Prof: So for those of
you who weren't here yesterday-- or, last class,
first class, I'll say a couple words about
what happened, basically four words.
The course is really made of up
four different elements. The first part is the standard
financial theory course that grew up in the last ten years at
a lot of major universities, pioneered by a bunch of guys
who won Nobel Prizes in business schools.
And it's the method,
some of them quite clever and I think fun, methods for pricing
financial assets and making optimal financial decisions.
So you're going to learn all
these tricks and how the financial system works,
and you'll learn it both from a theoretical point of view,
the way they thought of it in these finance schools,
and also from a practical point of view since many of these very
same problems come up all the time in the hedge fund I helped
start. So that'll be the main part of
the course, but there are three other things that I want to
concentrate on in the course. So the second point is
reexamining the logic of laissez-faire and regulation.
This is a dramatic moment in
our history now where there's tremendous pressure on--
temporarily anyway--on the government to establish all
sorts of new regulations. There's also tremendous
resistance to establishing the new sorts of regulations.
So there's a debate going on
now in Congress and in the halls of academia about what kind of
regulations should we put in place,
what regulations would have prevented the crisis we've just
lived through. The crisis, by the way,
which I don't think we're done with yet.
So there's a very powerful
argument in economics. The most famous argument in
economics, the invisible hand argument
that basically says markets work best when they're not encumbered
by government interventions. So we're going to reexamine
that argument in the context of financial markets.
Then the third thing I'm going
to discuss in this course at some length is the mortgage
market and the recent crisis. After all, my hedge fund is a
mortgage hedge fund. We founded it in 1994,
by the way, which was-- the five years before that I
was running the Fixed Income Research Department at Kidder
Peabody, which was the biggest player in
the mortgage market then on the sell side.
The hedge funds buy mortgages,
investment banks create and sell the mortgage securities.
So I was running the research
department at the firm that did twenty percent of the market in
what's called CMOs, and then I changed to the buy
side and was at a hedge fund that bought those kinds of CMOs,
and bought sub-prime mortgage, CDOs,
everything. So it seems I suffered greatly
through the last two years of the mortgage crisis and it would
just be foolish not to explain what was going on and what it
felt like to be in a mortgage hedge fund while the rest of the
world was collapsing around us. And for quite a while it's
given me some great embarrassment to have been part
of it all. On the other hand,
now I feel like one of those survivors.
Hundreds of our counter-parties
and much bigger mortgage players went out of business and we
didn't, so I don't feel quite as bad
about it as I did before. And I don't know every detail
of what went on in my hedge fund,
because after all I'm only part time there,
but there's a lot I do know about and so I'll try and tell
you some of that. And then the fourth thing is
Social Security. This is the biggest government
program and it's a financial problem what to do about
retirement, and Social Security is the
biggest government program of all.
The only thing close is the
military budget in terms of annual expenditures.
And so I'm going to explain how
that works, and what the problem is, and how it arose,
and what I think the solution is.
So those are the four things
the course is going to concentrate on.
The mechanics of the course,
again, are homeworks,
every week there's going to be a homework with little problems
illustrating what we're talking about.
So there's one already on the
web, Tuesday, today, every Tuesday there will
be one on the web. It'll be due the next Tuesday.
The sections will always meet
between Thursday and Monday, so the problem set will come
Tuesday. You'll have two days of classes
on the material that the problem set will cover and then you can
talk to the TAs about stuff between Thursday and Tuesday
when I presume you'll do the problem set.
And that's twenty percent of
the grade. Twenty percent is the first
midterm. Twenty percent is the second
midterm and forty percent is the final.
Two midterms takes a lot of
class time, on the other hand, and it also takes a tremendous
amount of effort by the TAs. And so I appreciate their
willingness to grade two midterms,
but I think you'll find it's helpful to study the course in
two pieces than try to do the whole thing--
It'll be much better for you I found in the past to have two
midterms. Oh, and one warning.
The course doesn't require
difficult mathematics, but for me, as I said in the
first class, it's very interesting that
there are so many subtle things that affect a financial
decision, and you have to think about
what you know and all the different things you know.
You have to think about what
the other guy knows who's taking the other side of the market.
You have to think about what he
knows about what you know, and you have to think about
what he knows about what you know about what he knows,
and all that thing in the end boils down to one number,
the price. So it's a philosophically
interesting problem, interactive epistemology.
Some people have described
economics as interactive epistemology.
It's more complicated than
standard epistemology and philosophy because there they go
in circles thinking about what one person knows and whether you
can know that you know and stuff like that.
In economics you have to worry
about what you know, what the other guy knows,
what you know about what he knows about what you know
etcetera. So it's a more complex problem,
and yet at the end there's just one number which can be right or
wrong. And so when I was a freshman
here at Yale my roommate who was a classics major said that his
subject was much harder than mine--
that was math--because all I had to do was be right.
And so I'm going to take
advantage of that simplicity and every problem is going to have a
number that you're supposed to find.
And so it's not complicated
mathematics, but it involves lots of numbers.
And so if you hate numbers you
shouldn't take this course. And as I said before,
there have always been people who, you know,
you can be very smart. You can also have a great
future in finance and not like numbers.
You can like making deals and
things like that not thinking in terms of numbers.
So just because you don't like
numbers and maybe shouldn't take this course doesn't mean you
should be discouraged about finance.
It's just how I happen to teach
the course because that's what's comfortable for me.
So I'm just warning you about
it. It won't be hard,
but it'll be relentless. I want to talk today about that
second problem, about the logic of the free
market and to do that I'm going to have to introduce a model.
So it raises the question of
what is a model in economics. Many of you have taken
economics before. You sort of know what this idea
is, but I think it's worth spending a minute on it because
it represented a revolution in thought.
So for an economist a model
means you distinguish exogenous variables from endogenous
variables. The exogenous things people
can't control. They're just the weather and
things like that. The endogenous variables are
things they can control and you're trying to predict what
the endogenous variables are going to turn out to be like,
what will the prices be, what will the consumptions be,
things like that. How much income will people
have? Those are the endogenous
variables. So you have a theory.
So the theory is couched in
terms of equilibrium. There's a bunch of equations
which have to be satisfied, F of E and X.
So given the endogenous
variables and the exogenous variables,
exogenous and endogenous, I wrote them in that order,
there's a set of simultaneous equations,
F, that have to be satisfied. And so you find equilibrium
when given the exogenous variables E you find the
endogenous variables X of E that solve that system of
simultaneous equations. All our equilibrium models are
going to have that form, and one very important thing
they allow you to do, which is the heart of economic
analysis is comparative statics. If you change the exogenous
variable E it'll require a different X to solve the
equation. So E has an effect on X in
order to restore equilibrium. And so the prediction that a
change in E has a certain effect on X is called comparative
statics. Now, how would a historian
describe that? A historian would say,
"Well, that's counterfactual reasoning.
