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PROFESSOR: All right, so today
we're going to continue our
discussion of consumer choice.
If you remember the set-up
from last time, the main
motivation is you're trying to
understand what underlies
demand curves, how consumers
ultimately decide to trade off
price and quantity of goods.
We said that ultimately that
came from the principle of
utility maximization, and that
utility is maximized when
individuals maximize the utility
function, which is
this mathematical representation
of preferences.
And last time we talked about
how if individuals were
unconstrained how they choose
what they want, they would
just like more of everything,
and their ranking across
different bundles would
depend on that
underlying utility function.
Now, of course, what's stopping
individuals from
consuming everything they want
is their budget constraints.
And so today we're going to turn
to the second part of the
problem, which is talking about
budget constraints.
Now, we're going to make a very
simplifying assumption
here for most of the semester,
which is we are going to
assume that your income
equals your budget.
That is, you spend your
entire income.
That is, we're going to ignore
the possibility of savings
until about the third lecture
from the end.
Now, this turns out not to be a
terrible assumption for the
typical American.
The typical American doesn't
save. So actually, it's not a
terrible assumption for us to
work with if we think about
typical consumers.
In practice, savings is going
to turn out to be a very
critical part of what we're
going to do to think about
economics, so we'll
come back to that.
But we're going to ignore
savings for now and assume
that your budget equals
your income.
So let's say that your parents,
probably a good model
is you guys, you guys probably
aren't in saving mode.
You've got some budget saved
from your parents.
Let's call it y.
And let's say that your parents
give you some budget
at the start of the semester,
y, and they say this is your
money you have to spend,
say each month or
for the whole semester.
And let's imagine that you have
to allocate that budget
only across two goods,
pizza and movies.
So once again, unrealistic,
but this is the kind of
simplifying assumption that lets
us understand how people
make decisions.
So that gives you your
budget constraint.
You've got some income y that
your parents have given you,
and you can allocate that
across pizza and movies.
So how do you allocate that?
Well, you can buy movies, the
number of movies you can get,
plus the number of pizzas.
Well, how many of each
you can get, that
depends on their price.
In particular, budget constraint
is the number of
movies times the price
per movie plus the
number of pizzas --
plus the number of pizzas times
the price for pizza.
That's your budget constraint.
It's the number of movies times
the price per movie or
the number of pizzas times
the price for pizza.
And this is easiest to
see graphically.
If you go to figure 5-1, this is
a graphical illustration of
a budget constraint.
Now, let's just carefully talk
through this for a moment.
You're going to be really good
at dealing with budget
constraints.
You're going to have to
be this semester.
So let's carefully talk about
where this comes from.
OK, the x-axis is going to be
how many movies you could have
if all you did with your income
was consume movies.
Well, if all you did with your
income was consume movies, you
could have y over
p sub m movies.
If you decided to devote your
income solely to movies, then
you could have y times y
over p sub m movies.
If instead you decided to devote
all your income to
pizza, then you could have
y over p sub p pizza.
So the y-axis is going to be
the point where you consume
zero movies and all pizza.
It's going to be where
you devote your
entire budget to pizzas.
And then there'll be some
combination in between, which
is our budget line.
Which is the combinations of
pizzas and movies you can
consume given your
total income y.
And the slope of that line is
going to be the price ratio.
Or the negative of
the price ratio.
The slope of that line is going
to be minus pp over pm.
The slope of that line is going
to be the change in the
ratio of the price of pizza
to the price of movies.
OK, what am I doing
wrong here?
Negative of the price ratio.
Have I got this right?
Rise over run.
Yeah.
Have I got this right?
Yeah.
AUDIENCE: I think that the pp
and the pm's are in the
denominators, because it's y
over pp [INAUDIBLE PHRASE].
PROFESSOR: Right.
It's the denominators, that's
what I did wrong.
Right, so it is pm over pp.
Sorry, my bad.
OK, right.
Because they're the
denominators.
Because it's the rise over run
in terms of the quantity.
So that's what I did wrong.
OK, so basically it's the
negative of the price ratio,
minus the price of movies over
the price of pizzas because
they're in the denominators as
you said, because as the price
goes up, the quantity
goes down.
So the negative of the price
ratio of the price of movies
to the price of pizzas
is the slope.
So let's just do a
simple example.
Imagine that income
equals $96.
Imagine your parents
give you $96, say
a month or a semester.
Imagine that the price of movies
is $8 and imagine the
price of a pizza is $16.
