[SQUEAKING]
[RUSTLING] [CLICKING] JONATHAN GRUBER:
Today we're going to start talking about what's
underneath the demand curve. So basically, what
we did last time, and what you did in
section on Friday is talk about sort
of the workhorse model of economics, which
is supply and demand model. And we always start the class
with that, because that's the model in the course. But I think as any good sort
of scientists and inquisitive minds, you're probably
immediately asking, well, where do these supply and
demand curves come from? They don't just come
out of thin air. How do we think about them? Where do they come from? And that's what we'll spend
basically the first 1/2 of the course going through. And so we're going to start
today with the demand curve, and the demand curve is
going to come from how consumers make choices, OK? And that will help us
drive the demand curve. Then we'll turn next
to supply curve, which will come from how firms
make production decisions. But let's start with
the demand curve, and we're going to
start by talking about people's preferences, and
then the utility functions, OK? So our model of
consumer decision making is going to be a model
of utility maximization. That's going to be our
fundamental-- remember, this course is all about
constrain maximization. Our model today is going to be
a model of utility maximization. And this model's going
to have two components. There's going to be
consumer preferences, which is what people want,
and there's going to be a budget constraint,
which is what they can afford. And we're going to put
these two things together. We're going to maximize people's
happiness, or their choice-- or their happiness
given their preferences, subject to the budget
constraint they face. And that's going to be the
constraint maximization exercise that actually,
through the magic of economics, is going to yield
the demand curve, and yield a very sensible
demand curve that you'll understand intuitively. Now, so what we're going to
do is do this in three steps. Step one-- over the
next two lectures. Step one is we'll talk
about preferences, how do we model people's tastes. We'll do that today. Step two is we'll talk
about how we translate this to utility function,
how we mathematically represent people's preferences
in utility function. We'll do that today as well. And then next time, we'll talk
about the budget constraints that people face. So today, we're going to
talk about the max demand. Next time we'll talk about
the budget constraint. That means today's
lecture is quite fun. Today's lecture is about
unconstrained choice. We're not going to worry
at all about what you can afford, what anything costs. We're not going to worry
about what things cost. We're not going to worry
about what you can afford, OK? Today's the lecture where
you won the lottery, OK? You won the lottery. Money is no object. How do you think about
what you want, OK? Next time, we'll say, well,
you didn't win the lottery. In fact, as we learn
later in the semester, no one wins the lottery. It's an incredibly bad deal. But next time, we'll impose
the budget constraints. But for today, we're just going
to ignore that and talk about what do you want, OK? And to start this,
we're going to start with a series of
preference assumptions. A series-- remember, as
I talked about last time, models rely on
simplifying assumptions. Otherwise, we could
never write down a model. It'll go on forever, OK? And the key question is,
are those simplifying assumptions sensible? Do they do violence to reality
in a way which makes you not believe the model,
or are they roughly consistent with reality
in a way that allows you to go on with the model? OK? And we're going to pose three
preference assumptions, which I hope will not violate your
sense of reasonableness. The first is completeness. What I mean by that is
you have preferences over any set of goods
you might choose from. You might be indifferent. You might say, "I
like A as much as B," but you can't say, "I don't
care," or, "I don't know." You can say, "I don't care." That's indifference. You can't say, "I don't know." You can't literally
say, "I don't know how I feel about this." You might say you're
indifferent to two things, but you won't say, "I don't know
how I feel about something." That's completeness, OK? The second is the assumption
we've all become familiar with since kindergarten
math, which is transitivity. If you prefer A to B and B
to C, you prefer A to C, OK? That's kind of-- I'm sure that's pretty clear. You've done this a
lot in other classes. So these two are sort
of standard assumptions you might make in
any math class. The third assumption is the one
where the economics comes in, which is the assumption
of nonsatiation or the assumption
of more is better. In this class, we
will assume more is always better than less, OK? We'll assume more
is better than less. Now, to be clear,
we're not going to say that the
next unit makes you equally happy as the last unit. In fact, I'll talk about
that in a few minutes. Well, in fact, the next
