The following content is
provided under a Creative Commons license. Your support will help MIT
OpenCourseWare continue to offer high quality educational
resources for free. To make a donation or view
additional materials from hundreds of MIT courses, visit
MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: Hi everyone. So I am Esther Duflo. I am the other person who
teaches this class. You had Abhijit for
the first class. I am going to start by doing
a bit of housekeeping. Keeping in mind that maybe
some people are going to arrive, so it is your
responsibility to inform everybody else of what
I said today. I got some requests of
clarifying what was the requirements for this
class, so I'll just go through it once. So we are going to post
essay topics. For 10 topics. And we are going to give
three or four choices. You can also make
your own essays. Whatever it is. You do have a chance to
write up to 10 essays. But you don't need to
write that many. You are going to be graded
out of the best five. So you can write any between
one and ten. And if you have one you're not
going to have a very high grade but-- Any between five and ten and
then we'll just take the best five, OK? I think the syllabus said seven
and Abhijit said five, so I went for the
easier thing. So that's one thing. The syllabus also said that we
might not grade all of them but, actually, we are going
to grade all of them. So I would suggest that you do
the first one so that you get used to it. Traditionally, it has been the
case that when students can decide how to arrange their
deadlines, they think that it's efficient to set all the deadlines late in the semester. I can tell you by experience
that it's actually exposed not to be such a good idea. So if I were you, I would
arrange things to do as many of them early as possible
so you don't get panicked by the end. So that's one. The other component of the
requirement for this class is to do the readings. And so to be prepared to
discuss in the class. One way in which we're going
to ensure that you're doing the reading is a very,
very short pop-quizes every once in awhile. It also means you have
to come to class. It's not a class that's
very difficult. But one thing that it requires
is that you actually come. And so we're going to have those
at any random times. Very simple. 2, 3, 4 questions just to check
that you've actually read the thing. And today the questions for the
first topic were already posted on Stellar. So you already have access to
them as well as the deadline for the first thing. And that's it. Other than that, I think I gave
a version of this spiel in 14.74 yesterday. There are two development
classes. If you're wondering which one
you should be in, this one is going to be more based
on the readings and discussion and lectures. And the other one's going to go
more in the detail of the techniques of papers and
solving the models and replicating empirical
papers, et cetera. So this one's a better
introduction and the other one is better if you already have a
fair amount of economics and econometrics. So that's the trade off. Other than that, obviously, the
themes that are going to be covered are going to
be pretty similar. So my sense is, probably, that
you don't want to take both at the same time. Although you could think of
taking them both in sequence. Then you would do 73
first, 74 second. I don't recognize any 74
students, but you shouldn't want to take 74 and then 73. That would be a bit boring. So you're welcome to shop a
little bit for some time and then decide what's
more appropriate. You're welcome to take both but
I would have warned you that there will be some overlap
between the two. That's it for housekeeping so if
you have questions, that's a good time. I'm happy to answer questions by
email also but chances are that if you have a question on
the logistics, a lot of people share it as well. Any questions? No. The class is being recorded,
that's for OpenCourseWare. But don't worry about saying
anything embarrassing. That would be edited out. I'm the only one-- and Abhijit-- is going to be the only ones who
are being recorded on tape saying things embarrassing. I'm assuming if you say
something extremely smart we can keep it though. AUDIENCE: [LAUGHTER] PROFESSOR: So there
is no danger. Feel free. Just ignore them. And hopefully, the idea is that
if it works well, it will be one of these classes that
people can take on their own down the line. Anything else? Any questions? No questions? When you speak, at the
beginning, if you at least would state your name so
that I can possibly get to know who are. I can address you
by your name. That would be nice. And otherwise, we're
ready to roll. Shall we dive in? Let's dive in. So, in the video that you saw
last time, you saw quite a few people who were maybe trapped in
some kind of poverty trap. So for example, there was this
farmer who, before he was given fertilizer, had
very low yield. And because he had
very low yield he didn't have much money. Because he didn't have much
money, he couldn't buy fertilizer and, therefore,
he continued to have very low yield. And what the Millennium Village
Project did is to give him the fertilizer. And the hope was, that with this
first gift of fertilizer, his yield would increase by a
sufficient amount that, down the line, he would be able to
buy his own fertilizer. And grow more and more maize. And then, progressively, maybe
start feeding his children better and buying them books
and all of those things you want to think about. So in that video, the Sachs and
Jolie video that you saw last time, this argument that
there might be these poverty traps keep coming over
and over again. So for example, in the Kennedy
story with the farmers, you see it in the schools. The schools don't have computers
so the kids cannot really learn well. You start putting computers
and kids can learn better. They will then make
more money. They will then be able to buy
computers for their schools, et cetera, et cetera. So one of the things that we
are going to do a lot of in this class is to try to
understand when there are such poverty traps and
when, in fact, maybe it's not so obvious. And for that, we have to
understand what creates the conditions for such poverty
traps to emerge. So what I want to do today-- we are going to delve in on one
example of one particular poverty trap and how
that could work. Which is going to be the fact
that we are physical, biological bodies. But what we're going to go
over as a mechanism, it's going to carry us during
the entire class. We are going to have to be
looking for the same type of conditions. So I want to start with
a story of someone that actually I met. I met some guy called
Pak Solhin. Pak means mister. Mister Solhin. So people in Indonesia don't
really have a first name and last name. They just have a name. And so, for example, Mrs.