It's a good pizza.
So what this means is that with
your income of $96, you
could either get eight
pizzas or 12 movies.
So that means that the price
ratio of the slope of your
budget constraint
is minus 1/2.
The price ratio is minus 1/2.
So the slope of that budget
constraint is minus 1/2.
Now, we have a name
for this slope.
We're going to call this
the marginal rate of
transformation.
The marginal rate of
transformation is our label
for this slope.
Now, why do we use that name?
Well, it means that's the
marginal rate at which you can
transform pizzas into movies.
The rate at which you can
turn pizzas into movies.
Now, once again, like I talked
about last time, you're not an
alchemist. You're not actually
turning pizzas into movies.
But the market essentially is
giving you a rate at which you
can do that given a budget,
given that you have a certain
amount of money.
Given that you have a certain
amount of money, $96, and
given the prices that you face
in the market, you could
transform pizzas into movies
by trading one
pizza for 1/2 a movie.
Now, once again, you're not
actually doing the physical
transformation, but that's the
trade-off that you face when
you're trying to transform
one to the other.
So effectively, it's the same as
if you're trading them for
each other.
As I talked about last time.
it's essentially the same as
you're trading, and that's
because of the key economic
concept we'll come back to
over and over again
in this course--
the concept of opportunity
cost.
The opportunity cost is the
value of the forgone
alternative.
The value of the forgone
alternative is the opportunity
cost. So basically what that
means is if you decide to
forgo a pizza, that's the same
as forgoing two movies.
Likewise, if you decide to forgo
a movie, it's the same
as forgoing half a pizza.
So the opportunity cost of a
movie, what essentially the
movie is costing you,
is 1/2 a pizza.
Now, really it's costing you $8
and a pizza costs you $16.
But when we think about
trading off goods, the
opportunity cost of that movie
is that you've forgone the
ability to eat half a pizza.
That's the opportunity cost
of the situation.
So that's basically
how we're going to
think about this trade-off.
We're going to think about
trading off goods as the
opportunity cost of consuming
one good instead of another.
The opportunity cost of that
movie is that you haven't
gotten to eat 1/2 a pizza.
The opportunity cost of the
pizza is that you've forgone
seeing two movies.
And the reason is because
you have a fixed budget.
If you had an infinite budget,
there'd be no opportunity
cost. But because you have a
fixed budget and you have to
allocate that budget, there's
an opportunity cost. If you
choose not to decide, you've
still made a choice.
I don't know whether that
quote's due to Shakespeare or
Rush, I'm not sure.
I have to look that up.
But basically, if you choose
to have one thing, then by
definition you're forgoing
another.
Now, to understand the budget
constraint, let's talk about
what happens when we shock
the budget constraint.
Let's imagine the price of
pizzas rose from $16 to $24.
Pizzas got really expensive.
We decided we only want gourmet
pizzas or something.
The price of pizzas went
from $16 to $24.
What does this do?
Well, let's look
at figure 5-2.
It'll show what that does.
What that does is it says our
new budget constraint, instead
of being 16p plus 8m equals 96,
which is what the budget
constraint was in our example,
it's now 24p
plus 8m equals 96.
That's the new equation for
the budget constraint.
Or, more relevantly, the slope
of the budget constraint has
flattened from minus
1/2 to minus 1/3.
The slope has fallen from
minus 1/2 to minus 1/3.
The price ratio has been reduced
from 1/2 to 1/3.
Now, forget utility
for a second.
Forget the fact that we
thought about utility.
Just looking at this, can you
tell whether you are better or
worse off from this
price change?
You shook your head
no, why not?
AUDIENCE: Because you don't know
if you like pizzas enough
to get any.
PROFESSOR: OK, well
in particular,
you can almost tell.
Who's the only person
who doesn't care
about this price change?
AUDIENCE: [INAUDIBLE]
PROFESSOR: No, no no.
Think about consumers, people
with different preferences for
pizzas and movies.
What would your preference for
pizzas and movies have to be
for you not to care about
this price change?
All movies.
So long as you care about
pizza at all,
you're worse off.
So in fact, the answer is your
opportunity set has been
restricted.
So we can think about
the opportunity set.
Your opportunity set is the set
of choices you can make
given your budget.
Before, you could make choices
all the way up
to the upper line.
Now your set of choices
that are
available have just fallen.
Now, you're no poorer-- it's
not like your parents
have cut you off.
They still give you the $96.