unit makes you less happy. But we will say you
always want more, that faced with the
chance of more or less, you'll always be
happier with more, OK? And that's the nonsatiation
assumption, OK? And I'll talk about that
some during the lecture, but that's sort of what's going
to give our models their power. That's a sort of new
economics assumption. That's going to give-- beyond
your typical math assumptions-- this is going to give our
models their power, OK? So that's our assumptions. So armed with those,
I want to start with a graphical
representation of preferences. I want to graphically
represent people's preferences, and I'll do so through something
we call indifference curves. Indifference curves, OK? These are-- indifference curves
are basically preference maps. Essentially, indifference
curves are graphical maps of preferences, OK? So for example, suppose your
parents gave you some money to begin the semester, and you
spent that money on two things. Your parents are rich. They gave you tons of money. You spent your money on
two things, buying pizza or eating cookies, OK? So consider preferences
between pizza and cookies. That's your two
things you can do. Once again, this is
a constrained model. Obviously, in life, you can do a
million things with your money. But it turns out, if we consider
the contrast between doing two different things
with your money, you get a rich set
of intuition that you can apply to a much more
multi-dimensional decision case. So let's start with a two
dimensional decision case. You've got your money. Either you can have pizza
or you can have cookies, OK? Now, consider three choices, OK? Choice A is two
pizzas and one cookie. Choice B is one pizza
and two cookies, and choice C is two
pizzas, two cookies. OK, that's the three
packages I want to compare. And I am going to assume-- and I'll mathematically
rationalize in a few minutes-- but for now, I'm
going to assume you are indifferent between
these two packages. I'm going to assume
you're equally happy with two slices of pizza
and one cookie or two cookies and one slice of pizza, OK? I'm going to assume that. But I'm also going
to assume you prefer option C to both of these. In fact, I'm going
to assume that, because that is what more
is better gives you, OK? So you're indifferent
between this. This indifference doesn't come
from any property I wrote up. That's an assumption. That's just-- for this
case, I'm assuming that. This comes to the third
property I wrote up there. You prefer package C
because more is always better than less, OK? So now, let's graph
your preferences, and we do so in figure
2-1, OK, in the handout. OK, so here's your
indifference curve. So we've graphed on the
x-axis your number of cookies, on the y-axis
slices of pizza, OK? Now, you have-- we've graphed
the three choices I laid here, choice A, which is
two slices of pizza and one cookie, choice B,
which is two cookies and one slice of pizza, and choice
C, which is two of both. And I've drawn on this graph
your indifference curves. The way your
indifference curves looks is there's one indifference
curve between A and B, because those are the points
among which you're indifferent. So what an indifference
curve represents is all combinations of
consumption among which you are indifferent. That's why we call it
indifference curve. So an indifference
curve, which will be sort of one of the big
workhorses of this course, an indifference curve represents
all combinations along which you are in different. You're indifferent between
A and B. Therefore, they lie on the same curve, OK? So that's sort of our preference
map, our indifference curves. And these indifference
curves are going to have four
properties, four properties that you have to-- that follow
naturally from this-- it's really three and 1/2. The third and fourth are
really pretty much the same, but I like to write
them out as four. Four properties that follow from
these underlying assumptions-- Property one is, consumers
prefer higher indifference curves. Consumers prefer higher
indifference curves, OK? And that's just all
from more is better. That is, an indifference
curve that's higher goes through package that has
at least as much of one thing and more of the other thing. Therefore, you prefer it, OK? So as indifference curve shifts
out, people are happier, OK? So on that higher
indifference curve, point C, you are happier
than points A and B, because more is better, OK? The second is that indifference
curves never cross. Indifference curves
never cross, OK? Actually, that's
third, actually. I want to come to that in order. Second-- third is the
indifference curves never-- Second is indifference
curves are downward sloping. Second is indifference
curves are downward sloping. Indifference curves
are downward sloping. Let's talk about that first, OK? That simply comes from the
principle of nonsatiation. So look at figure 2-2. Here's an upward sloping
indifference curve, OK? Why does that violate the
principle of nonsatiation? Why does that violate that? Yeah. AUDIENCE: Either, if you're--
