Taxes for factoring in negative externalities

WEBVTT
Kind: captions
Language: en

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In the last video, we first
thought about externalities,

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the negative externalities

00:00:05.610 --> 00:00:07.603
of having plastic bags around.

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It causes litter, it might damage animals

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and the environment in some way.

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We're assuming ... And
we assumed in that video

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that we were able to calculate the actual

00:00:16.613 --> 00:00:19.282
external cost of a plastic bag.

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This two cents a bag is the impact on

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litter in the environment.

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Then we were able to figure out

00:00:24.268 --> 00:00:25.667
that if we factor this in,

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instead of just having the regular

00:00:27.139 --> 00:00:28.540
marginal cost cover the suppliers,

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if we added that marginal cost curve

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to the external cost,

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we would get a supplier plus

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external costs, marginal cost curve,

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and then we'd get what is actually

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the optimal price and
quantity of plastic bags

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so that we actually do not eat into

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our surplus by creating all of this

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negative surplus where the total cost

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of the bags are higher than

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the total benefit.

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One thing that we did not touch on

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in that video, is how
does this actually happen?

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If we just let things be,

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and we just had the supplier's

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marginal cost curve

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and we have the consumer's demand curve,

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in this case, the consumers
were the supermarkets,

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then the equilibrium price that'll be

00:01:08.340 --> 00:01:09.932
reached will be right over here

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because although we're theoretically

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saying that there's this cost over here,

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the cost won't be factored in

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into the markets.

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So if you are the benevolent emperor

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in this society, what do you do?

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What do you do to get the quantity

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closer to this point right over here

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than what the equilibrium quantity

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will be when you don't factor in

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the external cost?

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There's a bunch of options here.

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You could just ban plastic bags ...

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ban plastic bags,

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you could put a quota on plastic bags,

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you could put a quota, so saying that

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more than a certain amount of bags

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could not be produced, or

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you could tax plastic bags,

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or you could tax plastic bags.

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Let's think about which of these will

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result in the most surplus,

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the most benefit to society in aggregate.

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One core assumption we're going to make

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is that this is an accurate assessment

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of the external cost per bag.

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If you were to just ban plastic bags

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as this benevolent emperor,

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maybe seemingly or hopefully

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benevolent emperor of
this society right here,

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if you just banned plastic bags,

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what would happen?

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Well, then this market just won't exist.

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All of this surplus
that could have existed,

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won't exist anymore,

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so you would actually
be destroying surplus.

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You could say, "No,
no, no ... plastic bags

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are horrible. They should
just be outright banned.

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There's no amount of benefit for which

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plastic bags are worth using,"

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but in that case, you're actually arguing

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this point right over here.

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You'd be arguing that, "No, it's not

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2 cents a bag, it's 10 cents a bag,"

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of negative externality,
and because of that,

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you would have this
curve shift up even more

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and then there's no
positive quantity there

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and maybe a ban would be all right.

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But if the 2 cents is the externality,

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the negative externality,

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and if you were to ban plastic bags,

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then you would actually be removing,

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you would be removing
this surplus from society.

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That doesn't seem like a good option.

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Now what about a quota?

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You kind of look at the
study right over here

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and you say, "Look, the optimal amount

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of plastic bags is 1.9
million bags per week,

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so I will just say that that's most

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that the market can produce."

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But when you say that, that's assuming

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that you really do understand what this

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demand curve looks like.

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I just drew a straight line here

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just out of simplicity, and

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assuming that you really do understand

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what this marginal cost curve looks like.

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Throughout this playlist,

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we've been assuming that we kind of do

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understand those things, but

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in the real world, it's actually very hard

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to know exactly what the marginal cost

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of the curve looks like,

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and it's also hard to know exactly

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what the marginal benefit curve,

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or the demand curve looks like,

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especially because
they're always changing.

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There's always more competitors,

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less competitors, more
substitute products,

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more R&D, things are
getting more efficient,

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less efficient; and so it's very hard

00:04:00.621 --> 00:04:03.615
to know what the true equilibrium

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quantity should be.

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A quota is difficult.

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We don't have quite the right information.

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A tax is interesting.

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A tax says, "Look, regardless of

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what the marginal cost curve really is,

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we're just going to
shift it up by 2 cents."

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We saw that when we
first talked about taxes.

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When we first talked about
taxes, we talked about

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they're introducing a dead weight loss

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because you're not
producing as much quantity

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as you would have otherwise, or

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as much quantity isn't being consumed.

