]??
JONATHAN GRUBER: Well,
let's come to the math then.
OK, let's come to the
mathematical derivation.
So that's the graphic.
So let's come to the math, OK?
Now, always a bit
of a tightrope act
when I'm doing math up here on
the board, so bear with me, OK?
But the key thing is the math
of constraint optimization
is all about the
marginal decision.
Remember, it's hard to say
how many cookies you want.
It's easier to say should
I have the next cookie, OK?
It's about constraint
optimization.
And what we want to ask is we
essentially want to compare
how do you feel about trading
off pizzas versus cookies
versus what will the market let
you do in sort of trading off
pizzas versus cookies.
That is the optimum
is going to occur
when we set your marginal
rate of substitution,
which, remember, we defined
as minus MUc over MUp, equal--
I'm going to get rid of this--
equal to your marginal
rate of transformation,
which we defined as
minus pc over pp.
And this is the fundamental
equation of consumer choice.
If you understand
this equation, you
can solve virtually
every consumer choice
problem I'll give you, OK?
That basically, at the optimum,
the ratio of marginal utilities
equals the ratio prices.
That is the rate at which
you want to trade off pizza
for cookies is the rate
at which the market will
allow you to trade off
pizza for cookies, OK?
Basically, it's saying
the ratio of the benefits.
Think of this as the benefits
and this as the costs.
Think of the MRS
as the benefits.
It's what you want.
MRT is the costs.
It's where you're constrained.
You want to set the
ratio of the benefits
equal to the ratio
of the costs, OK?
Now I find it actually easier
to think of it this way.
If you just rearrange terms,
you can write it as MUc over pc
equals MUp over p sub p.
I like this way of writing
it because I call this
the bang for the buck equation.
What this is saying, your
marginal happiness per dollar
should be equal.
This is sort of the happiness
per dollar spent on cookies.
This is the happiness per
dollar spent on pizza.
And you want those to be equal.
You want the bang
for the-- you want
to put your next
dollar where it's
going to make you happiest, OK?
And so, basically, think of
that as your bang for your buck.
So, for example, suppose
you were in a position
where the MRS was
greater than the MRT.
You're in a position where the
marginal utility of cookies--
and I'm getting
rid the negatives.
There's negative on both sides.
So I'm just going to get
rid of the negatives, OK?
The marginal utility of cookies
over the marginal utility
of pizza was greater
than the price of cookies
over the price of pizza, OK?
That is the slope of
the indifference curve
was greater than the slope
of the budget constraint.
This is the slope of
the indifference curve.
OK, this is slope of
the indifference curve.
This is the slope of
the budget constraint.
In absolute value, the slope
of the indifference curve
is greater in absolute value
than the slope of the budget
constraint, OK?
That would be true at points
like point A, point A where
you intersect--
where you basically intersect
from above the budget
constraint by the
indifference curve.
So a point like point
A has a steeper slope
of the indifference curve than
does the budget constraint.
What that says is
intuitively-- and, once again,
I want you to understand
the intuition--
the rate at which you
are willing to give up,
the rate at which you
are willing to give up
cookies for pizzas--
I'm sorry.
Let me say it--
let me say it a better way.
The marginal benefit to
you of another cookie
relative to another
pizza is higher
than what the market will charge
you to turn pizza into cookies.
Let me say it again.
The marginal benefit to you of
another cookie, which is this--
this is how much more
you want the next cookie
relative to how much more
you want the next pizza--
is greater than
what the market is
going to charge you to trade
in your pizza for cookies.
Therefore, you should trade
in your pizza for cookies, OK?
So let's say this
mathematically.
At a point like A,
point A, OK, you
have your marginal
utility for pizza
is the derivative of the
utility function with respect
to the number of
slices of pizza.
It's the marginal utility.
It's derivative of
the utility function.
So it's dU dp, which is equal
to 0.5 times C over square root
of P times C, OK?
And, at point A,
at point A, we had
two cookies and five pizzas.
At point A, P was five.
C was two.
OK, that's true of point A.
So we can evaluate the
marginal utility dU
dp, which equals 0.5 times C
over square root of P times C.