But you're effectively poorer.
You're effectively worse
off, and why is that?
Because the set of things you
could afford with that $96 has
just been restricted.
And unless you truly have no
value on pizza, unless all you
care about's the movie--
you're gluten and cheese
allergic or something, you
have no value on pizza--
then you're worse off.
Your opportunity set's
restricted.
And that's the key insight here,
is that you are worse
off because the price
has increased.
A price increase makes
you worse off.
It restricts your opportunity
set, because with the same
amount of income, you can
now afford fewer goods.
Your opportunity set has
been restricted.
Likewise, now let's talk
about what happens
when your income falls.
That's the next figure.
Now, let's suppose your parents
are pissed at you and
they cut you down to $80.
Because you didn't
do something.
You don't write enough or
call enough, so they
cut you down to $80.
Well, here the slope
of the budget
constraint has not changed.
Because what determines the
slope of the budget
constraint?
It's prices, and no prices
have changed.
The slope of the budget
constraint is unchanged
because prices haven't changed,
but your opportunity
set is once again restricted
because you
now have lower income.
So you can now afford fewer
pizzas and movies.
So now, instead of being able to
afford up to six pizzas and
up to 12 movies, you can now
only afford up to five pizzas
and up to 10 movies because
your income has fallen.
So once again, you're
unambiguously worse off.
Your opportunity set
has contracted.
So your opportunity set will
contract whenever income falls
or whenever price increases.
And how it affects the graph
will depend on whether it
affects prices, which affects
the slope, or just income,
which affects the intercepts.
Now, questions about the
budget constraints and
opportunity sets?
Armed with that--
Yeah, I'm sorry, go ahead.
AUDIENCE: Is the area under
the curve at all
indicative of utility?
PROFESSOR:No, it's not, because
that's going to be
determined by your
preferences.
It's indicative of, if you
will, potential utility,
because that's your
opportunity set.
But as the example here points
out, if you don't like pizzas
at all, you'll feel very
differently than if you like
pizzas a lot.
So it's indicative of sort of
your potential utility, but
not your actual well-being.
But now that's a great segue
to the next step.
Let's put that together and talk
about constrained choice.
Which is now, let's
put together--
we know what your preferences
are, we've mathematically
represented those by
utility function.
We know what your budget set
is, we've mathematically
represented that based on
your income and prices.
Now let's put them together
and talk about
how you make choices.
And the basic question you want
to ask is, what's the
highest utility you can achieve
given the constraints
your budget constraints
put on you?
Or, graphically--
so let's say you wanted to
understand this intuitively,
graphically, and
mathematically.
Intuitively the idea is quite
simple, I think, which is
just, what's the most you can
have given the constraints
that are placed on you?
Graphically, we represent that
as asking, what is the
furthest out indifference
curve you can achieve?
Because remember,
more is better.
Indifference curves that are
further out make you happier.
So what's the furthest out
indifference curve that you
can achieve given your
budget constraint?
So to do that, let's actually
do an example.
Let's imagine, as last time,
your utility is the square
root of pizza times movies.
Once again, this has no
fundamental meaning, it's just
a mathematical representation
of your preferences.
So your preferences are
mathematically represented by
utility equals square root
of pizza times movies.
And let's have the same
budget constraint
that we have up here.
Income is $96, price of movies
is $8, price of pizza is $16.
Now let's go to the
next graph.
Figure 5-4.
What this does is put together
our indifference curve
analysis with our budget
constraint analysis.
It's a little complicated.
The budget constraint line is
the vertical line running from
a y-intercept of six to
an x-intercept of 12.
The-- not the vertical line, the
straight line running from
a y-intercept of six to
an x-intercept of 12.
That's your budget constraint.
We saw that before.
Then we have here a series
of indifference curves.
These curves are drawn-- these
are a mathematical
representative of this
utility function.
These are points among which
you're indifferent if you have
that utility function.
And what we see is that the best
you can do is to choose
point D. Point D, with six
movies and three pizzas--
OK, that should be p on the
y-axis, not C. It should be
movies on the x-axis and
pizzas on the y-axis.
That should be p
on the y-axis.
The best you can do is
to choose a point D.
Now, to see that.
And that gives utility.
What's the value of your
utility at point D?
We understand value's
meaningless, but just so we
can compare, what's the value
of your utility at point D?
The square root of 18.
The value of utility is the
square root of 6 times 3,
which is the square
root of 18.