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But here, a tax could actually prevent

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a dead weight loss because if you have

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a 2 cent tax, essentially adding the cost

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of the negative externality
in the form of a tax

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on top of the supplier's
cost right over here,

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you are going to cause
the equilibrium quantity

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to be the quantity where you're not

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generating all of this negative surplus,

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and it's just a positive side effect,

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and once again, this is all assuming

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that this is the right number,

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but it would be a positive side effect

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that you would also generate some revenue

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for the government.

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What's good about the
tax in this circumstance

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right over here, you're
not assuming anything

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about what the marginal
cost curve looks like

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or what the demand curve looks like.

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As long as you're assuming that this

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is the right number,

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the tax will always shift whatever

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the marginal cost curve is,

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it'll always shift it to the right point

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to intersect wherever the demand curve is

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at this equilibrium point,

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that gives us an equilibrium price

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and an equilibrium quantity.

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So if this is the right number and

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you put a 2 cent tax per bag,

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a 2 cent tax per bag,

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then this is probably
going to be the best option

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in terms of optimizing the total surplus.


Negative externalities

WEBVTT
Kind: captions
Language: en

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Let's think about the
market for plastic bags.

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And I'm picking this
market in particular

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because there might be
some cost associated

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with plastic bags that aren't
captured when you're only

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looking at it from
the point of view

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of the suppliers
or the consumers.

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So right over here, you
have a demand curve.

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And that's really the demand
coming from the supermarkets.

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So this is the demand curve.

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You could also view it
as marginal benefit.

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So that very first bag
that gets produced,

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a supermarket gets a
lot of marginal benefit.

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They'd really want
to get that bag,

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because then they could
give it to the people who

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shop at the supermarket, and
they can carry their bags home.

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But then each incremental
bag after that,

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the marginal benefit gets
lower and lower and lower.

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And this green curve
over here-- we've

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seen this multiple times--
that is our supply curve, which

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we can also think of it as
our marginal cost curve.

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To produce the very first
bag, the opportunity cost

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for that very
first bag is about,

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looks like about
a penny per bag.

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And then it gets higher
and higher and higher

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as you produce
more and more bags.

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And we have an equilibrium price
and an equilibrium quantity.

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Our equilibrium quantity
looks like it's about 3

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and 1/2 million bags.

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We have an equilibrium price
of about $0.02 per bag.

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And if this were all of the
cost and all of the benefits,

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then this area right over
here would show the total,

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the aggregate total benefit
that the ecosystem here,

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that the suppliers
and the consumers,

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or the supermarkets or the
consumers in this case,

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are getting from
this transaction.

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Marginal benefit higher
than marginal cost;

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marginal benefit higher
than marginal cost.

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This whole area is
our total surplus,

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and we've seen that
multiple times.

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But now let's think
about that added cost

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that plastic bags have that
are not factored in to the cost

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and the prices, or the cost and
the benefits right over here.

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Plastic bags have a
negative externality.

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There's a cost associated.

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So it's negative because
there's a cost associated

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with plastic bags that is
not being borne by either

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in this situation, that
is not being factored

00:02:08.310 --> 00:02:10.112
into the marginal cost curve.

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You can also have
positive externalities,

00:02:11.820 --> 00:02:12.550
which are a benefit.

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Maybe you're talking about
the market for trees,

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and society benefits when
more plants or more trees

00:02:17.010 --> 00:02:18.687
are being planted, or whatever.

00:02:18.687 --> 00:02:19.520
And let's just say--

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And that negative
externality, that's

00:02:21.150 --> 00:02:22.590
coming from obvious things.

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You know, these bags
are going to be litter.

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They're going to be on
the side of the highway.

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The city has to clean them up.

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There's environmental
risks due to them.

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Animals might eat them
and choke on them,

00:02:32.230 --> 00:02:34.490
and turtles might drown,
and whatever else,

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because they're choking on
plastic bags and whatever else.

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And so they hire some experts.

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And this is not an
easy thing to do,

00:02:40.150 --> 00:02:43.060
but it's determined that
the negative externality

00:02:43.060 --> 00:02:46.440
of these plastic bags
is $0.02 per bag.

00:02:46.440 --> 00:02:48.680
Or another way to think
of it, the cost to society

00:02:48.680 --> 00:02:51.700
and the environment above
and beyond the marginal cost

00:02:51.700 --> 00:02:55.400
to the producers,
is $0.02 per bag.