So-and-so is Ebu-- I would be Ebu Esther,
for example. So this guy is Pak Solhin. And I met him in a village
in Indonesia-- in Java, which is one of the
richest parts of Indonesia. This is the main island, most
densely populated-- in the summer of 2008. In the summer of 2008, I was-- probably for you it's already
ancient history, it's before the great collapse of the
world economy and stuff. --One of the key events at the
time, for the developing countries in particular,
was that the food prices were very high. Basically since 2005, food
prices have increased enormously in the world for
reasons that are not fully understood. And then they collapsed
again when the whole economy went berserk. The world economy went away,
the food prices also collapsed, and they have started
to increase again. Part of the hunger that
you see now-- in Egypt, Tunisia, et cetera,
all over the Middle East-- part of it is fueled by a
re-increase in the food prices which are almost reaching
the 2008 level. For people in urban areas,
this has, of course, immediately threatened
their livelihood. Because they don't
produce food. They buy food. So as soon as the food prices
increase, that immediately affects them. So the beginning of 2008,
2007 you observed this kind of food riots-- nothing like we are seeing
now in Egypt-- but dis-content in various
urban areas. And generally, people were
wondering what was happening to food prices. What people have been thinking
is that there are several factors that are responsible
for the increase of the food prices. One is there are many more
people in China and India making more money. And as they are making more
money, not only they eat more but, more that that,
they eat more meat. And it turns out that to produce
1,000 calories of meat, you need much more
grain than to produce 1,000 calories of grain. That may sound strange, but it
turns out that the cow is not a very efficient way to
transform the calories from grain into calories
that we eat. The cow has started by using
a lot of it, et cetera. So to produce 1,000 calories
of cows, you need much more than 1,000 calories
worth of grain. So as China and India is
becoming richer and eating more meat, then there is a
demand for more grains. That's one. The second thing that is
happening is bio-fuels. With the increase in the world
prices of fuel there is more and more demand for bio-fuels,
so entire strips of Brazil have been covered into
maize that is being used to make ethanol. A third thing is oil is actually
an input into the production of food. Because oil is a very important
input into the production of fertilizer. So as the price of oil increase,
the price of fertilizer increase,
and therefore the price of food increases. So all of these factors are
fundamental forces which explains why, after the short
dip right after the crisis, the food prices again
started to increase. So that's the backdrop
of my visit to this village in Indonesia. And I met this guy. And he was all alone. He has a small, dingy,
little house. And he was a bit depressed,
or very depressed. And why was he depressed? Well he was depressed because
he was all alone at home. And he was all alone at home
because his wife had gone to the city to start working
as a maid. His oldest son had also gone to
the city to start working as an apprentice on a
construction site. And the two young kids were
with the grandparents. So he was all alone, he didn't
have anything in his house, he didn't do all that much,
and he wasn't happy. So the question is, why
did that happen? Why was he not working? And what he explained to me
is that he was not working because he didn't have a job. And he didn't have a job because
when the fertilizer prices increased, the farmers
that used to employ him decided that they had to do
something to cut costs. They weren't very sure whether
they were going to be able to sell their outputs and they were
facing those increases in expenditure. So they decided they
had to cut costs. And so they could have done
one of two things. What could they have done? Yeah? AUDIENCE: They could have cut
wages or cut the number of people employed. PROFESSOR: Right. They could have cut wages or
they could have cut the number of people who worked for them. So of course, if they had
cut wages, he still would have a job. But instead, they
cut employment. And why did they cut employment rather than cut wages? Well his theory was that if they
had cut wages, his wages would've been so low that he
would not have been able to buy enough food-- especially as the food prices
were rising at the same time-- with the equivalent of one day
of wage that would have been too little to sustain himself
to be strong enough to actually work for a whole day. So seeing that, the employer,
instead of cutting the wage and therefore making him unable
to work, then you give a wage of someone, let's
say, 1,000 rupiahs-- 1,000 rupiahs is not enough to
get yourself energetic for a full day of work. So you've spent your 1,000
rupiahs but the person can't feed himself for
a day of work. You get nothing out of him,
so there's no point. Yes? AUDIENCE: The question that came
to my mind was, is there any truth to his theory? Did you find any other examples
that would back up that that's the reason why the
farmer, that he used to work on his land, decided to cut
jobs instead of wages? PROFESSOR: Right. What you're asking
is whether-- that's fine-- whether maybe
it's a plausible theory. But is there any truth to it? We're going to spend a fair
amount of time on this very question, not on Tuesday,
but starting Thursday. In terms of the empirical truth
of his theory, in terms of the biological soundness
of it, it sounds plausible a priori. That you need to start with a
certain number of calories just to get going, right? Your body needs maybe 1,000
calories just to survive. So the first thousand calories
that you're consuming are not very useful to you to help you
to actually start exercising. Then, once you are alive,
the next calories will start being useful. So a priori, maybe
there was some plausibility to this theory. That's only one theory. So that means that he
lost his job so he couldn't do much of anything. He was not doing nothing,
otherwise I would not have met him. He would be dead. But he was doing things that
was not taking too much effort for him. For example, he was sitting next
to the bank of a lake and he was fishing. He was getting a little
bit of rice from the government program. He was getting a little bit
of meals from his brother. But he was not really
living a full life. He was sort of surviving. So at the heart of
his theory-- and I think your question of
whether this is true or not is a very interesting question
which certainly came to my mind when I was talking
to him-- but at the heart of this
theory was this purely biological mechanism. And then on top of this
biological mechanism, other things crept up. One is the fact that he was not
doing anything, and that his kids were gone. That made him depressed so
then it gave him very low energy to actually
you do anything. So even if his theory was
wrong, he sort of became trapped in a poverty trap that
may have been more of a psychological one. Because he was there, sitting
all alone in his hut, unable to do anything, thinking that
he was worthless, therefore, in some sense, becoming
worthless. There are other parts of his
stories where we start seeing other bits of poverty trap. For example, what happened
with his kid. So the kid who had to drop out
of school to start working as a construction worker was
actually a bright kid. So that's another place
where you see now an inter-generational
poverty trap. Where because the parents are
poor, the kid has to drop out of school because he has to go
to work and therefore himself will probably make less
money down the line. And that's another thing where
we have to ask exactly the same question you were
asking before. Is it an isolated example? Or is it something that
is generalized. That it's actually something
like the inability to work for the parents, or the lack of
income, that forces kids to stay out of school that
could have otherwise have gotten an education. That's another place where we
can find, potentially, a poverty trap. Where the kid got
some schools. He got a few years of school but
maybe not enough for it to be sufficient for him to
actually get a good job down the line. And for himself, he couldn't
work as a construction worker because he was too weak for the
basic jobs which require some strength, and too unskilled
for the better jobs, and too old to be an apprentice
like his kid. He was kind of trapped. So what is happening in this
story that you would think-- even if we accept the biological
mechanism, which I want to go back into in
