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PROFESSOR: We've been talking so far about basically

overviews of supply and demand relationships and

understanding how markets work.

Now we're going to step back and get behind the supply and

demand curves and understand where those curves

themselves come from.

So we talked about, given that we have supply and demand

curves, how they interact.

Now we're going to get behind that and see where these

curves actually come from.

Thank you, by the way for coming down.

I appreciate it.

So what we're going to do is, we're going to start with the

demand curve, and we're going to spend the next few lectures

talking about consumers and how consumer preferences are

ultimately what leads to the construction

of the demand curve.

Then after that and after the first exam-- that will cover

what's on the first exam--

after the first exam, we'll start talking about firms and

what determines the firm supply curve.

So today we'll talk about consumers and we're going to

talk about where the demand curve comes from.

And where it comes from, and where all consumer behavior

coming from in economics is from utility maximization.

That's where everything with consumers starts is with

utility maximization.

That's the basic building block of consumer behavior.

And basically, utility maximization--

that's what this lecture will be about, describing it.

But basically, an overview is, we posit some type of

preferences.

We posit consumer preferences, what consumers would like.

We posit some budget constraint, what resources

consumers have to get what they'd like.

And then we do a constrained maximization problem that

says, given your preferences, given what you'd like, subject

to the resources you have available, what

choices will you make?

And in particular, we're going to ask, the term we'll use is

we'll ask what bundle of goods makes you the best off?

Given your preference, given your constraints,

what bundle of goods?

So think about consumers choosing

across a set of goods.

Typically, we'll think about two goods because graphs are

easier to think about two dimensions than more.

So we'll typically think about trading off two goods.

So think about consumers with preferences across two goods,

some budget they can allocate, and how

they make those choices.

But this basic framework applies to the multiplicity of

choices we all make along many, many dimensions.

So doing two dimensions as one of the simplifying assumptions

I'll talk about.

But that's just a simplifying assumption.

So basically what we we're going to do is we're going to

go through this in three steps, not just in this

lecture, but over the next few lectures.

Step one, is we're going to talk about what assumptions we

make about preferences.

So I'll talk today about preference assumptions.

So the axioms that underlie how economists model consumer

preferences.

We'll then talk about how we translate these preferences

assumptions into mathematical tractability through the use

of the utility function, which is basically a mathematical

representation of underlying consumer preferences.

So we'll talk about how we basically take these

preferences and translate them into something that we can

work with here at MIT by making it mathematical, by

making a utility function.

And then finally, we'll talk about budget constraints.

And armed with these three things, we'll then be able to

model how consumers make decisions.

Now, importantly for today's lecture, we are not dealing

with budget constraints.

So this is not happening today.

So today we're not going to worry about the budget

constraints.

Today we're in a world where we're just going to talk about

what people want and we're going to put out of our mind

whether or not they can afford it.

So just talk about people want, and we'll put out of

mind for today.

We'll come back next time to whether they can afford it.

We're just going to think about unconstrained

preferences for today's lecture.

So let's talk about our preference assumptions.

So, to model consumers' preferences across goods,

we're going to impose three preference assumptions.

Three preference assumptions.

Assumption one--

now once again, let me remind you from the first lecture,

this is getting to some of the harder material.

I'm going to write messily and talk quickly, so stop me if

anything is unclear.

And if you don't stop me, I'll just go faster and faster

until I explode.

So basically, feel free to interrupt and stop me with

questions and such.

Three assumptions on preferences.

The first assumption is completeness.

The first assumption is the assumption of completeness.

When comparing two bundles of goods, you prefer one or the

other, but you don't value them equally.

OK when comparing two bundles of goods, you prefer one or

you prefer the other, but you're not indifferent.

Completeness is the same as no indifference.

So what we're saying is whenever I offer you two

bundles of goods, you could always tell me

what you like better.

Now it could be infinitesimally better.

I'm not saying you have to have strong preferences.

But you cannot say I'm indifferent.

You can never be purely indifferent.

There always at least some slight preference for one

bundle of goods over another.

That's the completeness assumption.

This is an assumption we make.

Now in reality, oftentimes we are indifferent.

Well once again, this is one of these simplifying

assumptions that will make the model work.

And in fact, in reality if forced, you can always decide

whether you like one thing better than another, we just

often follow heuristic rules which say we're roughly

indifferent.

We're just going to say, more precisely, you are never

purely indifferent.

So, I'm not sure is not an option.

You can never say I don't know, I don't know which I

prefer, I'm indifferent.

I'm sorry, let me back up.

I'm using the wrong word.

Forget I said indifferent, because we'll want to use that

word in a different context later.

You can't say, I'm not sure.

You can't say, I'm not sure.

You can't say, I'm not sure, can't say I don't know, I

don't know how I feel about that.