00:02:55.400 --> 00:02:57.700
Now, given that, if we
assume this statement right

00:02:57.700 --> 00:02:59.510
over here-- and it's
not an easy thing

00:02:59.510 --> 00:03:01.750
to come up with this
number-- but if we assume

00:03:01.750 --> 00:03:03.940
that this number
is true, what then

00:03:03.940 --> 00:03:06.970
is the optimal amount
of bags to purchase?

00:03:06.970 --> 00:03:09.074
And what are we
actually doing if we--

00:03:09.074 --> 00:03:10.990
What is the optimum
amount of bags to produce?

00:03:10.990 --> 00:03:13.510
And what are we doing when
we do produce this much?

00:03:13.510 --> 00:03:16.070
And to think about that,
let's create a new curve.

00:03:16.070 --> 00:03:17.864
This is the supplier's
marginal cost.

00:03:17.864 --> 00:03:19.280
Let's create another
curve that is

00:03:19.280 --> 00:03:22.390
the supplier plus
society's marginal cost.

00:03:22.390 --> 00:03:24.960
So that first bag supplier,
his opportunity cost

00:03:24.960 --> 00:03:27.010
is about a penny,
but for society it's

00:03:27.010 --> 00:03:28.350
costing another $0.02.

00:03:28.350 --> 00:03:32.170
So supplier plus society
is costing almost $0.03.

00:03:32.170 --> 00:03:35.440
And so we can plot
out another curve

00:03:35.440 --> 00:03:44.010
which we can view as the
supplier plus society

00:03:44.010 --> 00:03:46.560
marginal cost.

00:03:46.560 --> 00:03:50.400
So now we can think of things
in terms of total benefit,

00:03:50.400 --> 00:03:52.720
or total net benefit, I
guess, that's happening.

00:03:52.720 --> 00:03:55.130
That very first
bag, the supermarket

00:03:55.130 --> 00:03:58.470
that buys it is still getting
that over $0.05 of benefit.

00:03:58.470 --> 00:04:01.260
But now if we think about
the net benefit to society,

00:04:01.260 --> 00:04:04.110
it's not this whole height
all the way down to a penny.

00:04:04.110 --> 00:04:06.340
It's only this part
right over here.

00:04:06.340 --> 00:04:08.870
It's only the difference
between five and three

00:04:08.870 --> 00:04:12.970
is the marginal net benefit, if
you take the marginal benefit

00:04:12.970 --> 00:04:16.140
and you subtract out the total
marginal costs, including

00:04:16.140 --> 00:04:17.649
the externalities.

00:04:17.649 --> 00:04:20.510
And so the next bag, the total
cost gets a little higher,

00:04:20.510 --> 00:04:22.670
the marginal benefit
gets a little bit lower.

00:04:22.670 --> 00:04:25.230
And you keep, it makes
sense for society--

00:04:25.230 --> 00:04:27.650
It will keep getting
benefit from this,

00:04:27.650 --> 00:04:29.250
if we think of the
entire ecosystem,

00:04:29.250 --> 00:04:33.060
will keep getting benefit until
we hit this other equilibrium

00:04:33.060 --> 00:04:34.680
point over here.

00:04:34.680 --> 00:04:36.580
And once we get past
that equilibrium point,

00:04:36.580 --> 00:04:38.080
now when we think
holistically, when

00:04:38.080 --> 00:04:42.010
we think of the environment and
the government and all of that,

00:04:42.010 --> 00:04:45.280
now all of a sudden the marginal
cost of each incremental unit

00:04:45.280 --> 00:04:48.200
is higher than the
marginal benefit.

00:04:48.200 --> 00:04:50.060
So if we were to
produce beyond that,

00:04:50.060 --> 00:04:52.300
now we're incurring costs.

00:04:52.300 --> 00:04:53.952
Now we're essentially
eating out all

00:04:53.952 --> 00:04:55.660
of the benefit that
we would have gotten.

00:04:55.660 --> 00:04:58.420
And if we were to produce all
the way to our old equilibrium

00:04:58.420 --> 00:05:02.620
point over here, we more, in the
way-- I was just eyeballing it,

00:05:02.620 --> 00:05:04.900
the purple area is more
than the yellow area--

00:05:04.900 --> 00:05:08.040
we're now getting a negative
total benefit to society.

00:05:08.040 --> 00:05:10.760
Or you could say a
negative total surplus.

00:05:10.760 --> 00:05:13.340
And we haven't visualized
it this way in the past.