either you're less happy with you have more cookies, or you're
less happy if you have more pizza. And like there's-- and
that violates nonsatiation. JONATHAN GRUBER: Exactly. So basically, you're
indifferent-- on this curve, you're indifferent with one
of each and two of each. You can't be indifferent. Two of each has got to be
better than one of each. So an upward sloping
indifference curve would violate nonsatiation. So that's the second property
of indifference curve. The third property
of indifference curve is the indifference
curves never cross, OK? We could see that
in figure 2-3, OK? Someone else tell
me why this violates the properties I wrote up there,
indifference curves crossing. Yeah. AUDIENCE: Because B and
C [is strictly better. JONATHAN GRUBER: What's that? AUDIENCE: Because B and
C, B is strictly better. JONATHAN GRUBER: Because the
B and C, B is strictly better. That's right. AUDIENCE: [INAUDIBLE] JONATHAN GRUBER:
But they're also both on the same
curve as A. So you're saying they're both-- you're
indifferent with A for both B and C, but you can't be, because
B is strictly better than C. So it violates transitivity, OK? So the problem with
crossing indifference curves is they violate transitivity. And then finally,
the fourth is sort of a cute extra
assumption, but I think it's important
to clarify, which is that there is
only one indifference curve through every
possible consumption bundle, only one IC through
every bundle. OK, you can't have two
indifference curves going through the same bundle, OK? And that's because
of completeness. If you have two
indifference curves going through the
same bundle, you wouldn't know how you felt, OK? So there can only be one
going through every bundle, because you know how you feel. You may feel indifferent,
but you know how you feel. You can't say I don't know, OK? So that's sort of
a extra assumption that sort of completes the
link to the properties, OK? So that's basically how
indifference curves work. Now, I find-- when I took
this course, before you were-- god, maybe before your
parents were born, I don't know, certainly
before you guys were born-- when I took this course,
I found this course full of a lot of light
bulb moments, that is, stuff was just
sort of confusing, and then boom, an example
really made it work for me. And the example that made
indifference curves work to me was actually doing
my first UROP. When my UROP was with a grad
student, and that grad student had to decide whether he
was going to accept a job. He had a series of job
offers, so he had to decide. And basically, he said, "Here's
the way I'm thinking about it. I am indifferent-- I
have an indifference map and I care about two things. I care about school
location and I care about economics
department quality. I care about the quality
of my colleagues, and the research it's done
there, and the location." And basically, he
had two offers. One was from Princeton,
which he put up here. No offense to New
Jerseyans, but Princeton as a young single person sucks. OK, fine when you're married
and have kids, but deadly as a young single person. And the other-- so
that's Princeton. Down here was Santa Cruz. OK, awesome. [INAUDIBLE] is the most
beautiful university in America, OK? But not as good an
economics department. And he decided he was roughly
indifferent between the two. But he had a third offer
from the IMF, which is a research
institution in DC, which has-- he had a lot
of good colleagues, and DC is way better than
Princeton, New Jersey, even though it's not
as good as Santa Cruz. So he decided he would take
the offer at the IMF, OK? Even though the IMF had worse
colleagues than Princeton and worse location
than Santa Cruz, it was still better in
combination of the two of them, given his preferences. And that's how he used
indifference curves to make his decision, OK? So that's sort of an
example of applying it. Once again, no
offense to the New Jerseyans in the room, of
which I am one, but believe me, you'd rather be in Santa Cruz. OK, so now, let's
go from preferences to utility functions. OK, so now, we're going to move
from preferences, which we've represented graphically, to
utility functions, which we're going to represent
mathematically. Remember, I want you understand,
everything this course at three levels,
graphically, mathematically, and most importantly of
all, intuitively, OK? So graphic is
indifference curves. Now we come to the
mathematical representation, which is utility function, OK? And the idea is that every
individual, all of you in this room, have a
stable, well behaved, underlying mathematical
representation of your preferences, which
we call utility function. Now, once again, that's
going to be very complicated, your preference over
lots of different things. We're going to make things
simple by writing out a two dimensional representation
for now of your indifference curve. We're going to say, how
do we act mathematically represent your feelings
about pizza versus cookies? OK? Imagine that's all you