Scratch what I said a few minutes ago, because I want to

use indifference differently.

Completeness is not about not being different, we're going

to use that.

What I'm saying is it's about not being sure.

You've got to value every bundle of goods.

You've got to be willing to value every bundle of goods

that's given you.

So you can't say that I don't know, I don't know how I feel

about that.

You've got to have some feeling about stuff.

You can't say I'm not sure.

You've got to have a complete set of preferences over all

bundles of goods that are given you.

OK, that's completeness.

The second is transitivity.

Which is something we've been learning since kindergarten

about transitivity, right?

And also, it's a different context.

That's just if you prefer x to y, and y to z, you've got to

prefer x to z.

OK, you guys should do transitivity in

your sleep by now.

OK, so the standard transitivity we always assume

in math class, we're going to assume here as well.

OK, that should be pretty noncontroversial.

OK, and then finally, and probably most controversial,

is we're going to assume non-satiation.

Or the famous economic assumption that

more is always better.

OK.

More is always better, that is, you never would turn down

having more.

Now we're going to talk later today and tomorrow about why

you might not like the next unit as much as you like the

current unit.

But you'll always like it greater than zero.

You're always happy to have more.

You never say, I've had enough, I literally value at

zero the next unit.

You may value it as epsilon, but you'll always value it as

greater than zero.

That's the non-satiation assumption,

more is always better.

Now, this is the most controversial.

And obviously we can think of many contexts in

which that's not true.

But if we don't allow for this assumption, the modeling gets

a lot trickier.

So once again, let's put it out of our mind.

Realistically, we know once we've eaten a certain amount,

we literally do not want any more.

OK, so we're going to put that aside.

Assume we're always in a space where we can always eat a

little bit more.

OK, we'll call it the Jewish mother space.

OK, you can always eat a little bit more.

OK, you can always eat a little bit more.

We're just going to assume we're in that space for now.

OK.

And so, for large ranges, we can see it is not an

unreasonable assumption.

Although, I think in extremes, you could see this becomes

unreasonable.

OK, so those are assumptions.

Completeness, which once again, I screwed up in

describing.

Come back to the second way I described it, which means you

can't say you're not sure.

You always have preferences over things.

That doesn't seem unreasonable.

Transitivity which we've been living with since we were

kindergartners.

And non-satiation, which could be a little controversial, but

we'll live with it for now.

Now given these, we're going to talk about the properties

of what we call indifference curves.

This is why I screwed up before.

Of course you can be indifferent between things.

That's the whole point of economics.

I don't know why I got that wrong.

I haven't taught this course about six years, so I lost

track of things.

Properties of indifference curves.

So indifference curves are our name for what you could also

think of as preference maps.

In economics, we like to be able to describe everything,

as I said, three ways, intuitively, graphically, and

mathematically.

Preference maps are the graphical representation of

people's preferences which we do through graphics that we

call indifference curves.

So now let's go to the example I'm going to use that I'm

going to use throughout these next couple lectures of a

decision you have to make.

Now I tried to think of a cool way to make this example cool,

and I just couldn't.

So its going to be a boring example.

It's going to be, imagine your parents gave you some money

and you had to decide whether to buy pizza or see movies.

I tried to make it at least a little bit relevant even if I

couldn't make it cool.

You've got to decide whether to buy pizza or see movies.

That's your decision.

That's the trade-off you're making.

We're in a world with only two goods, pizza and movies.

And you're deciding how to allocate the money your

parents gave you over pizza and movies.

Now let's say we're going to consider three choices of

pizza and movies.

So go to figure 4-1a.

We're going to consider, you could have two pizzas and one

movie, that's point A. You could have one pizza and two

movies, that's point B. Or you can have two of both, that's

point C. That's just three choices you're facing.

Once again, we're ignoring paying for them.

Budget constraints is next time.

Now we're just saying I'm giving these three choices.

Well how do you feel about them?

Well let's assume that you're indifferent--

and this is why you can be indifferent.

What I said before, just strike.

Let's say you're indifferent between two pizzas and one

movie, and one pizza and two movies.

Let's say, if you had two pizzas and one movie, or one

pizza and two movies, you pretty much feel the same

about them.

But clearly you like two pizzas and two movies better

than either of the first two combinations.

Then what we can do is we can draw what we call

indifference curves.

And that's in figure 4-1b.

These are maps of your preferences.

An indifference curve is the curve showing all combinations

of consumption along which the individual is indifferent.

And I'll say that again, very important concept.

An indifference curve is a curve showing all combinations

of consumption along which an individual is indifferent.

So you have an indifference curve.

I said you were indifferent between A and B. So you have

an indifference curve that runs between A and B. That

means that all, and I'm assuming that all combinations

along this curve, you're indifferent.