So that's 1 over the
square root of 10.
That's the marginal utility
of the next slice of pizza.
The next slice of
pizza makes you
1 over square root of 10 happy.
Once again, that
number is meaningless.
So we only care
about it in ratios.
So we need the ratio.
So let's do the marginal
utility of cookies.
That's dU dC, which
is 0.5 times P
over square root of P
times C, which is 2.5
over the square root of 10, OK?
So the marginal utility of pizza
is 1 over square root of 10.
Marginal utility of cookies is
2.5 over the square root of 10.
Therefore, your marginal rate
of substitution is minus 2.5.
Remember, marginal rate of
substitution is MUc over MUp.
So your marginal rate of
substitution is minus 2.5.
What does that mean?
Can anyone tell me
what that means?
Your marginal rate of
substitution is 2.5.
What does that mean?
That is a meaningful concept.
Utils are not, but that is.
Yeah, say it loudly
so we can hear.
AUDIENCE: You're
willing to trade--
you're willing to trade
two pizzas for one cookie.
JONATHAN GRUBER: You're
willing to trade.
Exactly, you're willing to
give up 2.5 slices of pizza
for one cookie.
That's what that number means.
And that is a meaningful number.
That's not an ordinal.
That's cardinal.
We can use that.
You are willing to give
up 2.5 slices of pizza
to get one cookie.
What is the market
asking you to give up?
How much pizza do you have
to give up to get one cookie?
Half a slice.
You are happy to give up
2 and 1/2 slices of pizza
to get a cookie,
but the market is
saying we'll let you
have a cookie for half
a slice of pizza.
So what should you do?
AUDIENCE: Trade.
JONATHAN GRUBER: Eat less pizza.
Eat more cookies.
That will unambiguously
make you happier.
And that's why you should move
from point A towards point D.
OK, that's the intuition, OK?
You basically want to
trade pizza for cookies
until these things are equal.
Indeed, I'd like you to go home
and do the same math starting
at point B. If you do the
same math starting at point B,
you'll find the MRS
is much below 1/2.
That is, at that point,
you are happy to give up
tons of cookies to get pizza
because, jeez, you've got 10
cookies and one slice of pizza.
You'd give up tons of
cookies to get pizza.
But the market says you
only have to give up
two cookies to get pizza.
So you'll happily do it, and
you move back towards point D.
And that's sort of in a bundle
sort of the intuition and math
and graphics of how we do
constrained optimization.
OK, that is hard
and very important.
Questions about that?
Don't hesitate to ask.
OK, that is hard
and very important.
If you understand
this, you're sort of
done with consumer theory, OK?
This is sort of the core of what
consumer theory is all about.
It's all about
this balancing act.
The whole course
is fundamentally
all about one equation,
which is marginal benefits
equals marginal costs, OK?
Everything we do is going
to be about weighing
the marginal benefit
of an activity
against its marginal costs.
If we take the next
step, what's the benefit?
And what's the cost?
Well, here the marginal
benefit is the MRS.
The marginal cost is the MRT.
We want to set them equal.
And this sort of example
I hope explained why, OK?
So that is how we think
about constrained choice.
Now I want apply it.
I want to apply it by looking at
the example of food stamps, OK?
Now food stamps are not actually
called food stamps anymore.
When I was a kid, they
were called food stamps.
It's basically a program
the government has
that provides money
for individuals
to buy food if
they're low income.
Essentially, we have in the US
what's called the poverty line.
And I'll talk a lot more about
this at the end of the class,
but the poverty
line is essentially
a measure of what's a
minimum level of resources
you need to live in America.
The poverty line for an
individual is about $14,000.
OK, for a family of
four, it's about $28,000.
How you feel about
that number obviously
is going depend on
where you're from.
If you're from Boston,
you'll say that's insane.
If you're from some rural
part of the country,
you think, yeah, that's
poor, but manageable.
OK, we'll talk later
about the poverty line,
what's good and bad about it.
But, in any case, if you're
below the poverty line
in America, roughly speaking,
you get help with buying food.
And that comes through a
program we now call SNAP.