Which is going to be square root
of two, or three times
square root of two, but we'll
just call it square root of 18
for comparison.
Now, let's talk about why that's
the best point for you.
Let's think about some
alternative points.
For instance, why is that
better than point E?
Somebody raise their hand and
tell me, why is point D better
than point E?
Yeah?
AUDIENCE: E is unattainable
with your budget.
PROFESSOR: E would be better,
that'd be great.
We'd love eight movies
and four pizzas, but
we can't reach it.
So E's unattainable.
Why is it better than point A?
Point A you can afford.
So why's point E better
than point A?
You could afford point
A just like you can
afford point D. Yeah?
AUDIENCE: Because the utility's
only root 10.
PROFESSOR: Because what?
AUDIENCE: It's only root 10.
PROFESSOR: Yes, exactly, because
the utilitity's only
the square root of 10.
You're on a lower indifference
curve at point A. So it's true
you could afford point A,
but you're on a lower
indifference curve.
Your utility's a lower value,
it's only square root of 10.
So point A is dominated by point
D. What about point C?
Well, point C you
have the same--
point C is just an inward shift
from point D, but here
that's a dominated choice.
Once again your utility's
lower.
It's the square root
of 4.5 times 2.2.
And basically that's dominated
because you could afford more.
So basically, the point is that
the point which will make
you happiest is the point at
which your indifference curve
is tangent to the budget
constraint.
Because that is the point of the
farthest out indifference
curve that you can reach given
your budget constraint.
The tangency of the indifference
curve and the
budget constraint is the point
which makes you best off given
your available budget and
the available prices.
And that's the point where the
slope of the indifference
curve equals the slope of
the budget constraint.
The tangency is the point
where the slope of the
indifference curve equals
the slope of the budget
constraint.
Or, more relevantly--
OK, let me stop there.
That's the graphic intuition.
With a sloping indifference
curve because the slope of the
budget constraint is the
optimum, because by
definition, that is the point
of the furthest out
indifference curve you can
reach given your budget.
The point of tangency is the
point of equal slopes.
Are there questions about the
graphical analysis here?
This is very, very
important, so.
Yeah?
AUDIENCE: This is sort of about
the graphical analysis,
but if it only matters in terms
of the ordinal values of
the utility function and p and M
are always positive, does it
matter if you got rid
of the square root?
Would anything change if
it was u equals pm?
Because the the marginal
rate of substitution,
transformation, all that would
still be the same, right?
PROFESSOR: In this particular
example, it would not.
So actually, you're asking
a great question.
Because it's ordinal, you can
typically do transformations
for the ranking of bundles.
You will always get the same
ranking with a monotone
transformation of the
utility function.
That's exactly right.
Later in the course, we'll show
different ways why the
functional form matters, and
I'll show you why I did square
root, because it's going
to turn out that
that's going to matter.
But for other things--
but for the ranking
bundles, you're right.
The ranking of bundles is
consistent with the
transformation.
So that's the graphical.
Now let's come to
the mathematical
derivation of this.
So let's talk about the
mathematics of utility
maximization.
Now what I'm going to do here
is, I'm going to do this sort
of casually, as is my wont.
Friday in section, you're
going to work on the
underlying calculus that lies
behind the mathematics that
I'm going to present here.
Now, let's talk about
what it means that
these slopes are equal.
Well, remember, what is-- does
anyone remember what the slope
of the indifference curve is?
What do we call the slope of
the indifference curve?
Yeah?
AUDIENCE: The MRS.
PROFESSOR: The MRS. The slope
of the indifference curve is
the marginal rate
of substitution.
Which is defined as what?
What is the marginal rate
of substitution?
The ratio of what?
AUDIENCE: [INAUDIBLE]
PROFESSOR: No, the marginal
rate of substitution.
This is just about
preferences.
What's the marginal rate of
substitution defined as?
It's the ratio of
what to what?
Yeah?
AUDIENCE: The amount of one good
you have to get to give
up a unit of the other good.
PROFESSOR: I'm sorry?
AUDIENCE: The amount of one good
you have to get to give
up a unit of the other good.
PROFESSOR: So graphically
that's what
it's defined as, exactly.
It's the slope of the
indifference curve.
Mathematically, what was it?
What was it in terms
of utility?
Does anyone remember?
Yeah.
AUDIENCE: The ratio
of the partials.
PROFESSOR: Ratio of the
marginal utilities.
In particular, it's the negative
of the marginal
utility of movies over the
marginal utility of pizza.