So you're equally happy getting two pizzas and one

movie or one pizza and two movies.

But point C, which is two pizzas and two movies is on a

different indifference curve.

You're not indifferent between point C and points A and B.

You're indifferent between A and B--

I'm just assuming this, I'm not saying you are.

But I'm just assuming, let's imagine you are.

But you clearly like two pizzas and two movies better

than one of one and two of the other.

Yeah?

AUDIENCE: Does that break the completeness rule for the--

PROFESSOR: Does that break it?

Why would that break it?

AUDIENCE: Do you prefer pizza over movies

or movies over pizza?

PROFESSOR: No.

Because this is my screw up before.

Completeness just means you know how you feel about

everything.

So strike from the record my initial description.

Completeness means you just know how you feel about

everything.

You're allowed to be indifferent.

Completeness just means you can't say, I don't know, I

don't know how I feel about pizza.

You've got to have feelings for pizza.

OK.

You've got to know how you feel about stuff.

That's what completeness is.

So armed with those assumptions, there are four

key properties of indifference curves that we have

to keep track of.

Four key properties of indifference curves.

The first is that consumers prefer higher

indifference curves.

So you prefer higher indifference curves.

Prefer higher indifference curves.

What I mean by that is, the further out the indifference

curve, the more you prefer it.

And this comes naturally from the non-satiation assumption.

Given that we've assumed non-satiation, you must always

prefer an indifference curve that's further from the origin

because it's more, and more is better.

OK so given non-satiation, you will always prefer an

indifference curves that are further from the origin.

That follows directly from non-satiation.

The second point is that indifference curves are always

downward sloping.

Indifference curves are always downward sloping.

Indifference curves are always downward sloping.

And that, once again, comes from non-satiation.

To see this, let's look at the next figure, an upward sloping

indifference curve.

Why does an upward sloping indifference curve, someone

tell me, violate non-satiation.

Yeah?

AUDIENCE: Because you're indifferent to getting more.

PROFESSOR: Yeah.

Because this would say you're indifferent

between (1,1) and (2,2).

It's not quite drawn right.

We ought to just have this go through to point (2,2).

But basically, this would say you're indifferent between

getting one pizza and one movie or two

pizzas and two movies.

You can't be because that violates more is better.

So indifference curves can't be upward sloping, they've got

to be downward sloping by the non-satiation assumption.

OK, that's the second property of indifference curves.

The third property of indifference curves is

indifference curves cannot cross.

Indifference curves cannot cross.

Why can't indifference curves cross?

Well here I forgot to have Jessica do a pretty diagram,

so you'll have to deal with my ugly handwriting here.

So why can't indifferent curves cross?

Well imagine a situation where you have your

pizza and your movies.

And imagine a situation where you have one indifference

curve that looks like this, and one indifference curve

that looks like this.

OK, two indifference curves.

And you've got, let's label these points A, B, and C.

Now could someone give me, based on the properties of

indifference curves that we talked about over here, given

these three properties, can someone tell me

why this is a violation?

Yeah?

AUDIENCE: Because A and B are on the same curve, meaning

you're indifferent between A and B. A and C are also on the

same curve because you're indifferent between the two.

But that means you're also indifferent between B and C

which can't be true because more is better.

PROFESSOR: Exactly.

So transitivity says I must then be indifferent between B

and C through the logic you just laid out.

But I can't be indifferent between B and C because B

dominates C. B has a basically the same number of movies, but

more pizza, so I must like B better.

So by the combination of transitivity and non-satiation

indifference curves can't cross.

And finally, completeness, which is the most awkward of

these assumptions, it simply means you can't have more than

one indifference curve through a point.

So basically, the idea of every possible bundle has one

indifference curve.

You can't have two indifference curves through it

sayin, I'm not sure which indifference curve I'm on.

I'm not sure how I feel about this.

You know how you feel.

There's one indifference curve through every bundle.

There's not two indifference curves through a bundle.

So this is the way we think about preference maps which is

the sort of core building block of utility theory.

Now I was an undergrad here, took this course, but I never

really understood indifference curves until I had a year off

with a grad student who was trying to decide where to take

a job and he did it through just showing me an

indifference map.

He said look, I'm trying to decide where to take a job,

and I care about two things.

I care about how good the place is and where it is.

So he said here, he had location and he

had academic rank.

And he said look, I'm indifferent between Princeton

which has a shitty location but a wonderful academic rank.

I'm from New Jersey, but it's still a shitty location.

OK, and Santa Cruz.

And Santa Cruz which has not such a good academic

reputation, but a pretty awesome location.

And he said here's my indifference map.

And where did he end up going?