detail in a moment-- something else could
have happened. So for example-- if we're thinking that his
being out of a job is a temporary phenomenon-- maybe he could have gotten a
loan to sustain his family so that the kid could at least stay
in school until the time for him to graduate. Then at least you wouldn't
have that inter-generational trap. So at the heart of it, we have
this biological phenomenon and then other things sort of creep
in that maintain him in this position that creates
the poverty trap. So what I want to do now
is go through the biological story in detail. And then we're going to see how
the other things add up, creep in, and create
that trap. So let's go through the
biological poverty trap. I should say that it's
one of the most ancient ideas in economics. A very old idea . It dates at least
from the 1950s. And this is an old
idea exactly in this form of the biology. So the idea is that the first
few calories that you get to consume are used by your
body just to survive. So they don't make you strong. And then, when you start eating
enough to survive, the next calories start giving
you strength. So that's when you can start
working out or you can work. So someone who is very poor,
like Pak Solhin, may not have enough to eat to be very
productive but if he could eat more, then he would
become productive. So at the heart of this is this
idea of what they call a capacity curve. And a capacity curve has
something like this shape. It relates how much effort you
can exercise to how much income you have, and, of course,
how much income you have is supposed to be related
to how much you consume. So what is the assumption that
is underlying the fact I have put income here on the x-axis? Yep? AUDIENCE: The more money you
have the more you eat. PROFESSOR: Right. The more money you have
the more you eat. So for example, the simplest
case would be, all you have, you eat. Of course, we know that it's not
true because you also need to take care of your
basic needs. You need to clothe yourself. You need to pay your children's
school fee. Maybe you need something
for your housing. So maybe you will only consume
a part of your income. But maybe some fraction
of what you have, you're going to eat. So that creates a relationship
between the income you have today and how much
you get to eat. So instead of income here, we
could have calories consumed. And one first big question that
we'll have to answer next time is, how steep is this
relationship between how much income people have and how
much they are eating. Here we are assuming that there
is some relationship and it's formidably steep enough. So whenever you have income,
you start eating. And what we have here on the
left, on the x-axis is the work capacity. So how many bushels of wheat
are you able to harvest or something like that. How many trenches can you dig. So the work capacity,
you think of it as physical output. But of course, there could be
a relationship between this physical output and your
income tomorrow. Because, for example, you could
be paid by the piece. So if you're paid by the piece,
however many bushel of wheat you harvest, you
get that much income. That creates the work capacity
and your income tomorrow are related one for one. Right? So here we have income
today, work capacity. And instead, we could
have income today and income tomorrow. OK? Now why is this shaped
the way it is? What does the shape represent? AUDIENCE: The left part is the
part where your body is just able to survive. And then afterwards he gets a
chance to actually make more money tomorrow because
[INAUDIBLE]. PROFESSOR: Exactly. So the left part is the first
part where you're just getting enough to survive. You are just eating
enough to survive. So the first few calories are
good because they keep you alive so you can actually
move about. But after that it just keeps you
at this kind of low level. Right? And then you start having, maybe
1,200, 1,500 calories. And then suddenly, it's a good
breakfast you're eating before going out for your run. It shoots up and then, why does
it flatten out again? Yeah? AUDIENCE: Because after a while
you're satisfied and it levels out once [INAUDIBLE]. PROFESSOR: Right. After a while it satisfy
and it levels out. And if we had continued the
curve, what would happen? It would really go down. Just think of post-Thanksgiving
slump and she probably gets a deep
down going line. So that creates this kind of
funny shape between you're income today and your work
capacity and, therefore, between your income today and
your income tomorrow. Or it could be within a week or
something like that, right? Which seems to have a reasonable
biological sense. Now what happened when the
price of food went up? What does it do to the
work capacity? Yeah? AUDIENCE: I suppose it goes down
because those people have to spend more of their
income on food and then buy less food. PROFESSOR: Exactly. So what happens when the price
of food goes up is that, in terms of bushels of wheat,
that's the same thing. But in terms of actual income
that the bushel of wheat transform into-- how
much income-- that creates a jump down. Because to go from income to
work capacity, to create from income today to calorie,
that's more expensive. So the curve shifts down because
for every dollar that you spend, or rupiah that you
spend on food, that's fewer calories and, therefore, that
shifts down whatever you are able to achieve in terms
of capacity, right? So if we have it in the form
of income to work capacity, the prices of food going up
makes the curve going down. Yeah? AUDIENCE: Could you also, if
you were talking about students, instead of saying the
word capacity, I'd put the way you pay attention? Would they pay more attention
if they ate more? Or is it just physical spending
that [INAUDIBLE] PROFESSOR: Right. Here, if we're thinking of Pak
Solhin, we are thinking about physical [INAUDIBLE]. But if we're thinking about
Pak Solhin's children, for example, it could well be their capacity to focus in class. And it could easily have
the same shape. In fact, there are other thing
that competes also for calories for children. For example, whether or not they
have intestinal worms. And the intestinal worms also
shift your work capacity, your attention capacity,
down because they are eating your food. Therefore, that tends to make
the kids anemic and less likely to be listening. That's exactly right. Yeah? AUDIENCE: And so increase in
food prices, does that cause a shift or a stretch? PROFESSOR: It specifically
causes shift and a-- how would you call it,
west-southwest, right?-- It is both a shift
and a stretch. Which is, it will take more of
your income today to have you switch to the-- think of it going this way. And alternatively,
what happens when the wages go down? That's another thing
we can look at. What happens to the
work capacity? Not to the work capacity, but if
we put income on the y-axis now and the wages go down? AUDIENCE: It shifts lower. PROFESSOR: It again will do the
same thing because now the same work capacity will
translate into less income. So what was happening in
Indonesia in 2008 was, on the one hand, food prices
were going up. On the other hand, farmers were
stressed out because the input prices were going up. So at the same time they wanted
to reduce the wages when the prices were
increased. And both of these phenomenon
create this southwest shift in the capacity curve. Yeah? AUDIENCE: Why didn't the farmers
just increase the prices they were selling the
crops at [INAUDIBLE]? PROFESSOR: That's an excellent
question, so why didn't the farmer just increase
the prices? The thing is that with the
agricultural cycle, you produce and then-- so you put
your fertilizer in the ground, then you put your crop
in the ground and then you wait around. Then the crop comes and
you try to sell it. And you're exactly right, the
fact that the input prices have gone up while the demand,
in principal, would not have gone up. It would have meant that the
food prices sold by the farmer would probably go up. But what happened is that they
weren't very sure whether or not the food prices were going
to go up by the time they sold their food in proportion
to the input prices. So the situation that prevailed
in 2008 is a lot of volatility. The prices were high but they
were also increasing. And that was true for the input
prices and that was true for the output prices. And when you were talking to
the farmer, everybody felt that they were holding the
short end of the stick. The farmers were saying,
well, yes, the food prices will increase. But we don't know whether it
will increase enough to cover our input prices. Moreover, the farmers found
it difficult to get loans, for example. So even if they know that the