Remember, it's the negative of
the marginal utility of the
x-axis over the marginal
utility of the y-axis.
So marginal rate of substitution
is the rate at
which you're willing to
substitute between movies and
pizza, which is a function of
your marginal utilities.
If your marginal utility for
movies is very high, then you
need a lot of pizzas.
Then you wouldn't trade a movie
unless you get a lot of
pizza for it.
If your marginal utility of
movies is very low, you'd be
happy to give up a movie
even for a small
fraction of a pizza.
So that's the marginal
rate of substitution.
That's about preferences only.
At the same time, we're saying
that that marginal rate of
substitution is equal to--
this slope is equal to the
slope of the budget
constraint.
Well, the slope of the budget
constraint we call the
marginal rate of transformation,
which is the
price ratio.
The slope of the budget
constraint is the negative of
the price ratio.
That's where you were sort of
one step ahead of us here.
So preferences give us this,
the marginal rate of
substitution.
The mechanics of the market give
us the marginal rate of
transformation.
And utility maximization gives
us that those are equal,
because they're equal
at that tangency.
At that tangency is where you
get to the highest possible
indifference curve.
So at the optimum, you get that
the ratio of marginal
utility equals the
ratio of prices.
Now, I want to try to see you
understand this a bit more
intuitively, given
this mathematics.
The way I like to think about
this is, think about the ratio
of the marginal utilities
as the marginal benefit.
So it's the benefit of another
movie in terms of pizza.
The marginal rate of
substitution is the benefit of
another movie in
terms of pizza.
It's how much you like that
next movie relative to how
much you like that next pizza.
The marginal rate of
transformation, the cost, is
the price of that next movie
relative to the price of that
next pizza.
So what we're saying here is
we're setting benefits equal
to the costs.
In particular, we're setting
marginal benefits equal to
marginal cost.
The marginal benefit, the
benefit to that next movie in
terms of pizza, has got to be
equal to the marginal cost,
the cost to you in terms
of that next
movie in terms of pizza.
And this notion that the optimum
will be where marginal
benefit equals marginal
cost will pervade
through the whole course.
When we do firm maximization,
it'll be the same thing.
Any maximization we'll do in
this course, any optimization,
will be about equating
these margins.
Setting the marginal benefits
equal to marginal costs.
Now, this is different than
benefits equals cost, because
it's about the next unit.
It's saying, how do we feel
about that next movie compared
to the price of that
next movie.
Now, prices here we have
being constant.
You could imagine prices of
movies changing as you see
more, but that gets
complicated.
We'll worry about that later.
For now, the price
is constant.
But the marginal utilities
are not constant.
Marginal utilities are obviously
changing the more
moves you see.
Once again, with intuition,
you have to
develop your own intuition.
The way that I like to think
about this intuitively is to
actually rewrite this a little
bit, and rewrite it as saying
that the marginal utility of
movies over the price of
movies equals the marginal
utility of pizza over the
price of pizza.
At the optimum, this'll
be true.
I like this because to me this
term sort of says, look, the
bang for the buck has to be
the same across all goods.
For each dollar of movie
expenditure, what's it buying?
What's that next dollar of movie
expenditure buying you?
This is saying, what's that
next dollar of pizza
expenditure buying you?
And they've got to be equal.
If the next dollar of movie
expenditure buys you a lot
more happiness than the next
dollar of pizza expenditure,
then you're not at
the right place.
You should shift your money and
spend more on movies and
less on pizza.
If the next dollar of pizza
expenditure buys you a lot
more happiness than the next
dollar of movie expenditure,
then you're not in the
right place either.
You should see fewer movies
and buy more pizza.
So basically, it's where the
marginal benefit to you--
the bang for the buck of that
next movie is the same as the
bang for the buck of
that next pizza.
So to see this, let's go back
to figure 5-4 and let's
actually think through the
mathematics of a couple of
these points.
Let's take point A. At point
A, you have two pizzas and
five movies.
So pizza equals two, movies
equals five at point A. So
utility is equal to square
root of 10 at point A.
Now, in particular, your
marginal utility for pizzas at
that point--
what's the marginal utility
for pizzas?
Well, we can differentiate.
That's the derivative of the
utility function with respect
to prices, du/dp.
Which is going to be 0.5 times
movies over the square root of
p times m, which at these values
is going to be one over
the square root of 10.
That's your marginal
utility of pizzas.