It used to be
called food stamps.
I've got to update my notes.
Supplemental Nutrition--
I don't know.
I know the N is for nutrition.
OK, so, basically, what
the SNAP program does
is it gives you a debit card.
If you qualify on income
grounds, you get a debit card,
and that debit card can be used
to buy food and food only, OK?
So you essentially get a
debit card from the government
that you can use to buy
food if you're poor enough.
And they give you sort of
a fixed amount every month,
and that amount can be
used to purchase food.
So here's the question.
Why go through this rigmarole?
Why not just give people cash?
This fancy thing, if we want
to give poor people money,
why don't you just
give them money?
And we're going to--
I don't want the answer yet, OK?
What I want to do is
show you graphically
how we think about
the trade-off,
and then we'll
come to the answer.
So hold your thoughts.
So let's actually graph how
we think about food stamps.
Let's go to figure 3-5A.
And let's start with
a cash transfer.
So here's the setup.
Imagine people start
with an income of $5,000.
That's super poor, OK?
$5,000 is their whole family
income for the year, OK?
And let's say all they can
spend it on is food or shelter.
Remember, as this gentleman
pointed out, in life,
there's more than two goods,
but it makes it a lot easier
to have two goods.
So imagine this case.
Your two goods are
food and shelter.
And, actually, quite
frankly, if you're that poor,
that probably is
the only two goods
you have to-- you can worry
about at that level of income.
OK, it's food and shelter.
So you $5,000 to devote
to food and shelter.
So you have some
original budget line,
which is labeled
there original budget
line, that runs from 5,000
in food to 5,000 in shelter.
And then you can have some of
in between, some along the way,
OK?
Now let's say we give
someone $500 in cash.
Obviously, this graph
is not to scale, OK?
It looks like you're doubling
his income, but it's only $500.
This just sort of makes it
easier, a not to scale graph.
Let's say we give someone-- we
say to them, look, you're poor.
We're going to give
you $500 in cash.
Well, now all we've done
is shift out your budget
constraint from 5,000 to 5,500.
OK, we've shifted out
your budget constraint
from 5,000 to 5,500.
What does that do
to your choices?
Well, consider two
different types of people.
Person y, OK, they used to
be on indifference curve I0.
They used to spend almost
all their income on food
and not a lot on shelter.
They were probably homeless, OK?
So they spent all
their money on food
and were basically homeless.
Now what do they do?
Well, they spend a little
more on food and a lot more
on shelter.
Maybe now they get--
you know, $400 still
doesn't buy you much shelter.
They spend a little more, OK?
Maybe, a night a week,
they can get shelter, OK?
So, basically,
that's what they do.
That's their constrained
optimization.
We're not saying
it's right or wrong.
This is not normative economics.
It's positive.
The positive thing is, given
their utility function,
they move from point y1 to y2.
Now imagine someone
like individual x.
They're different.
Their tastes are such that
they don't need to eat.
They just want to have shelter.
So they're up at
point x1 initially.
And you give them
that $500, and they
spend just a little bit more of
it on food and even more of it
on shelter.
They just love
their shelter, OK?
And they're just super--
they're super Weight Watchers.
They don't eat, OK?
So, basically, they
move from x1 to x2.
Once again, not
normative right or wrong,
it's just these are
feasible choices people
could make given the opportunity
set with which they're faced.
And that's what happens when
you give them the $500 in cash.
Questions about what I did
here on this graph alone?
Yeah?
AUDIENCE: Like, even
if like you gave them
money specifically for
food, couldn't they then
just reallocate
their other money?
JONATHAN GRUBER: OK,
that's a good point.
We'll come back to that.
That's time out if
you're not a sports fan.
OK, so we will
come back to that.
And, in fact--
OK, but do people
understand what the cash
transfer is, how it works?
OK, now let's go to SNAP.
And let's say, with SNAP,
instead of giving them $500,
we'll give them the debit card.
Instead of handing
them a $500 check,
we give them a debit
card with $500 on it
that can only be used on food.
How does this affect
their budget constraint?
Now we see where budget
constraints start
to get interesting and fun
and the kind of challenges
you're going to face in this
course in drawing budget
constraints.