The environment is E.
Why are you bothering to tell
me about what would happen if the environment changed from E
to E-prime?" Well, that's the heart of
economic analysis. So in history you hardly ever
get much. People talk about it a little
just to raise the question. How would the Vietnam War have
gone if Kennedy hadn't been assassinated?
So they all bring that up,
but you get two sentences. "Oh, he was really going
to pull out," or "Oh,
he had been sending more advisors.
It would have gone the same
way." That's about it.
In economics the heart of the
thing is to go off on a tangent and figure out what would have
happened if the environment had been different.
So why do a model?
Well, because many different
settings can be described by the same model.
So it just saves time.
It makes things much simpler.
From the counterfactual
reasoning you're making predictions.
It helps your understanding.
And then for the purposes of
the next few lectures the most important thing is there's some
properties of equilibrium. Like, for example,
equilibrium is so good you wouldn't want to interfere with
equilibrium because it makes everyone so well off and it
would be a terrible thing to regulate.
So those properties of
equilibrium are what we have to test the logic of.
So there's an obvious critique
you can make of modeling. The first person to make a
model was Ricardo, who you I'm sure have heard of,
the principle of comparative advantage.
He was the first guy who didn't
write verbally. He said, "Okay,
I'm talking about international trade and why free trade is a
good idea. I could make a verbal argument.
That's what everyone else has
done, but I'm not going to do it.
I'm going to say,
'Suppose that England produced with one hour of labor three
bottles of wine' and so on, " and he had a little
numerical example. And he solved it and he showed
that in that numerical example it's better to have free trade
as paradoxical as it might have sounded at the time.
The Portuguese had such lower
labor costs why shouldn't English workers be afraid of
being thrown out of their jobs when trading with Portugal where
the labor was so much less expensive.
Well he explained why that
turned out not to be the case, but in terms of a model.
So Malthus, who you've also
heard of, a contemporary of his and his
rival but also his friend, said, "This model stuff is
ridiculous because if you start making a model the point of a
model is to make deductions from it,
and to analyze it, and analyze it deeper,
and deeper, and deeper, and of course the model to
begin with is going to be wrong and as you go deeper and deeper
into the analysis of the model the error that you made at the
beginning is going to get compounded."
Like he said,
"The tailors of Laputa, who by a slight mistake at the
outset"-- doing their stitches,
go wrong--the stitch goes further and further wrong--
you "arrive at conclusions the most distance from the
truth." Anyway, that's what you might
think is wrong with models, and the very first model was
critiqued by that reasoning, but it's turned out
historically that modeling is the way to make progress in
economics and everybody does modeling now.
You'll find out as I talk more
about it that the Cowles Foundation,
which has been at Yale since 1955, was founded by a Cowles
[correction: Yale] undergraduate.
You'll hear the whole history
of it. I was the director of it for
nine years. That was the one most important
institution in the world promoting the uses of
mathematics in economics, and the revolution succeeded
and now all economists use models and mathematics.
Anyway, let's take an example
of the simplest model. There are so many different
ways of organizing price and trade.
At a supermarket the seller
just sets the price and you decide to buy it.
If you go to Jerusalem or
something in the old city you know that you're haggling over
everything. You offer this and the guy says
no and you walk away, and you come back and it takes
a half a day to argue the price, but that's another way of
arguing the price. Then there's--the government
could set the price. In the Paris Bourse the way it
worked is there would be a temporary price set and then
supply and demand-- people would announce how much
they wanted to buy, and if the supply didn't equal
demand the price would get changed.
So it was--tâtonnement
means groping, or groping to the price.
There's the commodities futures
just like the experiment we ran where people yell at each other.
There's computer bid/ask prices
where you do everything online. There's the specialist in the
stock exchange. There's one guy everybody has
to come to, and so he's responsible for clearing the
markets. So I might, in fact,
mention a little bit of the history of this sort of thing.
I don't know if I can hit
escape. It might be somewhat
interesting. So the first people who had
these well-developed markets and money were the Lydians.
They invented money in 640 B.C.
and they had gold coins,
and with all this money and trading they got very quickly to
gambling and prostitution for money.
And Midas, the Midas touch was
everything turned to gold was Lydian.
They've discovered all these
mints where their capital was so they know that they were making
all this money and gold and stuff like that.
So they had open-air markets.
They invented the retail
markets. Croesus was one of the most
famous Lydian kings, and he's the guy--rich as
Croesus is a famous expression. He's the one who went to the
Delphic oracle and asked if he should fight the great Persian,
Cyrus the Great and the Delphic oracle as usual mysteriously
said a great kingdom will be destroyed,
and since it was Cyrus the Great he figured it must be
Cyrus' and it was his kingdom that was destroyed.
So the Greeks copied a lot of
that stuff. They had their agora which was
the open market and they had lots of trade,
and they understood supply and demand, by the way.
This isn't the modern example.
In the politics there's a story
of Thales who predicts a bad harvest.
He's a great mathematician and
astronomer, and he predicts a bad harvest
and he figures if he corners the wheat market he'll make a
fortune, which he does.
Aristotle was famous for
saying, "Money is just a convention.
It's not really worth anything.
People just agree it's worth
something even if it's just pieces of paper or coins that
worth much more than the coins and how could that be,"
and anyway there's a long political connection to that,
the difference between nature and convention,
but anyhow he also said, "Loaning at interest was
unnatural and terrible," but all the while he was saying
it the Delphic oracle was lending at interest.
Economics is a Greek word,
household management, Xenophon wrote a whole book
about it. And just one more little
history or historical thing, Hermes, the messenger god,
the god of information, so remember the modern
financial view of information, markets and information,
anyway he was the Greek god, messenger god,
and god of information. The word commerce comes from
Hermes. And the Romans who took over
the same god and called him Mercury that's where we get the
word merchant from and market. Anyway, all right I'm not going
to bother with all this. I used to go on and on about
this. So the point is that in ancient
times the market was already established and this idea of
supply and demand had already been created but there are many
different kinds of markets, as I've just said,
and they work in many different ways,
but we're going to describe them in one model.
So just to mention a couple of
others, the model, the experiment we
ran in the class last time is called the double auction,
and the experiment I told you about and had you do was
actually an experiment that has been run before.