Your marginal utility of movies
is going to be du/dm,
which is going to be 0.5 times
p over square root of p times
m, which is going to be 2.5
over square root of 10.
So the marginal rate of
substitution between
these two is 2.5.
The marginal rate of
substitution, 2.5.
What does that mean
intuitively?
Can someone tell me what that
means intuitively, the
marginal rate of substitution
is 2.5?
What does that mean?
Someone explain that like you'd
explain it to someone
who's speaking English.
What does it mean that
the marginal rate of
substitution is 2.5?
Yeah?
AUDIENCE: You'd give up one
pizza for 2.5 movies.
Yes.
No, actually, the opposite.
You'd give up two
and 1/2 pizzas--
the marginal rate of
substitution is 2.5--
no, that's right.
You would give up 2.5--
one second, let's make sure
I have this right.
Right, so you would give up one
pizza to see 2 and 1/2--
no, it's the other way around.
You're getting a lot of pizza
and not enough movies.
So you would give up two
and 1/2 pizzas to
get one more movie.
This is confusing, OK?
You'd give up two and 1/2 pizzas
to get one more movie.
That's what it means.
You would give up two and 1/2
pizzas to see one more movie,
and why is that?
Why at a point like A would you
give up two and 1/2 pizzas
to see one more movie?
Yeah?
AUDIENCE: Well, if you just look
at the line tangent to
the indifference curve
at A, it's really
not a downward slope.
PROFESSOR: It's really steep,
which means what?
AUDIENCE: Which means you get
a lot more benefit--like you
don't care if you
give up a lot of
pizzas to see more movies.
PROFESSOR: Exactly.
Actually, that's a great way to
bring the graphics and the
intuition together.
Here's thinking of
it intuitively.
I'm getting a lot of pizza
at point A. I'm not
getting a lot of movies.
So I would happily give
up a lot of pizza
to get my next movie.
What you pointed out is the
tie to the graphics here.
The indifference curve is very
steep at that point through A.
A steep indifference curve in
that way means I don't really
care a whole lot at this point
about how many pizzas I get,
but I care a lot about
getting more movies.
So at a point like A where
it's very steep, you are
willing to give up two and 1/2
pizzas to see a movie.
But what do you have
to give up?
What's the market telling
you you have to
give up to see a movie?
How much pizza do you actually
have to give up to see a movie
in practice?
You're willing to give up two
and 1/2 pizzas to see a movie,
but how many pizzas do you
actually have to give up?
AUDIENCE: 1/2.
PROFESSOR: 1/2 a pizza
to see a movie.
So that can't be the optimum.
You're willing to give up two
and 1/2 pizzas to see a movie,
but you only have to give up
1/2 a pizza to see a movie.
So you can't be at
the right place.
You should be changing your
consumption bundle.
You should be changing your
consumption bundle, because
the market is only asking for
1/2 a pizza to see a movie,
but you're willing to
give up two and 1/2
pizzas to see a movie.
So at a point like A, you're
clearly not at the optimum.
Because you are willing
to make a trade.
Remember, we talked about-- we
can go all the way back to the
first lecture.
The key point was-- the first
or second lecture--
inefficiency happens
when trades aren't
made that people value.
Here's a trade that you value.
You're willing to give up two
and 1/2 pizzas to see a movie.
The market only wants 1/2
a pizza to see a movie.
You're not making a trade you
value, so that's not the
efficient outcome.
Likewise, let's do the same
mathematics at point B. Well,
at point B, if you do the math
and work it out, you see that
the marginal utility of
pizza is five over
square root of ten.
The marginal utility of
movies is 0.5 over the
square root of 10.
So the MRS is 0.1.
At this point, you'd only be
willing to give up 0.1 pizzas
to see a movie.
At a point like B,
the indifference
curve is very flat.
You're only willing to give up
0.1 pizzas to see a movie.
But remember, the market is
willing to say, look--
you can flip it around, the
market's willing to say, look,
you can get a movie.
You're only willing to give up
0.1 pizzas to see a movie.
Well, that means clearly that
you have too many movies and
not enough pizza.
You're clearly at that point
happy to say, wow, you mean
that I can gain a whole pizza by
just giving up two movies?
Heck, I'd be willing to give up
10 movies to get a pizza.
At the point I'm at right there,
I'd be willing to give
up 10 movies to get a pizza.
You're telling me we only
have to give up two
movies to get a pizza?
Great.
I'm going to do that trade.