He ended up going to the IMF, the international monetary

fund in DC which had a better location than Princeton--

worse than Santa Cruz, but a better reputation than Santa

Cruz and worse than Princeton.

So he decided he was indifferent along this map,

and he ended up choosing a point in the middle.

But indifference curves are just a way of representing two

dimensional choices.

Now very few choice in life are really two dimensional,

but that's a nice example.

Question in the back?

AUDIENCE: I was wondering if IMF, the point would be

actually not on the curve, but further out?

PROFESSOR: If it were further out.

A great question.

So imagine if IMF were here.

What should he have done?

Definitely go to IMF.

Here he was indifferent.

He could flip a coin and be equally happy at all three.

But if IMF were out here, and maybe it was because that's

what he chose.

That's a good point.

I don't know if IMF was here or here.

The fact that he chose IMF, it can reveal it

wasn't anywhere in here.

It's a very good point actually.

It can reveal it wasn't anywhere in here.

That we know.

But I can't tell if it was on the curve

or outside the curve.

It could have been on the curve because he's

indifferent, so who knows, he could have flipped the coin.

Or it could have been outside the curve because it's better.

We can't tell that.

That's a good point.

All right.

So that's a preference map.

That's indifference curves.

Now let's step from indifference curves, which is

a building block of preferences, to utility.

Now everything you need to know about preferences is

represented in those indifference maps.

The problem is they're pretty awkward to work with when we

need to actually prove theorems and solve and

understand how people make decisions.

That's a lot easier if we have a mathematical representation

of those preference maps.

And that's the utility function

So the utility function is a mathematical representation of

preferences.

That's all it is.

You're going to be hearing this term in your nightmares

for the next semester.

Utility functions.

But remember, it's just a mathematical representation of

people's underlying preferences.

Don't be scared of it.

And the key thing is that we assume individuals have these

well-defined utility functions, and by maximizing

those utility functions we can tell what choices they're

going to make.

So for example, suppose that I said that your utility

function over pizza and movies was the square root of pizza

times movies.

That's a utility function.

I'm going to say, what the hell does that mean?

Well, it doesn't mean anything,

it's a utility function.

It's your preferences.

It's a mathematical representation of your

preferences.

What does that mean?

What it means is--

it doesn't mean anything inherently, but it tells us

about your preferences.

What it tells us is that your preferences can be

represented.

If you flip back to figure 4-1b, it tells us those are

your preferences because you're indifferent between two

pizzas and one movie and one pizza and two movies.

Of course you're indifferent.

They both give a utility square root two.

But you prefer two pizzas and two movies because that gives

a utility of two.

So this is a mathematical representation consistent with

those utility indifference curves.

Not the only one.

There's other mathematical representations that could be

consistent with those indifference curves.

But let's posit that this is your utility function.

This is a mathematical representation of your tastes.

Now what does utility mean?

Utility means nothing in the sense that it is not a

cardinal concept.

It's only an ordinal concept.

So if I say to you that you get two utils from two pizzas

and two movies, that doesn't mean anything.

It just means that you get more than from one

pizza and one movie.

And we can even get the ratio that you get square root of

two more, than you get from one pizza and two movies.

We can do ranking and ordinality, but we can't

assign cardinality.

I can't say how happy you are in some abstract absolute

sense from two pizzas and one movie.

I can't give a cardinal form preference.

But this is an ordinal ranking of preferences.

I can tell what you like better than what else.

That's why utility function is a representation of

indifference maps.

They're just a mathematical tool for comparing bundles,

they're not some inner answer to the value of your soul or

something like that.

Don't imbue these with too much magic.

They're just mathematical ways of representing preferences.

The key concept, the single most important concept, for

consumer theory for understanding how consumers

make decisions is the concept of marginal utility.

We'll talk a lot this semester about marginal this and

marginal that.

And this is our first example.

Marginal utility.

That is how your utility changes with each additional

unit of the good, or the derivative

of the utility function.

If you want to do it in calculus terms, marginal

utility is the derivative of your utility function with

respect to one of the inputs.

But if you don't want to put it in calculus terms, it's as

you add each unit of one of the elements of the utility

function, how does utility change

So to see this, let's do an example of marginal utility.

Imagine for a moment that you have two pizzas, p equals two.

You've got two pizzas, they're there.

Your roommate's got them or something.

OK, now I want to ask, how does your utility change as

you see additional movies?

And to show that, let's look at figure

4-3 which isn't here.

Whoops.

There's no figure 4-3.

Do you got that figure 4-3?

AUDIENCE: There was never any figure 4-3.

PROFESSOR: There was never any figure 4-3.

So let's go to 4-5.

So basically--

AUDIENCE: Figure 4-4?

PROFESSOR: No but--

actually fine.

4-4.

