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  • 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,

  • thetonnement 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.

Prof: So for those of you who weren't here yesterday--

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