And for the last ten or twenty
years many economists have run these sorts of experiments.
It's amazing that before that,
before twenty or thirty years ago no one thought to do that.
You didn't think that students
with no training and no experience could ever be led to
do something that was sensible, but actually you did quite
brilliantly. And by the way,
I've been told that those of you who performed,
maybe you're still in the first two rows,
you have to sign, even those of you who were left
at the end unable to trade you have to sign a release form so
you can't sue Yale for your disappointed faces appearing on
the internet afterwards. So anyway, the fact is we're
going to see that the people who were left at the end were
actually very rational. In fact nobody made a mistake.
I've done this experiment now
ten or twenty times and I would say that half the time somebody
buys something for more than it's worth to them.
Nobody made a mistake and it
almost came out exactly as it should, but we'll come to that
in a second. Anyway, that double auction is
the most complicated kind of auction, but auctions have been
run for a long time. The first recorded auction you
may have heard about was--Herodotus describes the
Babylonian auction in 500 B.C. These are all going to be very
politically incorrect, but a lot of economics is
politically incorrect. Anyway, the first auction in
500 B.C. was the Babylonians auctioned
off all the 18-year-old women as wives and they auctioned them in
order of most beautiful to least beautiful.
And so they got a very high
price and the price went down and down and down until it hit
zero and then it started going negative,
but they used the revenue from the first wives to subsidize the
husbands who would accept the other wives as it kept going
down. The next most awful auction was
the Roman Empire itself was auctioned off.
So if you saw the movie
Gladiator you may remember that Marcus Aurelius is
the great emperor, and he dies,
and then the evil Commodus takes over,
and he dies as a gladiator there.
And then there's the senator
who you sort of hardly ever see, but you know he's the good
senator who somehow-- he appears a few times--you
know that he's a good guy and he's going to take over.
So his name is Pertinax,
and he does take over. But he's a good guy and he gets
killed almost immediately by the Praetorian Guard and the
Praetorian Guard then doesn't know who to make emperor so they
auction the whole empire off. And so it's bought by Didius
Julianus, and he doesn't last very long, and he gets killed
too. The Roman legions come back and
kill him. So anyway, I grew up in Urbana,
Illinois and I used to go to these livestock auctions where
they'd sell something. They'd talk incredibly fast
<<speaking gibberish very fast like an auctioneer>>
They talk like that and I don't
know how anybody can understand them,
and then there's the famous slave auction,
so--where they'd actually auction slaves,
and you've seen it in the movies maybe.
And that's where the
expression, "Going once, going twice,
third and last call, going,
going, gone," that's what they used to say at
the slave auction. So the double auction that we
saw was kind of what happened at the beginnings of the New York
Stock Exchange. The first traded
securities--there were only five of them, so how did they start?
There was the Revolutionary War.
A lot of states had borrowed
money and issued their bonds, and there are two banks,
Bank of New York and the National Bank of the U.S.
that had issued bonds.
Those were the only tradable
securities. And so a bunch of states had
issued bonds. So what happened was after the
Revolutionary War most people expected the bonds wouldn't be
paid back. After all, there was a huge
expense fighting the Revolutionary War.
The government didn't have very
much money. The price of the bonds had
already collapsed, and Jefferson wanted the U.S.
to just, you know,
wanted to leave the states and let them default.
And Hamilton said that that
would be terrible, that the reputation of the
country was going to be made at what happened at the very
founding of the country and it was important that the U.S.
never break a debt.
So he persuaded Washington to
have the federal government buy all the debt of the states and
basically pay it all off, so none of the debts were
broken. Jefferson argued,
"That's crazy. The people who originally
bought the bonds, who lent the money to the
government, the farmers who did it they didn't own the bonds any
more. They probably all sold it for
twenty dollars. It was all this despicable
speculators who held the bonds. You're only going to enrich
them by paying them off." So he just wouldn't budge.
And finally Hamilton,
supposedly--this is a famous story,
I assume it's true--Hamilton went to Washington and said,
"All right, move the capitol from New York
to Washington. That'll make Jefferson happy
because it's near his dear Virginia and in exchange get him
to concede that we have to pay off the debt."
So Washington brokered that
deal and the debt was paid, and the U.S.
since then has never defaulted
on its debt and virtually no other country can say that.
For example,
Russia has never paid a thirty-year debt.
It always has defaulted,
and we'll come back to that a little later when we talk about
the crisis of '97-'98. Anyway, so these five
securities--three government bonds and these two from the
Revolutionary War and two banks--
were the only securities sold and they used to be sold every
day in a double auction exactly as the kind that we described
where people would yell and scream at each other and the
whole thing would be over in a few minutes,
and that would be it for the day, and then the next day they
would do the same thing over and over again.
Well, they had to stop that
when Alexander Duer, who was Hamilton's assistant,
started using his inside information about whether the
government was or wasn't going to make all its payments and
whether they're going to issue new bonds and stuff like that to
try and speculate on the market. And he would do it all by
borrowing. He'd borrow a huge amount of
money and with the borrowed money he'd buy bonds,
and if the price went against him he'd lose a lot more because
he was leveraged. And so it caused gigantic
gyrations in the market and the whole thing had to be changed,
and it was made a much smaller group of people.
Anyway, so that was the
beginnings of it. And we're going to come back to
that because that view of the gyrations of the market being
caused by too much borrowing and speculation is exactly the view
that I'm going to take in explaining the most recent
crisis. So anyway, you remember what we
did in our experiment. We had eight buyers whose
reservation prices are those eight numbers up there.
That's what each person thought
it was worth to him. Each person knew his own price,
but not any of the others. I told you almost nothing about
what was going on. There was some context.
I gave an example of a person
who thought it was worth fifteen,
so you had some idea, probably, from that example
that the numbers weren't ten thousand,
plus you knew your own number. But other than that you knew
absolutely nothing and each buyer knew her own number and
not any of the other numbers. So here we have sixteen
different pieces of information. Everybody has an incentive to
keep her information secret. Why should anybody admit that
she's willing to sell at six? She'll get a worse price.
She's going to lie and say the
thing is much more. She's going to make an argument
that says, "Well, these are football,"
okay, I better try the guy here.
The forty-four guy,
he's going to say, "This is a football
ticket." No, sorry.
What am I going to do?
Let's say she's a forty-four.
She's going to say,
"Football tickets, they're completely
worthless." I'm doing a stereotype.
"These are completely
worthless. Who would want to go to a
football game? I certainly don't want to go to
a football game. They can't be worth any more
than twelve or something." So all the buyers,
the blue buyers, are going to be making
arguments suggesting the price should be low,
reasons why the stuff really isn't worth very much.