I'm going to move back towards
point D. So that's why this
idea of what you're willing to
do, which is the MRS, and what
the market's making you do, you
want to equilibrate those
to decide how much you
want to consume.
Now, obviously a point like--
let's talk about point C.
Point C is interesting,
because at point
C, what's true?
The marginal rate of
substitution is equal to the
marginal rate of transformation
at point C. The
slope of the indifference
curve and the budget
constraint are equal.
That's why you have to check
two conditions for
optimization.
First of all, those slopes
have to be equal.
Second of all, you've got
to spend all your money.
So it's true there's a whole
host of points-- in fact,
there's a vector running through
CDE, all which are
points where the margin rate
of substitution equals the
margin rate of transformation.
But only D is optimal, because
you also have to
remember more is better.
You never want to leave
money on the table.
So the two conditions you have
to meet is that you're at the
point where your desired
trade-off between pizzas and
movies is the same as the
market's, and where you're
spending all your budget.
And that's the optimum.
OK, questions about that?
So that's basically how we
think about optimization.
That's how we think about
consumers making their
decisions deciding between
consuming pizzas and movies.
Now, let's come back-- however,
this is a particular
case we've looked at.
This is a case in particular
where we've imposed that
there's an interior solution.
In fact, in practice you could
end up in these kinds of
choices with corner solutions.
So let's take a look at the
last figure, figure 5-5.
We've chosen a case where your
optimal bundle includes both
pizza and movies.
But you could imagine
a situation where
your optimal bundle--
and once again, that should be
a p, not a c in figure 5-5,
that should be p
on the y-axis--
where your optimal
bundle includes
only one or the other.
So this is a particular case--
we have the same budget line
as before, which is you're
trading off pizza and movies.
You have an income of 96, the
price of pizzas is 16, the
price of movies is 8.
So same budget line as before.
But now your indifference curves
look very different.
Now your preferences are such
that you've got these linear
difference curves of the
form I1, I2, I3.
You've got these linear
indifference curves.
What that means is
you've got--
these indifference curves mean
that you have a constant rate
at which you're willing to trade
off pizza for movies.
If we go back to figure 5.4,
the rate at which you're
willing to trade off pizza
for movies changes.
Your preferences
are such that--
because the square root function
as pointed out--
your preferences are such that
you are willing to make
different rates of trade
at different amounts.
In figure 5-5, your preferences
are constant, no
matter how many movies or pizzas
you have. You're always
willing to make that trade-off
at the same rate.
Well, in that case you can end
up with a corner solution,
where in fact, you're going
to consume only six
pizzas and no movies.
And why is that?
That's because this is a
person who loves pizza
relative to movies.
It's a very flat indifference
curve.
They love pizza relative
to movies.
And they love pizza so much
relative to movies that given
the prices they face, they'll
just go ahead and choose six
pizzas and no movies.
So that's a corner solution.
So mathematically, as you'll
go through a section on
Friday, you're going to have to
check for corner solutions.
You may solve these problems
and end up with negative
quantities and be befuddled
about what happens.
Well, if an answer looks
wrong, it is wrong.
If you solve problems with
negative quantities, that's
probably because there's a
corner solution to the
problem, and actually the
optimal quantity is to have
zero of one thing and spend
your entire budget on
something else.
Questions about that?
So now let's think about
applying this to the kinds of
decisions that you
all have to make.
So I talked about this
particular example of pizza
and movies.
And in fact, you might say,
well, that's sort of
unrealistic.
Gee, I spend my budget
on lots of things,
and how do I do this?
Well, in practice, what you'd
have to do is you'd have to
draw a multi-dimensional
graph and solve a
multi-dimensional problem.
And that's a bear.
But in practice, in fact, we can
often think about breaking
down the choices we make
into pairs of choices.
In practice, you could think
about saying, look--
many people do what a lot of
psychologists call mental
accounting, where basically they
say, look, yes, I have a
whole budget and lots
of things I can buy.
But in fact, I like to think
of my budget in sort of
subcategories.
I think of a certain amount
I'm willing to spend on
entertainment and a
certain amount I'm
willing to spend on food.
And I take my budget and
I mentally put it
in different buckets.
And within each of those
buckets, you can then do the
same kind of optimization
problem that we've done here.
So even though in reality we
choose across a whole host of
goods, in practice what you're
going to see is that people
will do this kind of mental
accounting, where they sort of
divide their goods into
different buckets and optimize
within each of those buckets.