prices are going to go up for that input in the future, in the
meantime, they still have to buy the fertilizer. So they sort of had
to cut costs now. So this is a little bit
what was happening. It's a mismatch between the
price you have to pay for the fertilizer today. And you're going to realize
the output in the future. So that creates this uncertainty
plus the fact that you need to finance it
one way or the other. Which is why, at that time,
there were two things going on which were both against
the poor guy. So this is what we have with
the capacity curve. So we've had this reasoning for
food but let's think a bit about other reasons-- forget that we are talking about
physical work capacity. Think about other reasons why
there might be a relationship between your income today
and an income at some point in the future. Think of the next generation,
think of next month, or anything like that. Can you think of other reasons
why this kind of funnily shaped curve might appear? So food might be one. What would be other reasons why
this funnily shaped curve might appear? Yeah? AUDIENCE: Over the long
term, maybe education. PROFESSOR: So let's go through
the education one. Why do you think-- AUDIENCE: Before, the less long
you can afford to keep you're children in school. And so their income capacity
isn't as low as yours was. But the richer you are, the more
schooling you can get and the higher income you
can [INAUDIBLE]. PROFESSOR: So this is right. That there is probably a
relationship between how long you can keep the
kid in school-- because if there are school fees
you might or might not be able to afford them. Or there might also be an
opportunity cost for the child to be in school. Like Pak Solhin's son couldn't
afford to be in school because he had to work. So I think it's not very
controversial to say there might be a relationship between
your income today and how long your kid will
stay in school. And then, there is probably a
relationship between how long your kids can stay in school
and their income. Which will create a relationship
between your income today and the income
of the child. So that creates a relationship
of some form or another. But what would be necessary for
this relationship to have this S-shape? So what you have explained, I
think and I think most people would agree-- we can ask around-- but I think
what you have explained clearly is that we might expect
through education-- a relationship between
income today and income of the children. Now what else do you need for
that relationship to have this funny shape? AUDIENCE: At the start, you
need to invest more. So like if they just learn to
fifth grade, or if they just learn to second grade, it isn't
going to make that much of a difference. But as they finish middle school
and high school, it's a much steeper curve. But then, going to college
versus Ph.D. levels off. PROFESSOR: Yeah. Sadly, going to a Ph.D usually
leads to a drop in income compared to having gone
to a Master's. Especially if you choose
the Master's properly. But this is exactly
that, which is we need one more thing. What you're saying
is exactly right. What's your name? AUDIENCE: Yousef. PROFESSOR: Yousef. But what she told us is you
need one more thing. You also need for the benefits
of the first few years of education to be relatively
low. And that's an empirical question
that goes back to the plausibility question that
you were asking earlier. Is it the case that the first
few years of education are useless, or not very useful? Or is it the case that every
year of education is a year of education. And there will be an S-shaped
based on education if the first few years of education
are not that useful. And [INAUDIBLE], if in fact,
even the first few years of education are that useful. I'm not going to answer
this question now. But we are going to answer it in
due course, whether or not this is the case. You see that this is not
something that we can just think of in the abstract. We have to find out. There could be reasons
the other way. You could feel, for example,
that the first years of education are amazingly useful
because this is when you learn to read. And once you know how to read,
who cares about all of these things that I'm trying to teach
you because you can teach yourself everything
you need to know. Or you could think that
education is not useful unless you have a secondary degree. Because that's what opens
the door to you for various formal jobs. Right? It could easily cut one
way or the other. I don't know if you guys
have an insight. For example, what
is your view? Do you think that this is likely
that the first few years of education are
not so useful or-- AUDIENCE: I think the first
few years are very useful because some people
learn to develop, like, love for reading. And actually realize that they
can learn things by reading [INAUDIBLE]. PROFESSOR: So for example, you
think that, the first few years of education
are very useful. So there would be a relationship
between income today and income
of my children. But it wouldn't have this shape
if that is the case. In fact, it might have a
completely opposite shape where it's more like an inverted
L as opposed to an S. So education would be one. What would be another
possibility for this funnily looking shape to appear between
income today and income at some point
in the future? Is it on my income in the future
or the income of my children or my income
next year? What would be other sources
of such shapes? Yeah? AUDIENCE: Access in knowledge
of, like, the job market. In the sense that if you were
raised in a family that's a higher income and so, therefore,
your parents would teach you more from a younger
age and would allow you to have a higher income. PROFESSOR: Right. So for example, for access
to the job market, it is possible-- if I can rephrase
what you are saying-- that people who live in a village,
their horizon is the village. Where they are growing
whatever. They are growing stuff and they
are making some income. But they don't have the
perspective in mind that they could go to the city where
there a number of other jobs available. So in that case, for people who
have very little money and live in the village, well, their
children will again also live in the village and have
very little money. If suddenly something opens the
possibility to go to the city-- for example, someone
comes into some money, gets the option to buy a train
ticket, goes to the city and figures out the options there. Then suddenly you have access
to a number of other opportunities, potentially
much more rewarding, that would potentially create
this S-shape. Where the fact of being poor
means that you live in a relatively restricted
environment. You stay there. And then when you become just a
bit richer, that opens this opportunity that helps you
you become much richer. That's a very nice example. Yeah? AUDIENCE: Another option is
savings which depends on how much income you have. Because the more you save, the
more you invest and the higher income producing activities. So the poor people have
no money to save so they're stuck there. But as they get more income you
can afford to save more and invest more and it pushes
your future earnings. PROFESSOR: Right. So saving is a very interesting
example. Again you could say-- well,
suppose for example, that people saved some fixed fraction
of their income. Then if I have more income
today I will save more. Therefore, I will invest more,
therefore, I will be richer in the future. Now if it was a fixed fraction
of my income, again, I would definitely see a relationship
between income today and income tomorrow just because
I save more. But if it's a fixed fraction of
my income, what else do I need for this S-shape to come? Yes? AUDIENCE: You need for poor
people to not be able to save this fraction. Because they, for instance,
spend their money on food or things that they need
to buy today. And so are either a fraction
of [INAUDIBLE] income or it's just lower
for poor people. PROFESSOR: Right. So the first possibility for
an S-shape to appear due to savings is that actually people
do not save a fixed fraction of their income. Is that for some reason, the
poor save less than the rich. So if that's the case-- and
let's talk through whether we have reasons to think that
the poor would save less than the rich-- but let's first take it as given
for a moment, and let's assume the poor save
less than the rich. And if that's the case-- assume the poor save nothing-- then if you're very poor, you
have no income tomorrow coming out of investments. And then if you start saving
when you become a little richer and that money is
invested, that starts creating some return for that money and
you get into this steeper part of the S-shape. So that's a first mechanism