All the sellers are going to be
making arguments saying the stuff is intrinsically
incredibly valuable. Football tickets are incredibly
important. So that's the facts.
Now you need a model and a
theory that fits the facts, and I'm belaboring the obvious,
but the obvious is always central to everything,
the obvious theory would go something like,
well, somehow these people are going to get matched up and
maybe thirty-eight will sell to forty-four and all eight things
will be sold. And the more transactions you
have the better. And what else might a theory
say, a wrong theory? It might say the more people in
red, or the more people making arguments that the price should
be higher the more compelling the argument will be.
You'll be overwhelmed by
numbers and you'll think that the price should be higher
because more people will be arguing for a higher price.
But the theory,
the economic theory is the exact opposite of all that.
So the economic theory is quite
a shocking theory, I think.
It starts with a situation
where people are arguing and talking about the price.
They're not doing anything else
but making arguments about the price and making offers about
the price. They're haggling about the
price. The whole of the activity is
about the price and how to change it and what it should be.
The economic theory,
the first theory, the most important theory of
economics, supply and demand,
is that--so that describes what happened,
is the exact opposite. The theory says let's suppose
that a price appeared out of thin air.
There was no arguing about the
price. Nobody even thinks they have
any chance of changing the price.
Somehow a price gets into
everybody's head, the price of twenty-five and at
that price of twenty-five everybody who wants to buy buys
as much as they want. So mister forty-four he thinks
the ticket is worth forty-four. If he can buy it for
twenty-five he'll want to buy. Forty thinks it's worth forty
and the price is only twenty-five so,
again, he's going to gain by buying, he'll want to buy.
Twelve thinks it's only worth
twelve. He's not going to pay
twenty-five for it. And similarly the sellers,
seller number ten, she's going to say,
"Okay, I can get twenty-five for it.
It was worth ten.
It's a good deal for me to
do." So the theory says somehow
miraculously the price comes out of thin air.
It's given.
Everybody taking that price as
given, figuring they have no power to change it,
buys or sells all they want at that price.
And so that's the theory.
So it's price taking,
out of thin air. The price comes from somewhere.
Everybody acts by maximizing,
doing the best for them given the price.
They all understand what the
price is, and the price has miraculously been imagined at
exactly the level that will clear all the markets.
So everyone who wants to buy is
able to, and everyone who wants to sell is able to.
That's the theory.
The theory's completely the
opposite of what common sense suggests since,
as I said, the whole thing was this grappling and groping and
pushing and shoving and yelling and arguing about what the price
should be and the theory says nobody says a word about the
price. They just take it as given and
then they act after that. So the most basic economic
model is a paradox, and good economics is almost
always a paradox. If you want to make a
convincing economic argument you almost always say it in a
paradoxical way. And so going back to the very
beginning where we said what a model is,
the standard economic model is you take the exogenous things,
which in this case are the reservation prices of all the
people, you have to solve equations
which are here, supply equals demand,
which determines the endogenous variables,
which are the price and who buys and who sells.
And the reason the theory is
always often paradoxical is if you change some exogenous
variable it looks like it's going to move things in a
commonsensical direction, but then when people react to
the changed environment-- X is a reaction to the change
in E-- and the change in X might be so
big and so important that it reverses the apparent change in
E. So you get these surprising
conclusions. "If everybody tries to
save more," Keynes said,
"It may be that everyone will end up saving less,"
things like that. So economics at its best takes
advantage of its paradoxical nature at its heart and uses
that as a rhetorical device. So it's a non-obvious theory.
Now, why do we believe the
theory? Well, all those different
examples I gave you of markets they all seem to fit.
I forgot where they were and I
don't even remember what they were.
I don't remember what they were.
The shopping center thing,
the haggling, the tâtonnement Bourse,
the commodities futures, all that, if you look after the
fact at what people wanted to do and what price emerged it seems
to fit the theory. So there's overwhelming
evidence that this theory seems to work.
And you saw that in our own
example, in our experiment where you had no training at all,
it came pretty close. So all these five red sellers
they all sold, I think, and the five buyers
the only difference was that instead of twenty-six buying
twenty bought, and the prices were all between
twenty and twenty-five, so they weren't exactly
twenty-five, but they were very close to
twenty-five. And the ten people who were
supposed to have bought and sold, well nine out of the ten
actually did buy and sell. So it's pretty hard to match a
theory like that with so little practice.
I mean, I've always found it
quite astonishing. Why is this happening?
Does anyone want to make a
comment or ask a question about this theory?
All right, well what are the
properties of equilibrium you get out of this?
Well, everyone trades at one
price. So this is going to be very
important for finance, the idea that there's one price
for everything. Then you can also define
the--so you know what the theory is.
I already told you the
exogenous variables are the reservation values.
The endogenous variable is the
price that emerges and who buys and who sells.
So why is this such a good
outcome? It seems like a terrible
outcome. There are those six people
standing there at the end unable to trade,
facing the camera, looking slightly embarrassed
that all their friends managed to buy and sell and they
couldn't do it and what's the matter with them.
So they feel bad.
They feel discriminated against.
It doesn't look like it's such
a great thing. We know that there's another
way of making all eight buyers purchase from all eight sellers
just by doing the corresponding one above.
What's so good about the market
outcome? It actually doesn't sound so
great. Well, the answer is it is great
and what's great about is that within two minutes the market
figured out enough about what everybody valued the football
tickets at to put the football tickets in the ten peoples'
hands who valued them most. All right, so in the end those
five blue guys-- almost without that one
exception--and the one, two, three red sellers,
those three sellers and those five buyers,
the top eight people ended up with the eight football tickets
and the bottom eight didn't end up with any football tickets.
So the football tickets got put
into the hands of the people who valued them the most.
And so, as I said,
if you just simply sat there and went through sixteen tickets
and sorted them into most and least and then tried to arrange
all the football tickets it would have taken almost as long,
and that would have been with benefit of knowing what all the
numbers are. Here the market does it not
knowing what the numbers are and the only accessed information is
through people who don't want to reveal their numbers,
and still the market figured it out.
All right, so that's the
message. So we have a model which is
surprising, which seems to describe the
facts, and which gives us a surprising conclusion and an
incredibly important conclusion. The market is an extremely
useful mechanism of eliciting information and turning the
information into something that allocates things efficiently,
and you couldn't do better than that.
No other arrangement would have
put football tickets in the hands of people who like them
better. So Hayek described the market
as a great calculating machine, and well so it is.