So basically what this is showing, what figure 4-4 is

showing, is it showing how--

no actually, let's go to 4-5.

They're out of order.

Let's go to 4-5.

What 4-5 is showing--

no, that's not going to work.

OK, back to 4-4.

What figure 4-4 is showing, is it's showing how your marginal

utility for movies evolves, how your utility evolves as

you get more movies.

Given that you have two pizzas, this is the evolution

of your utility as you get more movies.

So each additional movie increases your utility.

The slope is positive.

By more is better, we know that.

Even if it's some date movie, it still

improves your utility.

So it still improves your utility, but at

a diminishing rate.

And that's the key is that we assume

diminishing marginal utility.

The key assumption underlies everything we'll do for

consumers is diminishing marginal utility.

We assume that additional movie increases your utility,

but at an ever diminishing rate.

So basically, we can actually graph your margins.

And that's what figure 4-5 is, is a graph of

your marginal utility.

So basically, when you have two pizzas and one movie,

utility is square root of 2, right?

Now what I'm saying is if you get one more movie, your

utility is going to rise from square root of 2 to 2.

So the marginal utility of that next movie --

is that right?

Two movies.

1.4.

Yeah, it's going to rise by the square root of 2.

You're going to multiply your utility by the square root of

two, so your marginal utility--

you're going to go from the utility of square root of 2 to

utility of two.

So utility is going to increase by the

square root of 2.

Utility is going to increase--

I'm doing this wrong, hold on.

One second.

From one movie.

I see.

I see.

So, I'm sorry.

This isn't the delta, this is the level of marginal utility.

So I'm graphing the actual level of marginal utility.

Back up.

OK, so I'm graphing the actual level of marginal utility.

So when you have two pizzas and one movie, your marginal

utility, your actual utility--

I see, that's what this is.

This is the actual utility I'm graphing.

So I told you a minute ago, we can't measure utility as a

cardinal concept, but actually here I'm doing it anyway

because it's to illustrate marginal utility.

So your utility, OK.

When you have one movie is 1.4, square root of 2.

That's your utility.

Now when you move from one movie to a second movie, your

utility goes up from square root of 2 to 2.

Your utility goes up by 0.6.

So the marginal utility of that second movie is 0.6.

Utility was 1.4, was a square root of 2.

Now it's increased to 2.

So the marginal utility of the first movie is 0.6.

Now let's say you add another movie, you go to three movies.

What's your utility now?

It's the square root of 6.

So it's gone from 4, to the square root

of 6, which is 2.45.

So your marginal utility of the third movie is 0.45.

This graph is messed up because the first one is an

actual utility level.

So the first one I say, for one movie, you

have a utility 1.4.

And then for the second movie, I give the marginal utility,

the third movie marginal utility.

So, this graph sort of-- yeah?

AUDIENCE: It shows the marginal utility of the very

first movie.

PROFESSOR: Yeah, I guess that's right

because you're zero.

You're zero movies.

OK, right.

You're right.

OK, so the first one is the marginal utility of the very

first movie, you're right.

So the very first movie gives you marginal utility of 1.4

because you go from 0 to square root of 2.

That's right.

My bad.

So you go from 0 to square root of 2 to get a marginal

utility of 1.4 for the first movie From square root of 2 to

2, you get 0.6 the next movie.

From 2 to square root of 6, you get 0.45

for the third movie.

For square root of 6 to square root of 8, you only get 0.38

from the fourth movie, and so on.

So the key point is that these marginal utilities are ever

decreasing.

Each additional movie gives you less incremental utility.

And if you stop and think about it,

it's kind of intuitive.

Just stop and think, think about the movies you want to

see right now.

The four movies you want to see.

Presumably whichever you ranked first would give you

more utility to see than whichever you ranked second.

And if you think the movies that are out right now are

pretty crappy like I do, by the time you get to the fourth

movie, you're not getting much utility from it at all.

Thinking about movies that are out now, you're getting a lot

of utility from that first movie you see.

Marginal, extra utility from the first movie you see.

But each additional one is giving you less and less.

And that's the idea of diminishing marginal utility.

Likewise with pizzas, if you haven't eaten all day, that

first pizza can give you a very high marginal utility.

The enjoyment you get from eating that first pizza can be

very large.

But the second pizza, not so much.

You're already pretty full.

Third pizza, even less.

And then fourth pizza would probably violate

non-satiation.

So that's the basic idea.

Yeah?

AUDIENCE: I have a question.

Do we assume that the goods are homogeneous.

Is it the same movie watched four times?

Or different movies?

PROFESSOR: Actually, that's a great question.

And you have to specify that as part of the problem.

I haven't specified that here.

Obviously it can't be the same pizza eaten four times.

It could be the same kind of pizza eaten four times.