through which savings could create a relationship between
your income today and your income tomorrow that would
have this S-shape. Now what we do have to explain
is why is it the case that the poor would be able to save
less than the rich? And that is something that, I
think, we all have in mind. Say, yes, of course, the
poor don't save because they have no money. But one thing I want you to keep
in mind is that the poor have no money but they
have a present and they have a future. So unless they think that they
will have more money tomorrow or unless, for some reason, they
are extremely impatient, then the poor should want
to save as well. Because, of course, today
they have very little money for food. But tomorrow they'll have very
little for food as well. So we need to go a little
further than to say, well, of course the poor save because
they have no money. Right? Again, let's not go into
the details of that. I think there are good reasons
to think that the poor would be less able to save
than the rich. And we're going to have
a whole set of lectures about that. But just keep in mind that it's
not so obvious that the poor would be less
likely to save. Another-- sorry, you wanted to talk. AUDIENCE: [INAUDIBLE] access to healthcare
and medicine. PROFESSOR: Right. So let's go to health. Let's finish saving
and then I'll go back to you for health. Another reason why there might
be a relationship between income today and income
tomorrow of this form due to savings. Suppose that the poor and the
rich saved both a proportion of their income. There could still be a
relationship like that. Yeah? AUDIENCE: The rich could be able
to invest their savings more effectively. PROFESSOR: Exactly. It could be that the rich have
access to better investment opportunity. For example, it could be that
the bank is just not interested in very small
saving accounts. And in fact, it's the case
that the banks are not interested in very small
saving accounts. Because as soon as you're a bank
and you take the saving of someone, the government is on
your back to make sure that you don't run away
with the saving-- which is a good idea--
but that costs money. So maintaining a saving account
for someone costs some amount of money. And regardless of the size of
the account, it still costs the same money because you need
to do all the paperwork. So as a result, if you come to a
bank with your five rupiahs, the bank is going to say, thank
you, but I don't want your five rupiahs. Whereas, if you come with your
5,000 rupiahs they're, sure, I'm going to put it in this very
nice account for you with a nice return. So that's one reason
right there. That the poor might have to save
under the mattress where the money might disappear. Where it might be stolen. And so the return on
saving for the poor might be very low. It might even be negative. Whereas, the return for the rich
might be higher, either because they have access to this
savings account or they can, for example, start
a small business. For example, when you want to
start a small business, is it worthwhile starting a tiny
business with almost nothing? Maybe not. Maybe it needs to be large
enough for it to be worthwhile. So even if the poor and the
rich were to save the same amount proportionally, there
might still be something related, not to how much they
save, but what's the productivity of those savings. You were talking about
health care. Why don't you tell us what
you're thinking about healthcare. AUDIENCE: So at lower incomes
you can't really buy a lot of medicine. And maybe you can reach a point
where you can start buying medicines or
buying healthcare. And maybe towards the end when
you have higher income, it levels off because you don't
encounter the health problems that you might at low incomes
in the first place. PROFESSOR: Right. So healthcare might be another
source of that. For example, if you're very
poor, you might not be able to purchase very simple, relatively
cheap technologies that prevent you from
getting sick. It could be a covering
for your water. It could be a water filter. It could be a bed net to put on
top of your kids when they sleep so that they don't
get malaria. So all of these things might
all be like some fixed investment that, if you
can't afford them, you can't afford them. And then you are getting sick
more, therefore you are less productive, therefore you make
less money, et cetera. So that's another source where
we would have this S-shape. Then we again have to think
about these goods as things that are a little bit lumpy. Like a bed net, for example. Or a water filter. That you can either afford
or not afford. So if you have enough money you
afford it and then you can be generally healthier. You don't lose all your calories
to diarrhea and other nice things like that. And if you're poor you would
be sick all the time. Or paying for the doctors,
for example. So for example, if someone is
sick and very poor they might not be able to pay
for the doctor. Then they'll stay sick so
they can't earn money. And again, a doctor visit is one
big lump investment which you may or may not be
able to afford. That would be another source
of an S-shape like that. So the reason why I went through
all of these examples is that we are going to have a
lot to say about the exact story that Pak Solhin told
me about the food. Whether this was a real story
in this case or whether it's some stuff that he was telling
himself to explain the situation he was in but, really,
there was something else behind his problems
like depression or something like that. But the first time it was
formalized was in this context of nutrition. And it's very natural to think
of it in the context of nutrition but it could apply. And a very important part of the
discussion that I want you to keep in mind is that it's not
enough for there to be a relationship between income
today and income tomorrow. To create a poverty
trap it needs to have this funny shape. And I want to discuss why. So the way that we are going to
think of it is we are going to think about what
is the dynamic of someone's income over time. So let's start with this picture
which brings inherited income on the x-axis-- so think of it as
income today-- and income from work. What I have plotted here
is this S-shaped curve. Think of it, for example, as
coming from nutrition. But any of the examples that you
talked about if you don't like the nutrition one. And the line that goes through
the diagonal is the 45-degree line. So why is the 45-degree line
relevant and interesting here is that, , on the 45-degree
line, income today is the same as income tomorrow. Right, so we're going
to make use of it. Now I want to try and look at
the dynamic of someone's income over time. So suppose someone got this
little income, y prime 0. Where do I read their income
in period one? Yep? AUDIENCE: It would be going
from curvy line to the 45-degree line horizontally. PROFESSOR: Exactly. So to go from income y prime 0
to y1, I go on the vertical line up to the curve. That tells me this is what
someone who starts his life with some income, yi0, can make
his decision about how much to eat, creates some
calories, creates some work capacity, goes to work,
generates an income that he takes home. That's the income that we
have on the curvy line. And then I want to say, well,
that becomes y1, right? And then y1 is going to become
the y0 of tomorrow. So to find it, I'm doing exactly
what you're saying which is I'm going
horizontally to the 45-degree line. And I could go down again. So from y0, I go to y1. Then horizontally
on the 45-degree line gives me y1 again. And then how do I find y2? I go vertical again,
that gives me y2. I go horizontal again to
the degree line and I continue like that. And where will I end up? AUDIENCE: Where the two
curves intersect. PROFESSOR: I will end up at
the intersection of the 45-degree line and the
S-shape curve, right? At the first intersection. Now what if I start with
a higher income. If I start with the income
y 0 double prime. I go vertical to the curve. That gives me y1 double prime. I have to go horizontally
to find it when it becomes income tomorrow. Again vertically, et cetera. And I again end up at the
intersection of the 45-degree line and the S-shape curve
but now it's a higher intersection. Now what happens if I start at
the sixth point in the middle over there? Which way will that go? AUDIENCE: That will go down. PROFESSOR: That will go down. If I go to the sixth point,
I go vertical then left then down. So what is the key point after
which I will start going to the high point? Yeah? AUDIENCE: Where it intersects
the 45-degree line again. PROFESSOR: So the intersection
from below. So at this point P where the