Now, there are a couple other
things that you can get out of this model.
Another lesson of this model is
that the equilibrium price is equal not to the average of the
price of the buyers, or the average of the price of
the sellers, or the average of all the
prices or something like that. It's equal to what the marginal
buyer thinks it's worth. So there's a critical marginal
buyer and marginal seller. They're almost indifferent to
buying or selling. They could go either way.
They're pretty close to buying
or selling. The price is going to turn out
to be very close to that valuation of the marginal buyer.
So somehow the margin is going
to play a big--so the word marginal, this is an invention
in 1871, is going to play a big role in economic reasoning.
So it gives us a completely
different understanding. You might think that the price
of tickets has something to do with their total value or
average value or something like that.
It's got to do with the value
of a marginal person, the person just on the edge.
So then the comparative statics
are that the, as I said, the surprising thing
that if you change a non-marginal person,
you take mister forty-four, the buyer at the top,
you change him to fifty. Looks like the buyers are now
more desperate to buy, won't have any effect on the
price. You change that seller,
miss six, you change her to two or to eight,
again, it'll have no effect on the price,
because those two people, the guy at forty-four and the
lady at six, they're not marginal so they
don't affect the price. You add some more buyers you
might think that they're arguing for the price to be lower,
as I said you're going to end up raising the price or else
having no effect on it if they're not marginal.
Now one more thing,
one last thing, one last message of this model,
if you didn't know-- we knew the reservation prices
ourselves because I set up the experiment,
but if you didn't know it you could infer something from the
price. So part of finance is going in
the backwards direction. The theory says take the
exogenous variables. Predict what the equilibrium's
going to be. Financial theory does that,
but often it goes in the reverse direction.
We can see what the prices are.
That must tell us something
about the exogenous valuations. So financial theory says,
"Well if the price is such and such it must mean that at
least the marginal person values it at such and such and so
that's why the price is that. It's the value of some special
persons." So we'll come back to that
argument. So that lesson of economics,
that's the first economic model,
the most important economic model, we're going to now have
to generalize it in all kinds of ways,
but it's always going to come back to that same message.
And so Adam Smith he was the
one who first invented the invisible hand.
There was nothing mathematical
in what he said. Ricardo was the first one to
make a model. Marx said, I don't have time to
talk about Marx, but he had quite elaborate
models, actually, and his verbal arguments
conceal a huge mathematical apparatus.
On his deathbed,
by the way, he was trying to learn calculus,
incidentally. So Jevons, Menger and Walras
1871 right after Marx's famous Kapital came out in
1867 they invented the idea of the margin and things like that
and the critique therefore of Marx,
and Marx was trying to figure out what they were all about.
Anyway, Marshall was a great
economist, Fisher, Samuelson, Hicks,
Arrow, Debreu; these are the most famous
people who extended this model and the logic of laissez faire
and regulation which we're going to come to.
Now what are the two ways we
have to generalize, there are three ways we have to
generalize the model. We have to think of many
commodities, not just one. We have to think of people
buying more than one unit of a commodity.
That's called general
equilibrium. And then we have to put in
financial things. We have to put in stocks and
bonds and things like that. It sounds like things are going
to get so complicated, but in fact it turns out I'm
going to spend another class after this talking about this.
There's not that much
complication to get all those things in.
There'll be two more classes
about this. So I'm recapitulating all that
you have to know for the purposes of this class from
introductory economics and intermediate economics.
The only thing you have to know
you'll hear now in these two classes and some of you will
find it's incomprehensible, and so that's one good reason
for doing it now. You find out right at the
beginning whether it's too complicated to bother with.
So anyway, I'm going to keep
going now to extend the model. So the biggest advance,
the next advance, sort of, which was related to
this is Adam Smith said, "How could it be that
water which is so valuable has such a low price,
and diamonds which are so useless, basically,
to everybody has such a high price?
I mean, there's not some
marginal buyer who thinks that diamonds are somehow more
important to him than water, so how could it be that water's
got a much lower price than diamonds and everybody would say
that it's more valuable?" Well, to answer that question
what we have to do is we have to imagine that people are capable
of consuming more than one good. So for instance,
let's imagine that there's good X here which is the football
tickets we had before, and you remember our numbers.
Let's just go back to the
numbers for a second. I'll stay here for a while.
The first buyer thought one
ticket was worth forty-four. A second ticket was useless to
that buyer. Well, suppose we write utility
here. Now, this first buyer--let's
put this forty-four here--this first buyer you might say got
utility of forty-four for holding one ticket.
If he held half a ticket maybe
his utility would be twenty-two. Now, in fact we know that half
a ticket doesn't get you into a game so his utility would really
be zero. When we're talking about
thousands of tickets to a football game a half or one it's
not so important. Let's just say his utility went
up linearly with the quantity of tickets he had.
To make a discrete variable a
continuous variable his utility goes up linear at the rate of
forty-four per ticket. Well, after one ticket he gets
no extra utility out of holding any more tickets so his utility
might look something like that. But now let's imagine he wanted
two tickets and that the first ticket was important to him and
the second ticket he could take his girlfriend,
let's say, but he's not quite as worried about her as himself.
So let's say that he,
for the second ticket, gets an extra forty utils.
So after you get to ticket
number two his utility is going to be up to eighty-four,
which is forty-four and forty. Now you notice that the rate of
increase of utility per unit of ticket is forty-four here and
then it switches to forty. Okay, now, why do I--why do
I--okay, and if he wanted one more ticket maybe he'd only get
utility of one-twenty for the last ticket.
So for a third ticket his
utility would--three goes up like that, utility would go up
like this. It's a little flatter again.
So here we have a utility
function which is increasing the number of tickets you hold.
It's not restricted to just
having one ticket, but the rate of increase goes
down as you get more and more tickets from the rate of
increase of forty-four, to the rate of increase of
forty, to the rate of increase of thirty-six.
Now, if you ask this person how
many tickets does he want to buy, well what's he going to
say? How's he going to figure out
how much to buy? This is his utility,
but now I claim this person buying multiple tickets is going
to behave exactly like the top three people up there would have
behaved. So his utility at the top for
three tickets is one-twenty, for two is eighty-four,
for one is forty-four. Those sound like important
numbers, his total utility, but actually they're not
important numbers. The important number is the
marginal utility. So the marginal utility,
so if you go one, two and three here,
the marginal utility for the first ticket was forty-four.
The marginal utility for the
second ticket was forty, and the marginal utility for
the third ticket was thirty-six. So those are the important
numbers, the same numbers that are up there.
Why is that?