care about in the world, is pizza and cookies. How do we mathematically
represent that? So for example, we
could write down that your utility function
is equal to the square root of the number of slices of pizza
times the number of cookies. We could write that down. I'm not saying that's right. I'm not saying it works
for anyone in this room or even everyone this room,
but that is a possible way to represent utility, OK? What this would say-- this is convenient. We will use-- we'll end up
using square root form a lot for utility functions and a
lot of convenient mathematical properties. And it happens to jive
with our example, right? Because in this example, you're
indifferent between two pizza and one cookie or one
pizza and two cookie. They're both square root of 2. And you prefer two
pizza and two cookies. That's two, OK? So this gives you a high utility
for two pizza and two cookies, OK, than one pizza
and two cookie, or two pizza and one cookie. So now, the question
is, what does this mean? What is utility? Well, utility doesn't
actually mean anything. There's not really a thing
out there called utiles OK? In other words, utility
is not a cardinal concept. It is only an ordinal concept. You cannot say your
utility, you are-- you cannot literally say,
"My utility is x% higher than your utility," but
you can rank them. So we're going to assume
that utility can be ranked to allow you to rank choices. Even if generally, we
might slip some and sort of pretend utility is cardinal
for some cute examples, but by and large,
we're going to think of utility as purely ordinal. It's just a way to
rank your choices. It's just when you
have a set of choices out there over many dimensions--
like if your choice in life was always over one dimension
and more was better, it would always be
easy to rank it, right? You'd never have a problem. Once your choice is over
more than one dimension, now if you want
to rank them, you need some way to combine them. That's what this function does. It allows you essentially to
weight the different elements of your consumption
bundle, so you can rank them when it
comes time to choose, OK? Now, this is obviously
incredibly simple, but it turns out to be
amazingly powerful in explaining real world behavior, OK? And so what I want
to do today is work with the underlying
mathematics of utility, and then we'll come back. We'll see in the
next few lectures how it could actually be
used to explain decisions. So a key concept we're going
to talk about in this class is marginal utility. Marginal utility is
just a derivative of the utility function with
respect to one of the elements. So the marginal utility
for cookies, of cookies, is the utility of
the next cookie, given how many
cookies you've had. This class is going
to be very focused on marginal decision making. In economics, it's all about how
you think about the next unit. Turns out, that makes
life a ton easier. Turns out, it's way
easier to say, "Do you want the next cookie," than to
say, "How many cookies do you want?" Because if you want
the next cookie, that's sort of a very
isolated decision. You say, OK, I had
this many cookies. Do I want the next cookie? Whereas before you start
eating, if you say, how many cookies
do you want, that's sort of a harder,
more global decision. So we're going to focus on
this stepwise decision making process of do you want the
next unit, the next cookie, or the next slice of pizza, OK? And the key feature
of utility functions we'll work with
throughout the semester is that they will feature
diminishing marginal utility. Marginal utility will fall
as you have more of a good. The more of a good
you've had, the less happiness you'll derive
from the next unit, OK? Now, we can see that
graphically in figure 2-4. Figure 2-4 graphs on
the x-axis the number of cookies holding
constant pizza. So let's say you're
having two pizza slices, and you want to say, what's my
benefit from the next cookie? And on the left axis,
violating what I just said like 15 seconds
ago, we graph utility. Now, once again, the utile
numbers don't mean anything. It's just to give
you an ordinal sense. What you see here is that
if you have 1 cookie, your utility is 1.4,
square root of 2 times 1. If you have 2
cookies, your utility goes up to square
root of 4, which is 2. You are happier with
2 cookies, but you are less happy from the second
cookie than the first cookie, OK? And you could see
that in figure-- if you flip back and
forth between 2-4 and 2-5, you can see that, OK? The first cookie, going
from 0 to 1 cookie, gave you one-- so in
this case, we're now graphing the marginal utility. So figure 2-4 is the
level of utility, which is not really something
you can measure, in fact. Figure 2-5 is something
you can measure, which is marginal utility,
what's your happiness-- and we'll talk about
measuring this-- from the next cookie. You see, the first cookie gives
you a utility increment of 1.4, OK? You go from utility of
0 to utility of 1.4. The next cookie gives you
utility increment of 0.59. OK, you go from utility
of 1.41 to utility of 2. The next cookie gives