capacity curve intersects the 45-degree line from below. Anything to the right goes
to the high steady state. Anything to the left goes
to the low steady state. So this possibility that there
are two steady states depending on where you start
from is the formalization of the poverty curve. Which is anybody who is poorer
than the unstable equilibrium over there-- if someone starts with exactly
this income, where do they go? If someone starts with exactly
the intersection of the 45-degree line and the S-shape
curve, do they go down or do they go up? They just stay there. So it is also a steady state but
it's a very unstable one. If anything happens, any
small perturbation. If they go slightly
to the left, they go all the way down. If they go slightly to the
right, they go all the way up. So we call that an unstable
statistic. So there is one unstable
statistic and two stable ones. And those two stable ones is
what we're talking about. They could be a poverty trap. Yes? AUDIENCE: Why are they moving
toward that 45-degree line? PROFESSOR: Can someone
explain that? You want to know why we are
going horizontal to the 45-degree line? Yeah. Can someone explain that once? And then I'll re-explain
it as well. AUDIENCE: Because yesterday's
income is going to be your today's income. And your today's income
is going to be your tomorrow's income. So if we start with a value
zero, so that value can come from work. It's going to be tomorrow's
[INAUDIBLE]. So if you get the income from
work, the y-value of that will be your incurred income
tomorrow. So you have to go to
the 45-degree line. PROFESSOR: Exactly. The reason why we are using the
horizontal line is that-- so from y0, I know
that I go to y1. And then I want to know,
from y1 where do I go? For that I need to put
y1 on the x-axis. And the 45-degree line allows
me to do that because the 45-degree line is where the
vertical is equal to the horizontal. So I'm going right to find y1
on the horizontal line which helps me to find it
on the x-axis. And then I know that from
y1, I go to y2. And then again horizontal, and
then again vertical, and then again horizontal. That makes sense? Is it clear for everybody? It would be better if we were
all on the same page. That we have that here. This is not obvious. It's not meant to be obvious. Yeah? AUDIENCE: [INAUDIBLE] y0 or y1-- PROFESSOR: So, the first
one you mean? AUDIENCE: Oh, is that
because that's the-- PROFESSOR: That's the
capacity curve. Exactly. Your y0 is what you
start from. And then the curve gives us
what is the relationship between income today and
income tomorrow. So think of it with
the food example. You start with some income. You decide how much to eat--
let's say you eat 80 percent of it-- you eat it. That gives you some strength. You go work. That gives you some wage. That's your income from work. AUDIENCE: And then, when we're
determining the distance between y0 and y1, is that
determined just by the distance from the curve
to the 45-degree line? PROFESSOR: Exactly. So y0 goes to y1. Do you understand the first
vertical step here right? y0 goes to y1 for the
first vertical step. And then we're looking for y1 on
the vertical axis, but now we need to find a way
to put it back on the horizontal axis. And the 45-degree line helps us
to do that because on the 45-degree line the vertical
distance is the same as the horizontal distance. So the horizontal line is just
a trick to help us find where is y1 on the horizontal axis,
which helps us go to y2. That make sense? So from y0, I go to
y1 vertically -- that's just a capacity curve. Then the horizontal line
is just to the left. Now what is the new y0? The new y0 is y1. And then again, we go
vertically to y2. Horizontally to find it on
the horizontal axis, vertically, et cetera. Yeah? AUDIENCE: What's the
unit of time-- PROFESSOR: The unit of time is
whatever we think is the right unit of time depending on the
problem we're looking at. So, for example, if it is food,
that might be the date. If it's the income of your
children, that may be a generation. In some sense, once we have
decided what problem we are looking at, the unit of time
doesn't really matter. We adjust to it. Yeah? AUDIENCE: How did you determine
which states were stable and which ones
were not stable? PROFESSOR: Well, look at it,
and for any point, you're figuring out whether or not
you're going to stay here. Whether things tend to bring you
back here or things tend to pull you away from it. Think of it, for example,
as magnets. Either they cling together or
they are trying to go away. Or think of it as a stick. Does it stay vertical or
does it fall down? Suppose that we start with
income and the first income we are getting is y3. That's going to pull you. You're going to go vertical
a little bit, horizontal a little bit, et cetera. That's going to pull
you exactly at that first statistic. Right? So now, if you start from the
first statistic and something slightly pushes you away from
it, it is going to bring you back to it. If you are a little bit richer
than the first statistic, you're going to, again, go back
to the first statistic. If you're slightly richer,
it's pulling you down. If you're slightly poorer,
it's pulling you up. Now, if you're looking at the
one that's here on top, that's the same thing. At the very top, if you're
slightly poorer, it's pulling you up towards it. If you're slightly richer,
it's pulling you down towards it. Now if you look at the one where
the line intersects from below, if you're exactly
at it, you stay at it. But if you're slightly poorer,
where do you go? All the way down. If you're slightly richer,
all the way up. So that one is not stable. So basically, you follow your
arrows wherever they are going to take you. OK? Any more question? Yeah? AUDIENCE: What are the
axis labels for it? Like income from work. I thought we were trying to
connect on a time scale-- PROFESSOR: Right, so it
doesn't really matter. Think of it as income today
versus income tomorrow. Or income that you inherited
versus income that you create yourself. Whatever scales we are
talking about. So in the food example, it would
be the income you had at the end of today. And then, that would be
inherited income you inherited from yesterday. And then the income from work
would be the income of the end of the day. So here the scale would
be one day. In the education example, you
would go from your income to what your children will make. That's a whole generation. So the time scale, it depends
on the problem. I think in the food example,
it's useful to think of a day. In the health example
it might be a month. AUDIENCE: Why is there a
tendency to move to the intersections? PROFESSOR: Well, that's where
the arrows are pulling you, aren't they? Because the closer of
the intersection is where you are-- first, you go from wherever
you start to the curve. And then the curve is
trying to go back to the 45-degree line. So the closer you are
to the intersection, the less you move. Which is why this
is, everything pulls you back there. --Not all the intersections. No, it's the stable ones. The one to the left and the
one to the right, not the middle one. Which you have a tendency
to go away from. Any other questions
on how this works? Yeah? AUDIENCE: How do you guys
actually gather the data to [INAUDIBLE]? PROFESSOR: So that's an
excellent question. Right now, I've just
asserted that it's the form of the curve. And then we have to go back to
the question that a neighbor-- whose name I don't know-- asked
earlier, which is what is, actually, the shape
of the curve? And that's a key question. That's going back to the
questions we were asking in the case of education,
for example. Is the relationship between
income today and income tomorrow due to education? Is it really of this shape or
is it of another shape? That's what we have to
assert empirically. And it's going to have
to be gathered on a case-by-case example. So for example, for food. To create this shape, to know
what is the form of the shape, we are going to need
to know two things. We need to know what is the
relationship between how much income you have and how many
calories you consume. And what is the relationship
between the calories you consume and your
work capacity? And the product of the two
will be that curve. And the shape it has-- God knows, I mean, actually even
we know, but we're going to cover that next time. So this is assuming that
the capacity curve indeed has this shape. Then we can see how the poverty
trap can emerge. Now, if instead, the capacity
curve had this shape-- think of your example
of education. And think that, in fact, the
first few years of education are very valuable and the next
years you guys are kind of wasting your time-- not to speak
of me-- and the next years of education are