Well, let's ask the guy.
This person who now likes three
tickets, after here let's say he's flat
so it goes down to zero, let's ask him how many tickets
would he buy at the price of forty-two.
Well, from this utility
function you have to say if I bought one ticket I'd have a
utility of forty-four minus-- let's say my utility function
now is U of X and money is this function of X.
I'll call this U of X.
I don't want to write it out.
This is U of X plus M for money.
So he says, "If I buy one
ticket at a price of forty-four I lose forty-two from here,
but I gain forty-four from here, so I probably should buy
one ticket. If I buy a second ticket this
number goes up to eighty-four and now this one goes down by
forty-two twice, so maybe it's not such a great
idea." So what is he actually thinking?
All he's doing is he's looking
at the price in this axis and comparing it to his marginal
utility, the extra utility out of getting an extra ticket.
So if the price is forty-two
here he's going to say, "Well, at a price of
forty-two the first one's worthwhile.
I'm getting more utility out of
that. After that it's stupid to buy
another ticket because I'm getting extra utility of forty
compared to a price of forty-two."
So he's going to do exactly the
same thing as our single ticket buyers did over there.
One guy whose utility goes from
forty-four to eighty-four to one-twenty is going to behave
exactly-- provided he's got enough money
to afford to buy at these going prices--
his behavior will be exactly the same as the three separate
individuals over there. So in fact the marginal
revolution-- so Jevons, Menger,
and Walras in 1871 all came up with the idea at the same time
of diminishing margin utility, and they said if you have
people who consume multiple amounts of every commodity but
they have diminishing marginal utility they're going to behave
very much the same way as this little example.
So this little example,
in fact, is going to be extremely instructive.
In fact it contains all the
kernels of truth of a more general model where people
consume huge amounts of every good.
Just that they have diminishing
marginal utility. So I'm going to now describe a
slightly more complicated--so I'm going to describe this more
complicated model. So what's the way of building a
much more general, but hopefully still very simple
abstract model of general equilibrium that will capture
and generalize the example we already had?
Well, the idea is to start with
the exogenous variables-- this isn't going to move so I
don't want to do that-- do this--the exogenous
variables are going to be the people,
so I'll have individuals, i in I, so let's call them
individuals. So you see why I use the word I.
i in I, and what is it that
characterizes every individual, a utility function.
So each individual is
characterized by a utility and an endowment.
So to start with let's say--so
the individuals and we'll call the individuals and the goods c
in C. So let's just say there are two
goods X and Y. So an individual's going to be
characterized by utility function,
it's a welfare function of X and Y equals u_i of X
plus v_i of Y. And an endowment,
E_i equals E_i of X and
E_i of Y or (E_iX,
E_iY). So for example you could have,
I don't know, you could have,
this could be--so let's just think about this.
So this is exactly the kind of
situation we had before. We had precisely this going on
before. What was the endowment?
Every person began with money.
It could have been money before
and with football tickets. And we said that the story
that--so these original marginalists argued that it's
part of human nature that the more you get of something the
less and less extra advantage it brings you.
There may be exceptions.
Maybe you need two of something.
You need both shoes in order
for the shoes to help, but every pair of shoes after
that was going to be less and less valuable to you.
And so beside from these small
blips that come from indivisibilities or things like
that peoples' utility increases but at a smaller and smaller
rate as they get more of everything.
That's just human nature,
they claim. They even tried to measure
utility. So they would try and measure
the temperature of the skin and things like that and see how it
increased when you gave people more of something and whether
the rate of increase and how much they smiled and stuff like
that whether that would actually change in a lesser and lesser
way as you add more and more utility.
Well, they abandoned that sort
of thing eventually. But anyway, they kept the idea
of diminishing marginal utility. So we want to keep the idea
that u_i of X and v_i of Y show
diminishing marginal utility. So the way of saying that,
I told you this is one of the-- so the first handout in the
reading list was review of mathematics you should know,
or if you don't know you have to learn,
diminishing marginal utility means something that looks like
that. It's a concave function.
So here's X.
Here's utility,
and here's u_i of X, say.
It goes up as you get more X,
but at a rate that declines. So the slope is getting smaller
and smaller. That's diminishing marginal
utility. So this curve that's
increasing, but a lesser and lesser rate we can approximate
with a continuous differentiable curve that looks like that,
so it doesn't have the kinks here, and that's exactly the
kind of assumption that seems reasonable to fit the facts,
and at least for consumption. Our main interest,
of course, is at the bottom here in financial equilibrium,
but we have to know what's going on in the economy.
All these finance professors,
as I said in business schools, they ignored the part above.
They started right away with
the assets and the bonds. Said they didn't need to pay
any attention to what was going on in the economy,
because everything was going to be great.
But we're going to find that
there's a big interaction between the financial sector and
the economic sector. That's going to be the heart of
what we're doing even though it was ignored in finance most of
the time. So anyway, diminishing marginal
utility for both of these, so for instance we could have a
hundred X minus one half X squared plus Y.
That's one example of a utility
function. So that's going to be a
standard kind of utility function.
So the only two ones I'm ever
going to use are things like this, or one-third log X plus
two-thirds log Y. Whenever I write log I mean
natural log. This is linear quadratic.
So this is quadratic,
in fact linear quadratic, so maybe both will be
quadratic, and this is logarithmic.
Now both of these have this
property of diminishing marginal utility because I can take
derivative of this, the derivative of one hundred X
minus one half X squared so the marginal utility of X is equal
to one hundred minus X, and that obviously declines.
So it's diminishing marginal
utility. And then the derivative
here--the marginal utility with respect to X depends on X
again-- is going to be one-third times
one over X because the derivative of the log is one
over X, and as X gets bigger that also
declines. So these are the two functions
that we're going to use over and over again because I want to
make things concrete with actual numbers.
So we'll always solve examples
with quadratic stuff, maybe everything will be
quadratic or linear, and with logarithmic stuff.
Those are the only two
functions you really have to be totally comfortable with.
So you have to understand what
a derivative is. This is a partial derivative.
So how much extra utility do
you get out of consuming more X? If you've already got a certain
amount of X in your possession it's a hundred minus X.
How much more utility do you
get out of consuming more X? If this is your utility when
you're consumption's already a certain amount of X it's
one-third times one over X. So those are the two things you
have to be comfortable with using.
So that's utility.
What else do we need to
describe a person? It's his endowment.
So with only two goods,
so here's X and here's Y, so we could have an endowment
E_iX, E_iY.