utility increment of 0.45, the square root of 3. So now we flip back
to the previous page. We're going from the
square root of 4, we're going from the
square root of 4-- I'm sorry-- to the
square root of 6. Square root of 6 is only 0.45
more than the square root of 4, and so on. So each additional cookie
makes you less and less happy. It makes you happier, it has
to, because more is better, but it makes you less
and less happy, OK? And this makes sense. Just think about
any decision life starting with
nothing of something and having the first
one, slice of pizza, a cookie, deciding on
which movie to go to. The first movie, the one
you want to see the most, is going to make you
happier than the one you want to see not quite as much. The first cookie
when you're hungry will make you happier
than the second cookie. The first slice of
pizza make you happier-- Now, you may be
close to indifferent. Maybe the second slice of
pizza makes you almost as happy as the first. But the first will
make you happier, OK? If you think about-- that's really sort
of that first step. You were hungry, and that first
one makes you feel happier. Now, but you got to remember,
you always want more cookies. Now, you might say,
"Wait a second. This is stupid. Once I've had 10 cookies,
I'm going to barf. The 11th cookie can
actually make me worse off, because I don't like barfing." But in economics,
we have to remember, you don't have to
eat the 11th cookie. You can give it away. So if like say, you don't
want the 11th cookie, you can save it for later. You can give it to a friend. So you always want it. In the worst case,
you throw it out. It can't make you worse off, it
can only make you better off. And that's what our sort of
more is better assumption comes from. Obviously, the limit-- you know,
if you get a million cookies, your garbage can gets full. You have no friends
to give them to. I understand at the limit,
these things fall apart, OK? But that's the basic
idea of more is better and the basic idea of
diminishing marginal utility. OK, any questions about that? Yeah. AUDIENCE: Can the utility
function ever be negative? JONATHAN GRUBER:
Utility function can never be negative
because we have-- well, utility-- once again, utility
is not an ordinal concept. You can set up
utility functions such that the number is negative. You can set that up. OK, the marginal utility
is always positive. You always get some
benefit from the next unit. Utility, once again, the
measurement's relevant. So it could be negative. You could set it up-- I could write my utility
function like this, you know, something like that. So it could be negative. That's just a sort
of scaling factor. But marginal utility
is always positive. You're always happier,
or it's non-negative. You're always happier
or at least indifferent to getting the next unit. Yeah. AUDIENCE: So when
you're looking at 2-5, if you get like a
fraction of a cookie, is the marginal utility
still going to go up? JONATHAN GRUBER: I'm
sorry, you look-- figure 2-5-- no, the
marginal is going to go down. Each fraction of a cookie,
the marginal utility-- marginal utility is
always diminishing. AUDIENCE: So if you
start with zero, and you get 1/2 a cookie
based on this graph-- JONATHAN GRUBER: Well, it's
really hard to do it from zero. That's really tricky. It's sort of much easier
to start from one. So corner solutions, we'll
talk about corner solutions in this class, they get ugly. Think of it starting from one. Starting with that first cookie,
every fraction of a cookie makes you happier, but less and
less happy with each fraction. Good question. All right, good questions. All right, so now,
let's talk about-- let's flip back from the
math to the graphics, and talk about where
indifference curves come from. I just drew them out. But in fact,
indifference curves are the graphical representation
of what comes out of utility function, OK? And indeed, the slope
of the indifference curve, we're going to call the
marginal rate of substitution, the rate essentially
at which you're willing to substitute
one good for the other. The rate at which you're willing
to substitute cookies for pizza is your marginal
rate of substitution. And we'll define that as the
slope of the indifference curve, delta p over delta c. That is your marginal
rate of substitution. Literally, the
indifference curve tells you the rate at which
you're willing to substitute. You just follow
along and say, "Look, I'm willing to give up--" So in other words, if you look
at figure 2-6, you say, "Look, I'm indifferent between
point A to point B. One slice of pizza-- I'm sorry-- one cookie
and four slices of pizza is the same to me as two cookies
and two slices of pizza." Why is it the same? Because they both give me
utility square root of four, right? So given this mathematical-- I'm not saying you are. I'm saying, given this
mathematical representation, OK, you are indifferent
between point A and point B. So what that
says-- and what's the slope with the
indifference curve? What's the arc slope