The original budget
constraint continues
to be the original budget line
running from 5,000 to 5,000.
The new budget constraint
is this kinked line
that runs from 5,000 on
the y-axis to the point
x2 at 5,000 on the y-axis.
So it starts at 5,000 on
the y-axis, 0 on the x-axis.
There's a flat line that goes
to 5,000 on the y-axis, 500
on the x-axis.
And then it slopes down
parallel to the original budget
constraint to 5,500.
Can someone explain to me
why that's the new budget
constraint?
Yeah?
AUDIENCE: You can't
spend a negative amount.
So you can't spend
like negative amounts
of your non-food-stamp
money on food.
JONATHAN GRUBER:
Exactly, you have--
we are forcing you to
spend at least $500.
Compared to cash, where you can
do whatever the hell you want,
we are forcing you to spend
$500 of your money on food.
Coming to the
question back there,
it doesn't have to be a
specifically labeled 500.
It can be any 500.
But we're forcing you to
spend at least $500 on food.
Well, what does that
do to your choices?
Well, for person y,
it makes no difference
whether they get cash or
whether they get food stamps.
Now the person, light blue
shirt, turquoise shirt,
asked that question.
Why does it make no difference?
Yeah?
Why does it--
whatever, greenish, I
don't know, yeah, you.
Why does it make no
difference for person y
if I give him food
stamps or cash?
AUDIENCE: He's already spending
a lot of his money on food.
So any money he gets he can
just reallocate differently
so he can spend
some of the money
he would have used
on food on shelter.
JONATHAN GRUBER: Exactly, he can
just reallocate his money, OK?
That's exactly right.
So, for person y,
there's no difference.
Look, they're already
spending, what, $4,900 on food.
You give him a thing
labeled $500 for food.
It's not going to
affect their life.
They'll just take 500.
They'll just spend-- they'll
just treat it as $500 more
in cash.
They're indifferent.
So nothing affects them.
But what about person x?
Well, person x, remember,
the dashed portion
of this budget constraint is
from the old cash example.
And the dotted
indifference curve
is what they would
have chosen with cash.
Remember, person
x with cash would
have chosen to still spend
less than $500 on food.
Even when you gave
them $500, they still
only spent $300 on food.
So we are forcing them to not
be on their preferred budget
constraint.
Rather, we're forcing
them down to point x2,
which is they'll spend the
minimum they can on food,
but the minimum is $500, OK?
We are forcing them
down to point x2.
Now why do I say forcing them?
Why do I know for sure they
are being forced, that they're
less happy at x2 than they would
have been when they gave them
the cash?
How do I know that for sure?
Yeah?
AUDIENCE: They're at a
lower indifference curve.
JONATHAN GRUBER: Exactly.
Think of it this way.
The fundamental-- one
of the important things
is people always get
to the point that
makes them happiest, OK?
We call it the robustness
of economic equilibria.
People get to the point
that makes them happiest.
They want-- they
always before had
the choice of spending $500 on
food, and they chose not to.
Therefore, if you force
them to spend $500 on food,
they must be less happy, OK?
Think of it that way.
They always could have
spent $500 on food.
They didn't.
Therefore, in
forcing them, you're
making them less happy, OK?
So they are worse off, OK?
They are forced to spend.
They'd rather spend
some of that money
and find a nicer place to live,
but we're not letting them.
We're making them buy food, OK?
Do people-- I don't want--
I just want to know if people
understand the graphics here
and the conclusions I drew.
OK, now why?
Why are we doing this?
Why would you-- they're
better off with cash.
Why would we force
them to have food?
Yeah?
AUDIENCE: Say
because what makes--
what puts people on the
highest indifference
is just what makes them
happiest, but not necessarily
what makes them like
live the longest
or like have the best
health So, perhaps,
like if you never spend money
on food, and then you die,
that would be really bad.
JONATHAN GRUBER: OK, but,
basically, what you're saying
is you know better than the guy.
Let me-- I'm not accusing you.
I'm just saying, look,
if people knew best,
maybe they'd like to just like
have a nice house and die, OK?