00:05:13.340 --> 00:05:15.930
It's unusual for us
to see a dead weight

00:05:15.930 --> 00:05:18.550
loss on this side of
the equilibrium point,

00:05:18.550 --> 00:05:20.380
but you can also
view it that way.

00:05:20.380 --> 00:05:24.445
So this right over here
is negative surplus.

00:05:27.770 --> 00:05:29.840
And so what you really
want holistically

00:05:29.840 --> 00:05:33.789
if you are the benevolent
emperor of the society,

00:05:33.789 --> 00:05:35.830
and you really want to
factor in all of the costs

00:05:35.830 --> 00:05:39.270
and benefits of the plastic
bags, the ideal thing

00:05:39.270 --> 00:05:42.070
if you want to optimize
the benefit in society,

00:05:42.070 --> 00:05:43.570
you would want the
equilibrium price

00:05:43.570 --> 00:05:45.860
to be around here-- that
looks like about 350--

00:05:45.860 --> 00:05:49.880
and the equilibrium
quantity to be--

00:05:49.880 --> 00:05:52.240
this looks about 1.8 million.

00:05:52.240 --> 00:05:55.000
And you would not want all
of this excess quantity that

00:05:55.000 --> 00:05:59.690
is taking away, that is
less efficient for society.


Game theory of cheating firms

WEBVTT
Kind: captions
Language: en

00:00:00.255 --> 00:00:01.756
Male Voice: In the last video we saw how

00:00:01.756 --> 00:00:03.871
there could be an industry
that has two firms,

00:00:03.871 --> 00:00:07.040
a duopoly, and if those
two firms coordinate

00:00:07.040 --> 00:00:09.604
they could behave as a
monopolist and they could

00:00:09.604 --> 00:00:12.469
optimize their collective economic profit.

00:00:12.469 --> 00:00:14.284
In the last video we saw that would happen

00:00:14.284 --> 00:00:16.759
when they produced 50 units per period,

00:00:16.759 --> 00:00:18.404
and they could split
it, assuming these were

00:00:18.404 --> 00:00:21.340
two identical firms, by
each producing half of it.

00:00:21.340 --> 00:00:24.289
In the case of the last
video, it was 250 units

00:00:24.289 --> 00:00:27.206
per firm. Then we saw that
there was an incentive

00:00:27.206 --> 00:00:30.006
to cheat; that by producing extra units,

00:00:30.006 --> 00:00:33.075
from a market's point
of view, the marginal

00:00:33.075 --> 00:00:35.205
economic, or the economic profit on those

00:00:35.205 --> 00:00:37.538
incremental units would
be negative, so the whole

00:00:37.538 --> 00:00:40.876
economic profit would shrink a little bit

00:00:40.876 --> 00:00:43.202
as you produced units beyond that,

00:00:43.202 --> 00:00:45.208
but the cheater would get a bigger chunk

00:00:45.208 --> 00:00:47.138
of those units, or the
bigger chunk of that

00:00:47.138 --> 00:00:50.677
economic profit. The
cheater could actually gain,

00:00:50.677 --> 00:00:54.552
go from $250 per time period to $280,

00:00:54.552 --> 00:00:57.393
and it would be all at the
expense of the non-cheater,

00:00:57.393 --> 00:01:00.271
and then some, who would lose even more

00:01:00.271 --> 00:01:02.010
than what the cheater gained.

00:01:02.010 --> 00:01:04.742
Obviously who was
initially the non-cheater

00:01:04.742 --> 00:01:06.285
has an incentive now to cheat, and they'll

00:01:06.285 --> 00:01:08.707
both keep increasing,
they'll both keep increasing

00:01:08.707 --> 00:01:11.412
production so that if they wanted to keep

00:01:11.412 --> 00:01:14.802
doing this one-upmanship. They both have

00:01:14.802 --> 00:01:16.756
the incentive to keep
going assuming that they

00:01:16.756 --> 00:01:19.201
don't hold to their cartel agreement

00:01:19.201 --> 00:01:26.544
until you get to a
quantity where there's no

00:01:26.544 --> 00:01:30.143
economic profit left.
Right over here, the way

00:01:30.143 --> 00:01:32.653
I've drawn it, the demand curve intersects

00:01:32.653 --> 00:01:35.745
the average total cost
curve right over here,

00:01:35.745 --> 00:01:38.211
and there's no economic profit left.

00:01:38.211 --> 00:01:39.792
We're producing a good quantity.