But do you see the same movie?

I haven't specified that here.

So there's not a general assumption about that.

It depends on how I define movies.

Did I define movies as--

I don't know.

God, I'm terrible.

All I know that's out now is the Guardians of G'ahoole

because I've got a little kid who is interested in it.

Whatever movie's out.

Do I define movies as Guardians of G'ahoole, or do I

define movies as seeing a movie?

And I didn't specify that.

Implicit in my examples, I specify

movies as seeing a movie.

But you have to specify that to be more precise if you're

actually trying to figure out--

it depends what you're maximizing over.

If you're maximizing over seeing any movie or maximize

over seeing the same movie.

And I didn't specify here.

AUDIENCE: It can work in both cases.

PROFESSOR: It would work in both cases.

Clearly you could imagine, actually it's a very good

point, where do you think your marginal utility would

diminish more?

Seeing the same movie.

So what your example points out is that different goods

will have different rates of diminishing marginal utility.

OK, so marginal utility will always be diminishing, but at

very different rates for different goods.

So the general principle is that they'll be generally

diminishing marginal utility.

But at different rates for different goods.

So after all my mess ups, let me just review.

Marginal utility is diminishing because each good

is worth less to you.

It's always positive because of non-satiation.

And this graph represents the marginal utility you get from

each movie you see conditional on having eaten two pizzas.

Marginal utility is the increment from

the next unit consumed.

Now let's get back on track here.

Now let's go to thinking about--

now that we have this concept of utility and marginal

utility, let's now bring utility back

to preference maps.

Let's ask, given what we know about utility, what can this

teach us about the shape of preference maps?

What's the linkage between utility and preference maps?

And that linkage comes through something we call the marginal

rate of substitution.

The marginal rate of substitution is the

mathematical concept that links preference utility with

preference maps.

The marginal rate of substitution technically is

the slope of the indifference curve.

It's delta P over delta M. The slope of the indifference

curve is the marginal rate of substitution.

That's what it means graphically, but here's what

you have to understand at a deeper level.

What it really is, it's the rate which you are

willing to trade off.

The rate at which you are willing to trade off the

y-axis for the x-axis.

The rate at which you're willing to trade

off pizza for movies.

So that's what it means intuitively.

The slope of the curve tells you that you're indifferent.

Remember, you're indifferent between any points along with

this indifference curve.

You're indifferent between four pizzas and one movie,

you're indifferent between two pizzas and two movies, and

four movies and one pizza.

You're indifferent along all those

combinations of figure 4-6.

The MRS is the slope of that curve telling you the rate at

which you're willing to trade off pizza for movies.

Now just a side note here, you're never, of course,

actually trading.

There's not some market where you bring a

pizza and get a movie.

So I didn't say trade, it's not like baseball cards.

I said trade off.

What I mean is ultimately you have some budget, and you have

to allocate that budget.

So if you decide to allocate it on pizzas, you can't

allocate it on movies.

Or the more you allocate on pizzas, the less you can

allocate on movies.

So there's always a trade-off.

Remember, I said, economics is always about trade-offs.

Given your limited budget, there's always a trade off.

And the rate at which you're willing to trade off is your

marginal rate of substitution.

Given that you're going to have to trade off-- and we

haven't got a bunch of constraints yet, we'll get to

that next time--

the rate at which you're willing to is your marginal

rate of substitution.

Yeah?

AUDIENCE: Is that rate usually related to the price?

PROFESSOR: Ultimately no.

I'm sorry.

The marginal rate of substitution purely comes from

your preferences.

Ultimately to decide how much you actually consume, you'll

need to bring in the price.

So remember, I haven't talked about prices here, we haven't

talked about that here.

But this is a preference concept.

This has nothing to do with prices.

But you're getting ahead of us.

We'll see next time, to decide how much you actually consume,

you're going to relate the marginal rate of substitution

to the prices you face in the market.

And that will decide how much you consume.

This is just a utility concept.

Yeah?

AUDIENCE: Did you say it was the y-axis or the x-axis?

That would be negative?

PROFESSOR: It's negative.

Yes.

Of course.

Right, of course.

The point is how many movies are you willing to give up to

get another pizza?

How many pizzas are you willing to give up to get

another movie?

MRS, it's very hard to remember what's on the top,

what's on the bottom.

Be very careful on this.

But that's why I said remember it's the y-axis or the x-axis.

It's how many pizzas you're willing to trade off to get

another movie.

Basically remember when I say trade off, here, this is not

that you're literally trading, it's that ultimately you're

going to have to make that trade-off.

Ultimately when we come to the next lecture and face a budget

constraint, you're going to have to decide how do I want

to allocate my budget across pizzas and movies?

The way you're going to decide that is by the relationship of

how you feel about trading off one for the other.