If people knew
best, then there'd
be no reason to do this.
The reason to do this is because
we think they don't know best.
So, for example, let's change
the label on the y-axis, just
a small change.
Let's cross out shelter
and write cocaine.
[LAUGHTER]
OK?
Well, in that case, maybe
we don't feel so bad
about forcing the guy to buy
food instead of cocaine, OK?
In other words, this a
program which might make
sense if we are paternalistic.
Now we're getting into normative
economics, paternalistic.
If we think that people
won't necessarily
make the right decisions
for themselves,
then it may be worth
actually making them
worse off because
they're not worse off.
Their perceived
benefits are worse,
but they don't know
what they're doing, OK?
Now you can see why--
I hope you can
sort of immediately
see why this concept makes
economists a little nervous
because why do we know what they
want better than they do, OK?
So it makes people a
little bit nervous,
economists a little
bit nervous, and a lot
of people a little bit nervous
to say, gee, maybe they're
just happier doing cocaine.
And how do we know that
that's the wrong way for them
to spend their resources?
Yeah?
AUDIENCE: Well,
like can't you look
at it from the perspective of
like this is taxpayer money,
right?
So then aren't you
also just factoring
in how the taxpayer wants to
spend their money and then
their indifference curve
and all their information?
JONATHAN GRUBER: That's
a very good point.
Now but there's sort
of two points there.
First of all, if the taxpayers'
goal is to help poor people,
then why shouldn't you make them
as happy as possible, right?
If tax-- why am I giving
money to this poor guy?
Because I'm sad his poor.
But, what you're saying, I'm
not actually that sad he's poor.
I'm sad he's not eating.
If you're really
just sad he's poor,
then you should give him money.
If what you're
sad about is, gee,
I don't like how he's living--
I don't like his--
I'm sad he can't have better
food to eat, sad at the place
he lives.
Then you're starting to
impose your preferences,
but let's be important.
That's imposing
your preferences.
Yeah?
AUDIENCE: I feel like the
indifference curve only
goes for happiness or
like contentedness,
but, really, the point
of SNAP isn't really
with contentedness or
happiness, but rather
like what would be to a
more sustainable life.
JONATHAN GRUBER: Well, that's a
related point of the taxpayer.
If the taxpayer
cares about, look,
we want a healthy
populace that's
going to live a long time and
be productive and pay taxes,
then that would be
a reason to do this.
But, once again, I
want to emphasize,
OK, this is paternalism.
If you really just care
what makes people happiest,
you should give them cash, OK?
So that raises
two questions, OK?
First of all, first
question-- yeah?
AUDIENCE: So how about
like negative [INAUDIBLE]..
Because, for example, if
we pump a lot of money--
if we allow people to
spend a lot on shelter,
that's not really
going to help people.
It would just make the real
estate developers rich.
And say the amount
of shelter is kind of
fixed, but like the amount of
food that eaten [INAUDIBLE]..
So, if we let people
spend more money on food--
JONATHAN GRUBER: Yeah,
yeah, so, basically, that's
a great question.
And, in general,
we're going to--
I'm going to answer a
lot of those questions
with the same cheat
this semester,
which is we're going to assume
the markets are perfectly
functioning.
So there's no-- you're imposing
sort of a market failure.
If there's no market-- once
there's market failures,
all bets are off.
But, with no market
failure and no paternalism,
you'd want to give them cash.
So this raises an
important question.
Do food stamps actually
increase food purchases?
First of all, there's two
reasons why they might not.
Reason one is everybody
could be like y.
x is sort of a
silly case, right?
You're going to die if
you eat that little.
And food stamps
aren't that much.
They're maybe like
$3,000 a year.
Everybody is going
spend $3,000 on food.
So the first issue is the first
reason why food stamps may not
matter is that, in
fact, everybody is
spending at least that amount.
Everybody is like y,
and nobody is like x.
What's another reason
why it might not matter?
What's a way people could
get around food stamps?
Yeah?
AUDIENCE: Buy food with
food stamps and sell it.
JONATHAN GRUBER: Yeah,
they could set up
a black market where they,
essentially, say, look,
I only want $2,000 of food.