not so valuable. What is really important is
to learn how to read. Imagine that's the case. Then it means that the
relationship between income today and income tomorrow
is not as steep anymore. It starts very high and
then it tapers off. And so we can play the same
game again that we were playing before. We can say, well, let's draw
the diagonal line. Let's start with some
income, a1. To find out income tomorrow
what do we do? We go vertical. We find income, a2. Then we have to go horizontal to
the 45-degree line to find it on the horizontal line. We go vertical again to
find it on the curve. Horizontal again,
vertical again. Where do we end up? q. Now suppose we had started
above q, where would we end up? q. Suppose we had started anywhere
in between, where would we end up? q. So there is no poverty
trap, in this case. If there is only one
intersection because the returns are first high and then
low, then there won't be a poverty trap. It doesn't mean that there is no
relationship between income today and income tomorrow. There is one. But the point is, that
relationship is first steep and then tapers off. So for example, imagine that
the only type of businesses that you can run are businesses that you can run yourself. That for some reason, you are in
a business where you can't really have employees. Imagine. So in that case, your first
investment will be quite valuable, right? But then, eventually, you can't
really add much more because you won't have
enough time to sell all of these things. So your first dollars invested
will have a very high return. And then less and less
and less and less. And so in that case, everybody
will end up at the same place. An example that could make it
clear, is going back to our Kenyan farmer from the MTV
video, Kennedy fertilizer. If you put fertilizer
on your crop-- well when you put just
a little bit, the effects are very high. But when you start putting more,
eventually, the soil can't absorb it so the
effects are less and less and less high. So even if you don't have enough
to put on your entire field to start with, you could
imagine that you would first put it in the most productive
part of your field. Because the first unit of
fertilizer you are putting is very high return. The second, you need less
because you're going to the place of your field that is
less productive anyway. At the third, you
need even less. The fourth is really not that
productive because, now, you end up putting more where
you started from in the first place. So that's not really
helpful anymore. So in that case, the returns
don't have this S-shape. They have this inverted
L-shape. So in that case, there
is no poverty trap. And so that is where the
question that you were asking is essential. Which is, how do we know what
the shape of this curve? Because the shape of this curve
is going to crucially determine whether or
not we have a trap. And what I want you to remember
is that that's more than a relationship
between income today and income tomorrow. It has to be this relationship
of this shape. So that's the first thing, which
is if the relationship is inverted-- L-shaped like that, which
is the canonical case in economics, most of our
economics model-- what you learn in 14.01-- has production function
of this form. Where this production function,
which we called, have decreasing returns. Where the first unit invested is
very profitable and then it becomes less and less
profitable. We've already discussed a number
of reasons why the returns might not would
always be decreasing. For example, we discussed the
case of calories where there might be an increasing zone and
then a decreasing zone. We discussed education might
or might not be that way. We got an interesting example
about businesses where you might not have a very profitable
opportunity for your business if you don't
have enough money. We discussed savings, which may
or may not have this form. Where nobody wants your
small savings. So there are reasons
why it may not always be inverted L-shaped. But if it is inverted L-shaped
there won't be a poverty trap. --You might be very bored with
me repeating the same thing for the fifth time now, but
the reason why I insist is that this is a confusion that
we hear over and over again among policy makers. In the policy discourse,
whenever they're thinking of a double feedback loop-- for example, kids who have
less education, make less money, and parents who have
less money send their kids less to school. Immediately, people think, ha! If there is a double feedback
loop like that, that creates a poverty trap. And the point is, that that's
not sufficient. That's necessary but that's
not sufficient. Because if the double feedback
loop gives you a nice inverted L-shape, eventually, everybody
will end up nicely in the same place. OK? So there is more, which is, here
is another case where we have an S-shaped curve. But the S-shaped curve is a
little different, it's a little higher. So why would it be a little
higher, for example? Why has it moved up compared
to what we had before? Why could it have moved up? Go back to the food example. Sorry? AUDIENCE: Lower food prices. PROFESSOR: Lower food prices. So for example, the productivity
of the land might have gone up. Maybe the government came and
built some irrigation dams and the productivity of
land has gone up. So to produce the same amount of
food you need less effort. So the work capacity translates
into a higher income for moi. So for whatever reason,
the curve shifts up. So then what happened-- we gave some person
some income, y0. We find y1 by going vertical. We find it again on the
horizontal line, y1. Going back to y2, horizontal
again. Et cetera, et cetera. Where do we end up? At the intersection. And now there's only
one intersection. So wherever we start, we are
going to end up at the same intersection. In that case, is there going
to be a poverty trap? No. In that case there is no poverty
trap because, again, there is one statistic. So an S-shape is not even a
sufficient condition for a poverty trap. It is necessary but it's
not sufficient. Let's find another example,
which is this one. Where in fact, now it's
the opposite. There was some flood
and the land is now completely washed out. So people are very
unproductive. They have to work very hard
to produce very little. So what happened to
my poor S-shape? It's shifted to the
southwest, right? So now if I start from y0-- quite high-- where do I go? So I go up, but then
it's not enough. The 45-degree line
is to the left. I have to go left, down
again, down again, down again, and again. I'm going to end up at the
single intersection where I'm always pulled up, which
is a very low income. So in a sense, there is no
poverty trap here either. Because it's not that if you're
poor, you'll stay poor, and if you're rich,
you'll stay rich. Regardless, you're
going to be poor. AUDIENCE: [LAUGHTER] PROFESSOR: So you could think
it's a universal poverty trap or you can think that's
just the way is. Because if you ignore the right
side, we almost are in the inverted L-shape except
there are stuff that are a little bit irrelevant
to the right. The reason why they are
irrelevant is that, eventually, everybody's
becoming poor anyway. So again, we don't have
a poverty trap. So let's look at those
three examples. That's an example with
a poverty trap. That's an example that
doesn't have one. That's another example that
doesn't have one. What is different between the
one example with the poverty trap and the one which
doesn't have one-- or two? Yes. Can you tell me your name? AUDIENCE: Zachary-- PROFESSOR: Zachary. AUDIENCE: --it crosses the
45-degree line twice. PROFESSOR: Exactly. Well, twice or-- AUDIENCE: Three times. PROFESSOR: Three times. It crosses the 45-degree
line once from below. So the rule is that you're going
to have a poverty trap if the capacity curve-- or whatever is the curve between
the income from work and the inherited income-- crosses the 45-degree line,
at least once, from below. That is, there is at least one
unstable equilibrium where you're crossing from below. And that is necessary for
having a poverty trap. So what you need, in other
words, is to have a zone where income is accelerating. And this zone must to be at a
place where the income was relatively low to start with. And it needs to accelerate
enough that it's becoming high to start with. In other words, it needs to be
a zone where, if you're below the zone, you're making
less tomorrow than you started from today. And when you're on the right
of the zone, you're making more tomorrow than you
started from today. And you need to have
this point. Otherwise, there is
no poverty trap. All right? So that's the mathematical
expression of it. And now, in a sense, the game