Now here's the key feature of the MRS which

is the MRS is yeah?

Question?

Yeah.

AUDIENCE: That and exchange rates are always changing

depending on how much you happen to be trading.

PROFESSOR: Exactly.

The MRS is diminishing.

Technically when you go to grad school, you realize that

marginal utility isn't actually technically always

diminishing.

I said it is.

For this course it is.

But if you want to get mathematically correct, really

what's always diminishing that you prove is the marginal rate

of substitution is always diminishing.

So we have diminishing marginal utility for the

purpose of this course, but the really important concept

is you have diminishing marginal rate of substitution.

The rate at which you're willing to trade off pizza for

movies is going to fall as you have less

pizza and more movies.

So to see that, look at this graph, and let's compute the

marginal rate of substitution along each segment.

So let's localize.

Imagine the segments were linear, imagine we had two

linear segments between these points.

We don't.

But imagine for a second we did.

So the marginal rate of substitution from the first

point, four pizzas and one movie, to the second point,

two pizzas and two movies, the marginal rate of

substitution is -2.

You are willing to give up two pizzas to get one movie.

This is the same graph, figure 4-6.

This isn't on the graph, you have to write it on.

So going from that first point to that second point, you're

willing to give up two pizzas to get one movie.

So that rate of marginal substitution is -2.

However, when you're at two movies and two pizzas, and I

say OK, how about giving up one more pizza to see movies?

Now you say, wait a second.

To give up one more pizza, I need to see two movies.

My marginal rate of substitution on that second

segment is -1/2.

The marginal rate of substitution on the first

segment is -2.

The marginal rate of substitution on the second

segment is -1/2.

Once again, assuming they're not linear, so it's actually

changing everywhere, but if they were linear, that's what

it would be.

Can someone tell me why?

Why is the marginal rate of substitution falling?

Why is the marginal rate of substitution lower on that

second segment than on the first?

AUDIENCE: Because marginal utility increases the fewer of

something you have.

PROFESSOR: Exactly.

So go ahead, flesh it out, the fewer of somthing you have, so

tell me in terms of the trade you're willing to make.

AUDIENCE: You value it more, so you want to trade more of

something else for it.

PROFESSOR: The point is when I have four pizzas my marginal

utility of that last pizza is not very high.

And I'm fine to give up two pizzas--

and plus I'm only seeing one movie, there's a second movie

I really want to see.

So you say to me, look, I've got four pizzas,

I'm seeing one movie.

You say hey, there's a second movie out I

know you want to see.

I know you don't really value four pizzas.

At the end, you're totally full.

Would you be willing to give up two pizzas to see the

second movie?

And you're like, sure why not?

Well once you have two pizzas and you've seen two movies,

you're not that interested in a third movie and you'll be

hungry if you have less than two pizzas, so then you say,

wait a second.

If you want me to give up another pizza, you've got to

give me two movies.

Because my marginal utility of pizzas is rising, my marginal

utility of movies is falling.

And that's why the marginal rate of substitution

diminishes along the indifference curve.

So that allows us to write mathematically the definition

of the marginal rate of substitution is the negative

of the marginal utility of movies, or more generally

what's on the x-axis, over the marginal utility of pizza, or

more generally what's on the y-axis.

The marginal rate of substitution, the first key

formula you need to know for this course, the marginal rate

of substitution is equal to the

ratio of marginal utilities.

Now this is tricky.

Maybe you guys don't find it tricky, it's the kind of thing

I find tricky.

Which is I defined it as delta y-axis over delta x-axis.

And yet, when I defined here the marginal utilities, I

flipped it.

I did the marginal utility of what's on the x-axis over the

marginal utility of what's on the y-axis.

Why is that?

Can anyone tell me why that is?

Why is it flipped when defined in

terms of marginal utilities?

Yeah?

AUDIENCE: It's a denominator.

So utility over movies--

PROFESSOR: Well, let me try for slightly more, how does

marginal utility relate?

Yeah.

AUDIENCE: Marginal utility is delta P over

P. So it gets flipped.

Because of--

PROFESSOR: OK.

Yeah, you're giving the same answer, which

is technically right.

What I was more looking for but it's the intuitive version

of that, marginal utility is a negative function of quantity.

Marginal utility is a negative function of quantity.

So the fact that it's a ratio of the quantity of pizza over

the quantity of movies is the same thing as the marginal

utility of movies over the marginal utility of pizza.

Because marginal utility is a negative function of quantity.

The more quantity you have, the lower is

your marginal utility.

And that's the key to understand.

So it's the slope of the indifference curve which is

the ratio of the marginal utilities, but it's the

marginal utility of movies over pizza.