What this means in practice is
that in fact, if we now stop
for a second and think about
the government, and how it
affects our consumption
decisions, what this means is
that in practice,
the government--
so, one way we typically of
the government affecting
consumption decisions is through
the power of taxation.
So let's say for example,
the government decided
that pizzas were bad.
They caused obesity.
That there's too much obesity
because people are eating too
much pizza, and we need to
deal with that through a
government policy that
involves taxation.
Somebody talk me through the
analysis of how we'd think
about analyzing a tax on pizza
given these diagrams.
Let's go to figure 5-4.
And imagine I said that
we're going to place
a 50% tax on pizza.
So we're going to say that every
dollar you pay on pizza,
you're going to have to pay
$0.50 to the government.
Because we're really
worried people are
eating too much pizza.
What would that do the
budget constraint?
Yeah.
AUDIENCE: Well, effectively
you're increasing
the price of pizza.
PROFESSOR: Effectively you're
increasing the price of pizza
to the consumer.
AUDIENCE: The budget
constraint would
shift down like this.
PROFESSOR: It's actually going
to have the same effect as we
saw in figure 5-2.
In fact, I've just replicated
figure 5-2.
Because in figure 5-2, the price
of pizza went up by 50%,
from $16 to $24.
That's the same thing that the
government's just done.
It's raised the price of pizza
effectively from $16 a pizza
to $24 because instead of paying
your $16, you're also
going to pay $8 to the
government in tax.
So what's that going to do?
That is going to, in general,
lower consumption of pizza.
So that kind of price increase
is going to, in general, lower
the consumption of pizza.
So the government has tried
to accomplish its goal by
shifting people away from pizza
towards movies, away
from pizza toward
other things.
Yeah?
AUDIENCE: Would it be meaningful
to say that it also
affects the utility curves?
PROFESSOR: It would not be
meaningful, actually--
it will affect your
optimal choice.
In general, you will choose
a different amount
of pizza and movies.
We'll talk about
that next time.
But it's very important, it
would not be right to say it
affects utility.
Utility is like what you're
born with, it's an innate
concept about your underlying
preferences.
However, you're actually getting
to my point, which is
in fact, the way economists
typically think about this is
the government can't affect
your preferences.
But in fact, if people do
mental accounting, the
government maybe can affect
your preferences.
So let's say that basically the
way I think about it is,
let's say I think I have a
budget for food and I have a
budget for entertainment.
And let's say I think my budget
for entertainment's
pretty small because
I'm low income.
I've gotta have a
budget for food.
And so let's say I put pizza
in my budget for food, so I
allocate some of my budget
for food to pizza.
And the government can then
cause me to eat less
pizza by taxing it.
But what if somehow the
government could get me to
think of pizza differently?
What if somehow the government
could get me to think of pizza
as entertainment?
And suddenly I put it in that
bucket, where I'm trading it
off not against other food, but
against the fact that I
want to see a movie and I
want to download stuff
from iTunes, et cetera.
Maybe then I'd buy less pizza at
the same price because I'm
putting it in the bucket where
I have less money.
So in other words,
we've imagined a
world with two goods.
And the only way you can affect
the choice across those
two goods is to lower your
income or your price.
But in fact, if people have lots
of different bundles of
goods, somehow I could shift you
mentally from considering
pizza in a bucket where you have
a lot of money to putting
pizza in a bucket where you
don't have as much money.
I can lower your consumption
of pizza without affecting
prices, without an obtrusive
government tax policy.
This is the kind of thing
that we call in
economic policy a nudge.
And there's a new book called
Nudge by Richard Thaler, who's
a famous behavioral economist,
basically bringing psychology
into economics.
There's this very important
field now in economics called
behavioral economics, which is
all about, how can we bring
the lessons of psychology
into economics?
We don't do that in 14.01.
14.01's all about, we assume
everybody's these perfectly
rational people who would never
really be fooled into
thinking about pizza differently
just because of
what the government told them.
But in fact, in reality people
think about things differently
based on the kinds of
information they have. And
given that tax policies can feel
very intrusive-- imagine
some of you are like, wow,
they're raising my pizza to
$24, that seems very
intrusive.
If the government could somehow
through nudging you to
think about pizza differently
change your pizza consumption,
that might be a much more
acceptable and palatable
policy to many people.
And that's the kind of role the
government can play, or
policy-makers can play, is not
just by changing your prices
or income, but by actually
changing how you categorize
things mentally, they can change
the choices you make.