between point A and point B? The slope is negative 2. So your marginal rate of
substitution is negative 2. You are indifferent, OK? You are indifferent
between 1, 4 and 2, 2. Therefore, you're willing
to substitute or give away two slices of pizza
to get one cookie. Delta p delta c
is negative 2, OK? Now, it turns out you can
define the marginal rate of substitution over any
segment of indifference curve, and what's interesting
is it changes. It diminishes. Look what happens when we
move from two pizzas and two cookies, from
point B to point C. Now the marginal
rate of substitution is only negative of 1/2. Now I'm only willing to
give up one slice of pizza to get two cookies. What's happening? First, I was willing give
up two slices of pizza to get one cookie. Now I'm only willing to
give up one slice of pizza to get two cookies. What's happening? Yeah. AUDIENCE: You don't
want a cookie as much? JONATHAN GRUBER: Because of? AUDIENCE: Diminishing
marginal utility. JONATHAN GRUBER: Exactly. Diminishing margin
utility has caused the marginal rate
of substitution itself to diminish. For those who are really kind
of better at math than I am, it turns out technically,
mathematically, marginal utility isn't
always diminishing. You can draw up cases. MRS is always diminishing. So you can think of marginal
as always diminishing. It's fine for this class. When you get to higher
level math and economics, you'll see marginal utility
doesn't have to diminish. MRS has to diminish, OK? MRS is always diminishing. As you go along the
indifference curve, that slope is
always falling, OK? So basically, what
we can right now is how the MRS relates
to utility function. Our first sort of
mind-blowing result is that the MRS is
equal to the negative of the marginal
utility of cookies over the marginal
utility of pizza. That's our first key definition. It's equal to the negative
of the marginal utility of the good on the x-axis
over the marginal utility of the good on the y-axis, OK? Essentially, the marginal
rate of substitution tells you how your
relative marginal utilities evolve as you move down
the indifference curve. When you start at point
A, you have lots of pizza and not a lot of cookies. When you have lots of pizza,
your marginal utility is small. Here's the key insight. This is the thing which, once
again, it's a light bulb thing. If you get this, it'll make
your life so much easier. Marginal utilities are
negative functions of quantity. The more you have
of a thing, the less you want the next unit of it. That's why, for example,
cookies is now in the numerator and pizza is in the denominator,
flipping from this side, OK? The more you have a good,
the less you want it. So start at point A.
You have lots of pizza and not a lot of cookies. You don't really
want more pizza. You want more cookies. That means the
denominator is small. The marginal utility
of pizza is small. You don't really want it. But the marginal utility
of cookies is high. You want many of them. So this is a big number. Now let's move to point B.
Think about your next decision. Well, now, your marginal
utility of pizza, if you were going to go from
two to one slice of pizza, now pizza is worth a
lot more than cookies. So now it gets smaller. So essentially, as you move
along that indifference curve, because of this, you want--
because of diminishing marginal utility,
it leads this issue of a diminishing marginal
rate substitution, OK? So basically, as you move
along the indifference curve, you're more and more willing to
give up the good on the x-axis to get the good on the y-axis. As you move from the
upper left to the lower right on that indifference
map, figure 2-6, you're more you're
more willing to give up the good on the x-axis to
get the good on the y-axis. And what this implies is that
indifference curves are-- indifference curves are
convex to the origin. Indifference curves are
convex to the origin. That's very important. OK, let's see, they
are not concave. They're either
convex or straight. Let's say they're not concave
to the origin, to be technical. Indifference curves
can be linear. We'll come to that. But they can't be
concave to the origin. Why? Well, let's look at the next
figure, the last figure, figure 2-7. What would happen if
indifference curves were concave to the origin? Then that would say,
moving from one pizza-- so now I've drawn a
concave indifference curve. And with this indifference
curve, moving from point A to point B leaves
you indifferent. So you're happy to give
up one slice of pizza to get one cookie. Starting with four slices
of pizza and one cookie, you were happy to give
up one slice of pizza to get one cookie. Now, starting from
two and three, you're now willing to give
up two slices of pizza to get one cookie. What does that violate? Why does that not make sense? Yeah. AUDIENCE: Law of diminishing
marginal returns? JONATHAN GRUBER: Yeah, law of
diminishing marginal utility. Here, you were happy to
have one slice of pizza to get one cookie. Now you are willing to
have two slices of pizza to get one cookie,