Because what that's saying is that as you get more movies,

you care less about each additional movie and ditto

with pizzas.

Let's just look at this for a minute, think about it

intuitively for a minute.

We've seen it graphically, we're seeing it

mathematically, let's make sure we understand it

intuitively.

What this is saying is that as you get more movies--

so let's relate this to the graph.

As you get more movies and less pizza, as you move down

that curve, more movies, less pizza, what's happening?

What's happening to the marginal utility of movies as

you move down that curve?

What direction is it heading?

AUDIENCE: It's decreasing.

PROFESSOR: What?

AUDIENCE: It's decreasing.

PROFESSOR: It's decreasing.

Because you're getting more movies and marginal utility is

a negative function of quantity.

Likewise, the marginal utility of pizza is increasing because

you're getting less pizza so you care

about each pizza more.

And that's why the marginal rate of substitution

diminishes.

That's why it diminishes because as you move down that

curve, the numerator is falling, the denominator is

increasing.

And that's why we have everywhere diminishing

marginal rates of substitution.

So another way to think about this is imagine for a moment

what life would be like if we didn't have diminishing

marginal rates of substitution.

And once again I'm going to try, once again Jessica, next

year we'll let you make this pretty.

But I'm going to try to draw it crudely here.

Let's do pizzas and movies again.

Let's do pizzas and movies again.

Movies and pizza.

And that's one, two, three, four.

One, two, three, four.

Now let's imagine that instead of diminishing marginal

utility and instead of indifference curves being

convex to the origin, imagine if indifference curves were

concave to the origin, which is what increasing marginal

rate substitution would imply.

So that would be something where you'd be indifferent

between four pizzas and one movie, between three pizzas

and two movies, and between one pizza and three movies.

So your indifference curve would look like that.

Not quite to scale, but you get it.

It would be concave to the origin instead of convex to

the origin.

In this case, marginal rates of substitution would be

everywhere increasing.

That is, basically I'd be willing to give up one pizza

to get one movie.

But to get that next movie, I'd give up two pizzas.

But as you can see, that doesn't make sense.

It doesn't make sense that given that as long as you're

ranking movies, or even more in the example of seeing the

same movie over and over again, it's maybe more

compelling.

That basically what you can see is that if you're willing

to give up one pizza to see that movie a second time, why

would you possibly give up two pizzas to see it a third time?

That makes no sense at all.

If you only like it so much you only give up one pizza to

see it a second time, why would you possibly give up two

pizzas to see it a third time?

You wouldn't.

It doesn't make sense.

And that's why marginal rate of substitution has to be

everywhere decreasing, it can't be increasing.

Yeah?

AUDIENCE: Could it remain constant?

PROFESSOR: It could actually remain constant.

Yes, that's right.

You can be indifferent.

My indifference curves--

how many of you guys have seen Toy Story 3?

I think it's one of my 10 favorite movies of all time.

The greatest children's movie ever made.

I've seen it three times.

My indifference curve is virtually--

I've enjoyed it the third times as much as the first--

it's virtually flat with respect to Toy Story 3.

I could see it 10 more times and feel pretty much the same.

So that's certainly possible that it would be constant,

that I'd be willing to give up whatever I pay--

$10 a shot to see it.

It's possible.

So basically, almost always, inequalities will be greater

than or equal to, or less than or equal to in this course.

It's more fun to talk about the not equal to case, the

non-linear case.

But linear cases will exist as well.

It's just a can't be can't be opposite sign.

You can't have an increasing marginal rate of substitution.

Another question over here?

AUDIENCE: What about addictions?

You could want it more the second time.

PROFESSOR: That's interesting.

So how would addiction work? so basically--

AUDIENCE: Well it's not really decreasing.

You need more the second time, right?

So it has to--

PROFESSOR: That's very interesting.

I mean in some sense.

So you give up one pizza for the first shot of heroin.

And then, you're hooked, so then you'd be willing to give

up two pizzas for the next shot of heroin.

Yeah, I guess so.

I guess that's right.

I guess we're going to have to stay away from addiction in

this course.

I guess an addictive good could look like that.

That's a very good point.

Other questions, comments?

So what we're doing is we're going to stop here,

understanding that we're going to have--

leaving this example aside-- we're going to have

diminishing marginal--

yes one more question?

AUDIENCE: [UNINTELLIGIBLE]

PROFESSOR: Basically, we're assuming by non-satiation that

ever happens.

So once again, that would violate the non-satiation.

The problem with the addictiveness example is the

reason it wouldn't work in this course is eventually

you'd violate your budget constraint because you'd want

more and more and more.

Maybe not.

But in any case, we're going to ignore that example, assume

diminishing marginal rate of substitution, and we'll come

back next time as I put this together with a budget

constraint to actually dictate your choices.