The government is
making it worth $3,000.
I'll buy my extra
$1,000 of food,
and I'll sell it to
people who do want it.
And I'll end up still
eating $2,000 worth of food.
So we actually want to know do
food stamps actually increase
food consumption in practice.
Are they making a difference?
Well, actually, we've run
an experiment on this, OK?
We're going to talk
in this class a lot
about empirical
results in economics.
This class is mostly going
to be a theoretical class.
That is we'll talk
about models and ideas.
But we're also--
since, basically, I'm
an empirical
economist, we're going
to talk about empirical
economics, which is results
and testing the
theories we develop.
Empirical economics,
here's a great example
of empirical economics is we
set up a theoretical model.
You always want to
start with the theory,
but the theory sometimes
has predictions,
which are uncertain.
Here we have an uncertain
prediction from theory about
whether food stamps will
affect food purchases or not.
So let's test it.
And the way we test
it is we actually
have run food stamps cash out
experiments where we literally
take guys on food stamps
and give them cash instead
and watch what happens to their
consumption before and after.
It's a real randomized trial.
We literally flip a coin.
Heads, you keep
your food stamps.
Tails, we replace
those food stamps
with an equal amount of cash.
Then we watch what happens.
What happens is that people
spend about 15% less on food
when you give them cash
instead of food stamps.
That is food stamps is forcing
people to spend about 15%
more on food than
they would like
to unconstrained by the cash.
Yeah?
AUDIENCE: Yeah, this gets
you into the behavior of
[INAUDIBLE].
I remember reading an
experiment like, if you
have the price of gas go down,
the actual like amount of money
spent on gas is constant.
And this might
translate to food stamps
because like food stamps
are like explicitly on food.
JONATHAN GRUBER: Yeah, you
know, that's a great question.
And that's you're asking about
richer theory, richer theory.
And I'm telling you that
I'm going to give you
the empirical evidence.
So, whatever the theory
is, the empirical evidence
tells you what happens.
And there's different
explanations for why.
So the empirical evidence is
that, basically, the price
of our paternalism is 15%, OK?
We are making people,
effectively, 15% worse off.
We're making them spend 15%
more food than they want to.
So is it worth it?
Well, actually, the
evidence is starting
to pour in that it might not
be worth it because there's
starting to be a lot of
experiments where we're
giving people just cash,
especially in developing
countries.
In developing
countries, the answer
seems to be just
giving people cash
makes them better
off, that actually,
especially in
developing countries,
people use the cash
in productive ways.
So, for example, they have a
series of evaluation programs
where they've given people cash,
mostly in developing countries,
in Africa in particular,
some in the US.
And they find that people
spend relatively little
of that on drugs and
alcohol, but they actually
tend to spend it productively.
And, in fact, they found,
in developing countries,
this often provides valuable
resources for individuals
to start businesses.
So they ran experiment Uganda
where a nonprofit company
randomly offered
a group of women
$150, which is huge
relative to their income.
That's 50% to 100% of annual
income in Uganda, $150.
And what they found was, after
two months-- after 18 months,
these women had used that
money to start businesses.
And that actually
raised their earnings.
That actually effectively
doubled their earnings.
From that one
injection of cash, it
led them to actually double
their annual earnings, OK?
So that leads one to
think that maybe we
should stop being paternalistic
and just give cash.
Unfortunately, if you're a
reader of policy websites like
I am, the best one
of which is vox.com--
it's a great website--
they had an article just
the other day pointing out
how they actually followed
these women up nine years later.
And, nine years later, the
effect had totally gone away.
So the story isn't quite
necessarily positive,
but it's not negative.
They're not worse
off, but it looks
like, at least what
in the short run
made them better off, well,
that effect fades over time.
But the bottom line
is, at this point,
I think the evidence
is sort of probably
in favor of being
less paternalistic
and just giving
people cash, but that
runs into a lot of difficulties
in terms of our concerns
about how people will spend it.
So let me stop there.
We will come back
on Monday, and we'll
talk about how we actually go
from this stuff to the demand
curves we started
the class with.