that we're going to play all around this class is
to be looking for-- are we in this situation where
whatever is the relationship between income today and income
tomorrow crosses the 45-degree line from below. Or are we not in
this situation. And now we are in a much better
position to ask the question that Zach asked at the
beginning of the question which is, are we really
believing that there could be a poverty trap based on food? I didn't want to answer his
question to start with because I needed some time to specify
the question in a much more precise way. Now we can re-ask the question
and say, is it really possible that the relationship between
the calories I consume and my strength has this specific form
where it intersects the 45-degree line from below? And how does that intersect with
the fact that I choose how much to consume? Because, of course, if there
is indeed a strong relationship between the
calories consumed and the work capacity, then people should
try and get out of it by eating as much as possible
when they are very poor. So to the extent that people
can choose how much to consume, how much food to eat,
they should eat more when they are very poor in order to try
and pull themselves to the right of this point. And when they are richer then
it wouldn't really matter. So they would eat less. So that would create a force
that goes against an S-shape for the capacity curve. So we have to see-- and that goes back to
your question, where do you get it from? Well, we get it from looking at
the data and looking at-- to what extent people who have
more money eat so much more, and to what extent people who
eat so much more are so much more productive. And that's what we
are going to do. We are going to do
it for food. But now that we understand the
principle for food, we are going to do it for education. We are going to do it for
health, we are going to do it for savings, for businesses,
et cetera. Yeah? AUDIENCE: To go back to the
example with the start of the class, would you say that-- I forgot his name but-- that
the man was at an unstable equilibrium since as soon as he
lost his job, he seemed to go down and not be able
to eat enough to get another job, et cetera? PROFESSOR: Right. So that's a very
good question. What we can try now is to
re-interpret Mister Solhin's story in the context of this. And you could say, well perhaps,
it was exactly something like that. So what would have
happened to him? Let's see, I want to-- oops. What would have happened
to him? So we discussed that one thing
that might have happened to him is that something happened
to the capacity curve, right? We were saying that coincident
decrease in the wage and increase in the food prices
means that the capacity curve tends to move to
the southwest. So assume that Pak Solhin
was at the high equilibrium up there. Right? But right there. And then the curve moves
slightly to the right. Then, with the same income, he
suddenly is now below what would correspond to the new
equilibrium and it would start falling down, down,
down, down. And once he starts going down,
there is no going up again. It could also have
eliminated-- we might also be in a situation
where, at the beginning there was just
one equilibrium-- so we were, for example
in this situation-- and then once the curve moves
down, they are now two equilibria, including
the unstable one. So we may have started, in the
former situation, where people were productive enough that they
were always moving up. And then, with the increase in
food prices and the decrease in wages, that curve shifts down
and now it creates two equilibria. So some people get trapped
like he was. What was interesting in Pak
Solhin's villages is that, in the same villages, I
met people who were happily eating enough. So it seemed that there was both
kinds, which makes you think that these two things
were coexisting. So maybe what happened with him
is that we started from a situation like that, and then
we moved left and we end up with this double situation. That's possible So what we had in the
Sachs-Jolie video is-- we said when we just
started the class-- lots of examples of
poverty traps. And in each case, we could try
and think, well, what makes us think that there is indeed a
poverty trap in this case? Or what makes us think that
maybe there is no poverty trap in this case? So one example is what
happened with the farmer that they meet. So they claim that there
was a poverty trap. So what is the implicit argument
that they had in mind that would help us think that,
for a farmer, the decision to use fertilizer corresponds
to that problem versus that problem? What do we need to know about
fertilizer and fertilizer use to try and sort out whether we
are in the situation that they talk about or in the
other situation. Yeah? You go ahead, I have
a problem. AUDIENCE: You need to know if
there is some minimum of fertilizer used that becomes
useful for the farmer. PROFESSOR: Right. So there could be that, minimum
fertilizer used. But why would there be a minimum
fertilizer used? Yeah? AUDIENCE: Maybe it's super
difficult to acquire small quantities of fertilizer. PROFESSOR: So for example,
it might be sold by the bag or 50 kg. So in that case, what we have
is not so much S-shaped but something which is a degenerated
S where you get nothing if you can't invest
enough and then you get the return which are, potentially,
very steep at the beginning. So instead of a nice little
curvy S, we have a flat part and then an inverted L. But if we have a flat part and
then the inverted L, it would still work like an S. Because
there would still be an intersection where the curve
intersects from above on the flat part, an intersection where
it intersects from below at the beginning of the
L-shape, and another intersection where it intersects
from above at the end of the L-shape. So the S doesn't have to be a
proper S. It could be a flat part and then an inverted L. So
this example could be one, which is you can only buy
fertilizer by the 50 kg. What other situation
could we find? Yeah? AUDIENCE: The percentage of
chance for success in using fertilizer. So if you only had [INAUDIBLE]
over a small plot of land, it is, like, 20% chance
of actually improving your crop yield. You would have to use a larger
quantity to actually get an improved crop yield. PROFESSOR: So that could be a
possibility if the chance of success depends on
how much you use. I think it's not very likely
that it would be a purely physical thing because
fertilizer is quite scalable. But one way in which we could
have your story is if, to use fertilizer it requires
some learning. And there's no point doing
all that learning-- and asking all of your neighbors
how they do it, and try to understand
how they do it. Maybe experiment a little bit,
maybe it won't work first. --Maybe there is no point to
go through all of this learning if, at the end of the
day, you know that, no matter what, you will always be able
to use just a little bit. So that would be one way
in which you would, again, create this. You're not going to use any
fertilizer if you know that you, eventually, would be able
to use it on the substantial part of your field. Yeah? AUDIENCE: I think that the main
point they made in the video is that there needed
to be an initial push. So they needed a lot of
fertilizer and you needed to put it on all of the crops for
it to make a big impact. And the fact is, if you have a
little bit of fertilizer-- the point was why couldn't
they invest? So save would be paying for a
little bit of fertilizer. And then buy more fertilizer and
then continue to grow it until [INAUDIBLE]. You know, if you started off
with a small amount, you couldn't really invest
and grow your yield to make more money. PROFESSOR: Right. Then the third possibility is
that if you invest just a little bit-- let's say fertilizer scales
nicely, so you can invest just a little bit and
you can do it. But then, you're going to make
just a little bit more money. And then we need some other
mechanism which means that saving a little bit more money
is not feasible, or people are not going to do it. So then we need to bring in
something else which is along the line of what we
were discussing earlier in the class. We need to bring in something
else which is, the banks are not going to take your small
amount of money. Or if you have a small amount
of money, you are going to waste it. But if you have a lot, now
that's enough money to be worthwhile and you're
going to keep it. All right. So we are going to end
here for today. So make sure you understand this
because we are not ready to go back to it formally a lot,
but this is going to be with us all the time. And on Tuesday, we are going
to go through experiments.