even though you have less pizza and more cookies. That can't be right. As you have less pizza and
more cookies, cookies-- pizza should become more
valuable, not less valuable, and cookies should become less
valuable, not more valuable. So a concave to the
origin indifference curve would violate
the principle of diminishing marginal utility
and diminishing marginal rate of substitution, OK? Yeah. AUDIENCE: What if it's like
something like trading cards? JONATHAN GRUBER: OK. AUDIENCE: I mean, I mean, as
you get more trading cards, you have-- you're already
made a complete set. JONATHAN GRUBER: That's
very interesting. So in some sense,
what that is saying is that your utility
function is really over sets. You're saying your
utility functions isn't over trading cards. It's over sets. So basically, that's
what's sort of a bit-- you know, our
models are flexible. One way is to say they're loose. Another way is to
say they're flexible. But one of the challenges
you'll face on this course is thinking about what is the
decision set over which I'm writing my utility function? You're saying it's
sets, not trading cards. So that's why it happens. Other questions? Good question. Yeah, at the back. AUDIENCE: What about like
addictive things, where like, the more you have it,
the more you want to buy? JONATHAN GRUBER: Yeah, that's
a really relishing question. I spent a lot of my
research life, actually-- I did a lot of research
for a number of years on thinking about
how you properly model addictive
decisions like smoking. Addictive decisions
like smoking, essentially, it really
is that your utility function itself shifts as
you get more addictive. It's not that your
marginal utility-- the next cigarette
is still worth less than the first cigarette. It's just that as you
get more addicted, that first cigarette gets
worth more and more to you. So when you wake up in the
morning feeling crappy, that first cigarette
still does more for you than the second cigarette. It's just, the next day you
wake up feeling crappier, OK? So we model addiction
as something where essentially,
each day, cigarettes do less and less for you. You get essentially adjusted
to new-- you habituate to higher levels. And this is why I do a lot of
work-- you know, this is why, unfortunately, we saw
last year, the number-- the highest number of
deaths from accidental overdose in US history. 72,000 people died from drug
overdoses last year, more than ever died in traffic accidents
in our nation's history, OK? Why? Because people get
habituated to certain levels, and they get habituated
to certain levels. So people get
hooked on Oxycontin. They get habituated
to a certain level. They maybe switch
to heroin, and they habituate to a certain level. And now there's this
thing called fentanyl, which is a synthetic opioid
brought over from China, which is incredibly powerful. And dealers are mixing the
fentanyl in with the heroin. And the people shoot
up, not realizing-- at their habituated
level-- not realizing they have this
dangerous substance, and they overdose and die. And that's because they've
got habituated to high levels. They don't realize they're
getting a different product. So it's not about not
diminishing marginal utility. It's about different--
underlying different products. All right? Other questions? Sorry for that
depressing note, but it's important to be
thinking about that. That's why, once again,
we're the dismal science. We have to think
about these things. OK, now, let's come
to a great example that I hope you've
wondered about, and maybe you've already
figured out in your life, but I hope you've
at least stopped and wondered about,
which is the prices of different sizes of goods,
in a convenience store, say. OK, take Starbucks. You can get a tall
iced coffee for 2.25, or the next size, whatever the
hell they call it, bigger, OK? You can get, for 70 more cents-- so 2.25, and you can double
it for 70 more cents. Or take McDonald's. A small drink is $1.22 at the
local McDonald's, but for 50 more cents, you can
double the size, OK? What's going on here? Why did they give you
twice as much liquid, or if you go for ice
cream, it's the same thing. Why do they give you twice as
much for much less than twice as much money? What's going on? Yeah. AUDIENCE: Since your marginal
utility is diminishing as you have more coffee
available to you, you're willing to
pay less for it, so they make the
additional coffee cheaper. JONATHAN GRUBER: Exactly. That's a great
way to explain it. The point is it's all about
diminishing marginal utility. OK, when you come in to
McDonald's on a hot day, you are desperate for
that soda, but you're not as desperate have
twice as much soda. You'd like it. You probably want
to pay more for it, but you don't like it nearly as
much as that first bit of soda. So those prices simply
reflects the market's reaction to understanding diminishing
marginal utility. Now, we haven't even
talked about the supply side of the market yet. I'm not getting to how
providers make decisions. That's a much deeper issue. I'm just saying that this is