00:01:39.792 --> 00:01:42.205
It looks like it's
about 75 units combined;

00:01:42.205 --> 00:01:44.807
75 units for the whole market.

00:01:44.807 --> 00:01:48.171
But at this point, the market price

00:01:48.171 --> 00:01:51.013
is equal to the average total cost,

00:01:51.013 --> 00:01:53.458
and so there's no economic profit per unit

00:01:53.458 --> 00:01:56.724
on average. What I want
to do is think about this

00:01:56.724 --> 00:01:58.730
in kind of a Game theoretic way.

00:01:58.730 --> 00:02:01.378
Let's look at a bunch of states.

00:02:01.378 --> 00:02:05.128
This is the optimal state
that we are starting off in.

00:02:05.128 --> 00:02:12.959
You can actually call it
the Pareto optimal state,

00:02:12.959 --> 00:02:15.721
named after Vilfredo Pareto.

00:02:15.721 --> 00:02:19.051
All it means is that's
the state where there's

00:02:19.051 --> 00:02:20.791
no other state where you can make someone

00:02:20.791 --> 00:02:23.385
better off without making
the other person worse off.

00:02:23.385 --> 00:02:25.035
Any of the states here, there are states,

00:02:25.035 --> 00:02:26.656
for example, where blue is better off.

00:02:26.656 --> 00:02:29.070
For example, in this state right over here

00:02:29.070 --> 00:02:31.784
blue is better off,
but green is worse off.

00:02:31.784 --> 00:02:36.046
So that's why it's
called Pareto optimality.

00:02:36.046 --> 00:02:38.952
Now, what I want to think
about is how these characters

00:02:38.952 --> 00:02:42.049
will change their state
due to their incentives.

00:02:42.049 --> 00:02:44.918
Then we'll talk a little bit
about Nash Equilibrium as well.

00:02:44.918 --> 00:02:49.199
On this axis, up here,
lets' say this is one

00:02:49.199 --> 00:02:52.040
of the competitors. This
is where they produce 25,

00:02:52.040 --> 00:02:54.320
and let's say on the ultimate cheating

00:02:54.320 --> 00:02:57.887
quantity of 75, and this
is somewhat close to

00:02:57.887 --> 00:03:00.395
the market, or that is
the equilibrium quantity

00:03:00.395 --> 00:03:03.137
if this was perfect competition,

00:03:03.137 --> 00:03:05.461
they produce half of that, so this is them

00:03:05.461 --> 00:03:11.881
producing 37.5 units. As we
go from 25 to 37.5 units,

00:03:11.881 --> 00:03:16.551
they are cheating more.
This is more cheating

00:03:16.551 --> 00:03:19.801
and over here, this was no cheating.

00:03:19.801 --> 00:03:22.332
We can do the same thing
for the blue player.

00:03:22.332 --> 00:03:25.928
I'll write them as B.
This is them producing 25.

00:03:25.928 --> 00:03:29.325
This is them producing
37.5. As we go up and up

00:03:29.325 --> 00:03:31.713
and up, they are cheating more.

00:03:31.713 --> 00:03:36.751
This is a lot of cheating,
or more cheating.

00:03:36.751 --> 00:03:38.724
To think of it in a Game theoretical way,

00:03:38.724 --> 00:03:41.862
this is the Pareto optimal
state right over here.

00:03:41.862 --> 00:03:43.392
It's optimal in many ways.

00:03:43.392 --> 00:03:45.922
This is they've maximized
the total economic

00:03:45.922 --> 00:03:48.992
profit here. There's
no other state that one

00:03:48.992 --> 00:03:51.546
person would benefit without
making the other worse.

00:03:51.546 --> 00:03:53.460
Now, let's think about whether this is

00:03:53.460 --> 00:03:57.465
a Nash equilibrium. Let's remind oursleves

00:03:57.465 --> 00:04:01.132
what Nash equilibrium was.

00:04:01.132 --> 00:04:05.165
This was a state where
holding all the other

00:04:05.165 --> 00:04:07.473
players constant, so in
this case there's only one

00:04:07.473 --> 00:04:24.042
other player, a player can't
gain by changing strategy.

00:04:24.042 --> 00:04:25.532
In this case, changing
strategy is changing

00:04:25.532 --> 00:04:34.328
your output. Let's see if
that is true of this state

00:04:34.328 --> 00:04:38.065
right over here. Well,
let's hold A constant.