That's the endowment of X and Y
of a certain person, E_iX and
E_iY. So this person,
let's say it's this top guy-- a hundred X minus one over two
X squared plus Y-- he has a certain utility
function, he's got a certain endowment.
Maybe there's somebody else
over here who I can put in a different color.
Aha, I think pink is a good
color. So another person might be over
here and this is E_jY and E_iX.
So J has a lot more of Y,
and I has a lot more of X. They're two different people,
but you could imagine not two people you could imagine 150 of
you with different endowments and different utility functions,
or 300 million of you with different endowments and
different utility functions. And what general equilibrium is
about is saying, well, if you've got all these
people with well defined utility functions,
those are the data, we may not know them but they
know them themselves with all those utility functions and all
those endowments, and you throw 300 million of
them together, or 150 of you together,
can you predict what's going to happen and is the thing that
happens good for the society. So that's the problem of
general equilibrium. And it turns out that with
these simple utility functions it's very easy to solve for
equilibrium, predict what'll happen,
and things look great until you get to financial equilibrium.
And we'll be able to solve them
either by hand or on a computer, and we're going to take
advantage of that because we want concrete answers to
concrete problems, and we want to interact it with
the financial world to see what happens.
So remember,
what's the next step? The first step is exogenous
variables. So we define the exogenous
variables. The next step is endogenous
variables. So what are the endogenous
variables going to be? And the endogenous variables
are going to be the prices and the trades, or final
consumptions. You can always deduce a trade
from a final consumption because if you know your endowment,
the exogenous thing, and you're consuming more of X
than you're endowed with you must have bought that difference
somewhere. And if you're consuming less Y
than you started with you must have sold some of that Y in
order to end up consuming less. So the endogenous variables are
the prices and the trades. Now, how can we make a general
theory that for an arbitrary number of people,
an arbitrary number of goods, you can solve and figure out
what's going to happen that looks very much like the example
and has as a special case the example we did to begin with?
That's what happened with
general equilibrium, and I'm about to describe it.
So the next step is always to
write down the equilibrium as a bunch of simultaneous equations.
So what are all the equilibrium
equations going to be, and that's what's going to be
our model of what happens in the world.
Are there any questions?
How are you all doing here?
Is this painfully repetitive of
what you know. I need some feedback here.
How many of you haven't seen
this before? Everybody's seen this before?
What about all these people who
e-mailed me and said they were scientists and philosophers and
psychologists and they wanted to take economics the first day.
So you're one of those people.
Maybe you didn't e-mail me.
So this is a first for you,
but everybody else you've all seen this before.
Well, that's good.
I can move along here.
So I'll keep looking at you as
I proceed here. So don't feel bashful.
Speak up if it's not making
sense. So what was the great
conceptual advance? It was--one conceptual advance
was the budget set. Now, this will turn out to be,
in economics-- the rest of the 140 of them
have all got this down, but as soon as we turn it into
a financial problem they're not going to be able to do it again
even though it's going to be the same idea.
So this budget set was an
extremely clever idea which I'll now repeat for them and tell you
for the first time, but I can almost guarantee that
although they all think it's obvious,
when we do the first financial problem they aren't going to be
able to do it even though it's the exact same idea.
So what's the idea?
You begin with your endowment,
E_iX and E_iy.
So this person has to buy and
sell X and Y. So the person says to himself,
"I've started with this X and Y, I might like something
that's better." Now how can you illustrate
what's better for this person? Well, Edgeworth,
as I mentioned, Edgeworth invented the idea of
the indifference curve. So he says, "All the goods
that are of the same utility can be described by this
indifference curve X." This person,
her utility is one-third log X plus two-thirds log Y,
well if she consumes less of X, enough extra Y will make her
just indifferent to where she was before because there's a
tradeoff between X and Y. Economics is all about
tradeoffs. So this is her indifference
curve. Maybe his indifference curve
looks like that, a different slope,
entirely different. So he thinks a lot of Y.
A little diminution in Y you
better get a lot of X to compensate him.
She's kind of more balanced in
things, X and Y, unless she starts to get too
much of X in which case Y is more important to her.
She in general is more balanced
than he is. But anyway, so they have
different tastes, different utility functions,
and different endowments. So what's going to happen in
the end? Well, the budget set describes
what she can do. We're going to assume,
as we did before, that cornerstone of economic
reasoning, somehow when these hundred
million people, 300 million people get together
they're going to miraculously discover the price.
They're going to be screaming
at each other, but we don't care about that.
We just say for the purpose of
the big picture, some price of X and Y is going
to emerge. So equilibrium is going to be a
price of X and a price of Y. It's going to emerge and now
what can she do? Well, she can say,
"Given my X I can buy more X than I started with,
and if I do that the price of X is P_X."
So if I want to buy more--I
have this already. So I want to end up consuming
X_i, so final consumptions will be
X_i and Y_i, this is the final consumption,
so my trade, if I want to buy more,
I can express the idea that I'm buying more by saying my final
consumption is bigger than my endowment.
So I've had to buy,
I've had to trade to get this much more which means I had to
pay P_X times this difference.
Now, how did I get the money
for that? Well, I got the money for that
by selling some of Y. So I sold Y.
I started with E_iY
and I sold some of it because I ended up with less than I
started. So the money I got by selling Y
I can use to spend on buying X. That's the basic budget
constraint. Now, the cleverness is in
realizing that it doesn't matter which one--So here X_i
is bigger than E_iX. You're buying X.
Here Y_i is less than
E_iY. You're selling Y.
And so the revenue you get from
selling Y equals the expenditure you make on buying X.
So the cleverness is in
realizing it doesn't matter what the signs are.
If X_i is less than
E_iX this equation still makes sense because then
you get a negative number. You've gotten money by
consuming less X than you started with so that's money you
can use to buy Y. And then Y_i--you'll
be able to buy more Y than you started with so this number will
also be negative by the same amount as this.
This is the extra value on Y.
This is the extra value on X.
So whether the X's and the Y's
are bigger or smaller than the E_iX's or
E_iY's this equation defines the budget trading
opportunities of the agent. Did that go too fast?
You got that.
So you can write that a little
bit more simply by saying, putting a plus here and
reversing the order, making it more symmetric.
So this is Y_i minus
E_iY equals zero. So that's the budget set of
agent i. And in the diagram the budget
set--I'm out of colors that show up I think--
all the others got vetoed, I think orange was okay--
the budget set, then, will be something that
looks like this. That looks terrible.
How bad can you get?
So that budget set might look
something like--let's make it this way.
It looks something like that.
It's a linear line that goes
up--just forget this guy's budget set.
We'll do the other one.