diminishing marginal utility in action, how it
works in the market, and that's why you see this, OK? So basically, what you see is
that that first bite of ice cream, for example,
is worth more, and that's why the ice
cream that's twice as big doesn't cost twice as much. Now, so basically,
what this means is, if you think about our
demand and supply model, on a hot day, or any day, the
demand for the first 16 ounces is higher than the demand
for the second 16 ounces. But the cost of producing
16 ounces is the same. So let's think about this. It's always risky when I try
to draw a graph on the board, but let's bear with me. OK, so let's say we've got a
simple supply and demand model. You have this supply
function for soda, and let's assume
it's roughly flat. OK, let's assume sort of
the cost the firm proceeds within some range. The firm-- basically,
every incremental 16 ounces costs them the same. So that's sort of
their supply curve. And then you have
some demand curve, OK? You have some demand curve
which is downward sloping, OK, and they set some price. And this is the
demand for 16 ounces. Now, what's the demand for
the next 16 ounces, OK? Yeah, this isn't going to work. We have to have an
upward-sloping supply curve. Sorry about that. We have a slightly upward
sloping supply curve, OK? Now we have the
demand for the next-- so here's your price. Here's your $1.22, OK? Now, you say, "Well, what's my
demand when I sell 32 ounces?" Well, it turns
out demand doesn't shift out twice as much. It just shifts out
a little bit more. So you can only charge $1.72
for the next 16 ounces. Probably, if you want
to go to the big-- if you go to 7-Eleven, where you
can get sizes up to, you know, as big as your house, OK-- they keep these curves keep
getting closer and closer to each other. So those price increments
get smaller and smaller. And that's why you can
get the monster, you know, ginormous Gulp at 7-Eleven-- is really just not that
different from the price of getting the small
little mini size, OK, because of diminishing
marginal utility. All right, and so
that's how the market-- that's essentially how we can
take this abstract concept, this sort of crazy
math, and turn it into literally what you see in
the store you walk into, OK? Questions about that? Yeah. AUDIENCE: So how does this
[? place ?] [INAUDIBLE],, like if for example, you wanted
to buy a snack that you were going to have for
breakfast every day-- JONATHAN GRUBER: Awesome. Awesome question. AUDIENCE: And then
every single day, it was going to be your
first granola bar, right? So I think that it's going to
diminish every single time, but it's still
cheaper to buy in bulk than it would be to buy a single
granola bar every single time. JONATHAN GRUBER:
Great, great question. Yeah? AUDIENCE: I think that has
more to do with packaging cost than marginal utility. JONATHAN GRUBER:
Well, I mean, the risk of my going to this model
is, once we get nonlinear, the order we do
things in this class, we have to start
talking about supply factors I want to talk to. But there's two answers. One is packaging efficiencies. But the other is, if you
actually go to Costco and look at their
prices, for many things, they're not actually better
than the supermarket. So actually, the price
of buying the giant like, 8,000 bars of granola is
actually not that much more-- not that much less than 1,000
time buying eight granola bars. It's less, but it's not nearly
as much less of these examples as sodas in McDonald's,
which is exactly your point. Utility diminishes
less, so they don't want to charge as much
less for multiple packages. So you can actually--
if you compare the gap in perishable
product pricing by size, it's much larger than the gap in
nonperishable pricing by size. Great point. Yeah. AUDIENCE: Is there also
just like a different time frame to which
the utility starts diminishing for every product? Because you gave the example
of soda, but it's like, would that reset later in
the day, if we wanted-- were thirsty again, or-- JONATHAN GRUBER:
Awesome, and that is why they don't let you
walk back in with the same cup and refill it, right? That's exactly right, and
that comes to this point. It's sort of like
it's nonperishable as you get longer apart. But you know, it's all
just really interesting. So at Fenway, OK, you can get-- you get like a regular
sized soda, it's like crazy. It's like $6. Then for like $8,
you get a big soda. Then for $10, you get a
refillable big soda, OK? Now, the question is, can you
bring that refillable soda back to additional games? Technically not, but I do. [LAUGHING] And basically they
sort of understand-- so this interesting
question of sort of the perishability of
things and how that's going to affect things going on. It's a really-- it's an
interesting question. Other comments? OK, I'm going to stop there. Those are great comments. Thanks everyone
for participating. And we will come back next time
and talk about the sad reality that we haven't won
the lottery, and we have limited amounts of money.