I can get it better in the
picture. So this one's budget set,
his budget set might look something like that.
So his budget set,
never mind hers, it goes off the page,
his budget set he starts with this endowment.
If the prices are given
P_X and P_Y, P_X and P_Y
define a linear tradeoff between X_i and Y_i,
in this case j, because the more X you consume
the less Y you have to consume and there's going to be a linear
tradeoff between the two given by rearranging these terms.
P_X and P_Y
are fixed, so this is just a linear
equation in X_i and Y_i,
and so that tradeoff is given by that budget set.
So mister pink is going to try,
given his opportunities on this budget set, to pick the
combination of X and Y that's best for him.
And so that's going to turn out
to be something that's right here because no other
combination of X and Y will give him as much utility as that.
Did that make sense?
All right, so that's it.
That's the main lesson.
So how do you describe now the
whole equilibrium conditions? Well, so equilibrium now,
if you can see this, equilibrium is defined by what?
It's defined by P_X,
P_Y, and X_i and
Y_i for all i in I. It's just the prices that
emerge and final consumptions that everybody chooses of X and
Y. There are only two goods here.
So the price of X,
the price of Y what every person i ends up with
X_i and Y_i, and what has to be the case?
What has to be the case?
The first equation is going to
be that the final consumptions of everybody have to equal the
final endowments because everyone who buys has to be met
by another seller. Remember equilibrium was price
taking, agent optimization, rational expectations and
market clearing. Price taking means everybody
knows what the prices are, miraculously P_X and
P_Y, before they act.
Agent optimization we're going
to come to. It means they do the best thing
they can. Rational expectations means
even though they're only buying one good and there are thousands
in the economy they understand all the prices,
and when they act they're taking into account all of the
tradeoffs they could make. So they realize the whole
vector of prices. And market clearing means for
any buyer there's a seller, so market clearing means
summation from i in I of X_i has to equal
summation i in I of the endowment,
E_iX of X. So in this picture if I added
this to this, this is the endowment,
so I add this vector to that vector I get this thing over
here, and this is going to be the
total endowment in the economy. So this total endowment
E_iX, I add over every person i what
the total endowment is. So I add his endowment of X to
this guy's endowment of X and I get the total endowment of X.
I add her endowment of Y to his
endowment of Y and I get the total endowment of Y.
So the first two equations are
summation i in I. Y_i equals summation
i in I of E_iY. The third equation is everybody
is going to choose on their budget set.
Everyone, this person--mister
pink here-- he's going to choose not inside
his budget set, he can't choose outside of it
because there's no point in wasting money.
He's going to buy the
combination of X and Y that lies on his budget set that does as
well as he possibly can. So the equation here is going
to be that P_X times X_i minus
E_iX plus P_Y times
Y_i minus E_iY is equal to zero.
I could do this for j too just
since I've got a picture of--this is P_X,
this is P_Y. P_X times
X_j minus E_jX,
so I'm doing a special case now with two people,
Y_j minus E_jX equals zero.
Everybody's on their budget set.
So he's on his budget set,
she's going to be on her budget set.
Her budget set,
by the way, is better than his because her budget set is going
to look like this, right?
It's got to be parallel to his
because the prices she faces are the same and her endowment is
worth more than his. So her budget set is further
out. So that's what he does,
that's what she does, or that's what she does,
that's what he does. And now the fifth one--so now
we have the two mysterious equations that are left.
So how do we express the idea
that the choices X_i and Y_i by i,
that's her--and she's going to optimize by choosing here
somewhere. This is her indifference curve,
right, looked like that. So that's what she's going to
do. And remember he's going to
choose here. So how can you turn her choice
and his choice into an equation? Well, this was invented by a
German guy Gossen in 1851 and then rediscovered by Jevons,
Menger and Walras, the same three I mentioned
several times now. This is the marginal revolution
in economics. What they said is you can turn
the behavior of individuals, of humans as Gossen said,
"I can do for the bodies on earth what Copernicus did for
the bodies in heaven, find equations that describe
their motion." What is it that people are
going to do? To say that you're choosing the
best possible thing means that the slope of the budget set is
equal to the slope of your indifference curve,
but what is the slope of your indifference curve?
That's the tradeoff between X
and Y. So what does it mean?
If you get a little bit less X
you're losing the marginal utility of X.
If you get a little bit more of
Y you're gaining the marginal utility of Y.
If the price of X and Y are the
same then it had better be that the marginal utility of X is
equal to the marginal utility of Y because you can always give up
one unit of X and get one unit of Y.
If this is optimal,
and you can give up one unit of X and get two units--
sorry, if the marginal utility of Y was double the marginal
utility of X then you would give up that one unit of X and you'd
get two extra utils by taking the one unit of Y which you can
afford by selling one unit of X, and the utility would be much
higher than it was here. And so you wouldn't be
optimizing by doing that. So the final equation is you're
optimizing if and only if the marginal utility of i of X
divided by the marginal utility of i of Y equals P_X
over P_Y. And the last equation is the
same thing for j, the marginal utility of j of X
divided by the marginal utility of Y has to equal P_X
over P_Y. So why is that again?
That's the trickiest equation.
That's the one that Marx and
Adam Smith and not even Ricardo, the most brilliant one of them
all, not even Ricardo could figure
that out, this equation marginal utility,
wait until 1871. And again, to repeat it,
it's of course very obvious now but wasn't at the time,
how can you describe what these people are doing?
You have to figure out the
budget constraint, that's what they can afford,
and then they're going to choose the point on their budget
constraint which maximizes their utility.
But that just means in the
picture it makes the indifference curve tangent to
the budget set, which means that you set--so
and what is the slope of the indifference curve?
Well, the tradeoff between X
and Y that leaves you indifferent--how much X do you
have to give up to get an extra unit of Y and still be
indifferent? It's determined by the ratio of
the marginal utility of X to the marginal utility of Y because
those are the, you know, when you give up a
unit of X you're losing the marginal utility of X.
When you're getting a unit of Y
you're getting the marginal utility of Y.
If you can trade them off in
the market at 3:1 you optimize when, in your own personal
evaluation, you're trading them off on the margin at 3:1.
You really follow that?
That's an idea that took fifty
years to figure out and you claim you figured it out now in
five minutes, so that's good.
So you'll have a chance in the
problem set to get practice. So those are the equations.
We now basically have described
economic equilibrium. So we now have the ability to
play with all kinds of models, as we'll start in the next
class doing, solving for economic
equilibrium, figuring out what will happen,
and then complicating it by adding a financial sector and
see how that affects what goes on in equilibrium.