00:04:38.065 --> 00:04:40.144
If A is constant, we're
in this column right

00:04:40.144 --> 00:04:42.663
over here. Is there something B can do,

00:04:42.663 --> 00:04:44.803
is there change or strategy B can do,

00:04:44.803 --> 00:04:46.702
that would allow B to gain?

00:04:46.702 --> 00:04:49.461
Sure. B can increase production.

00:04:49.461 --> 00:04:50.794
That's what we saw in the last video.

00:04:50.794 --> 00:04:52.949
We would go from this bottom right state

00:04:52.949 --> 00:04:55.329
to one right above it.
Now B's economic profit

00:04:55.329 --> 00:04:58.796
is 280, A's is 200. The pie has shrunk,

00:04:58.796 --> 00:05:00.962
but B has got a larger chunk of it.

00:05:00.962 --> 00:05:03.539
That was not a Nash equilibrium.

00:05:03.539 --> 00:05:06.406
There is, holding all others constant,

00:05:06.406 --> 00:05:11.732
there is a player that can gain
by changing their strategy.

00:05:11.732 --> 00:05:14.956
The Nash equilibrium
definition, just to make sure,

00:05:14.956 --> 00:05:17.396
they say it's a state where holding others

00:05:17.396 --> 00:05:21.461
constant no player can
gain by changing strategy.

00:05:21.461 --> 00:05:23.334
We just showed that at
least one player can gain

00:05:23.334 --> 00:05:25.870
by changing strategy
holding others constant.

00:05:25.870 --> 00:05:27.595
The same would be true if we
went the other way around.

00:05:27.595 --> 00:05:31.288
If we held B constant at 25, A could gain

00:05:31.288 --> 00:05:34.630
by changing his strategy,
could go right over there.

00:05:34.630 --> 00:05:41.523
This is not a Nash equilibrium.

00:05:41.523 --> 00:05:43.159
Then regardless of what state we go to,

00:05:43.159 --> 00:05:44.856
if we go to this state, it's still not

00:05:44.856 --> 00:05:47.742
a Nash Equilibrium. If we hold A constant,

00:05:47.742 --> 00:05:51.274
B could improve by
increasing his production;

00:05:51.274 --> 00:05:53.866
or if we hold B constant, then A can still

00:05:53.866 --> 00:05:55.995
improve by cheating even more.

00:05:55.995 --> 00:05:57.861
None of these are Nash equilibriums.

00:05:57.861 --> 00:06:00.532
From any one of these states,
if you hold A constant,

00:06:00.532 --> 00:06:04.261
B could produce more; or
if you hold B constant,

00:06:04.261 --> 00:06:07.858
A could produce more and get some gain.

00:06:07.858 --> 00:06:11.059
Over here, A's going from
130 to 160 and getting

00:06:11.059 --> 00:06:13.581
some gain. You can imagine
this keeps happening

00:06:13.581 --> 00:06:15.328
incrementally. They keep
producing more and more

00:06:15.328 --> 00:06:17.595
and more. We kind of go
there, then we go there,

00:06:17.595 --> 00:06:19.859
then maybe we go there, then we go there.

00:06:19.859 --> 00:06:23.168
Then maybe A cheats some more, then B

00:06:23.168 --> 00:06:25.082
cheats some more, then A
cheats a little bit more,

00:06:25.082 --> 00:06:27.452
B cheats a little bit more,
maybe a little bit more

00:06:27.452 --> 00:06:29.753
past that, then A cheats
a little bit more.

00:06:29.753 --> 00:06:32.666
The whole time the whole
economic profit pie,

00:06:32.666 --> 00:06:35.326
which is the sum of A
and B, is getting smaller

00:06:35.326 --> 00:06:37.179
and smaller until finally A finally cheats

00:06:37.179 --> 00:06:40.828
and they're at zero economic profit.

00:06:40.828 --> 00:06:42.588
Now let's think about whether this is

00:06:42.588 --> 00:06:45.124
a Nash equilibrium.
Clearly, they won't want

00:06:45.124 --> 00:06:47.743
to move backwards. If you hold A constant,

00:06:47.743 --> 00:06:51.604
B would not want to
move down. Then he would

00:06:51.604 --> 00:06:54.858
lose economic profit. That doesn't work.

00:06:54.858 --> 00:06:56.442
He doesn't gain by doing
that. If you hold B

00:06:56.442 --> 00:06:58.665
constant, A wouldn't want
to move to the right.

00:06:58.665 --> 00:07:01.214
A would also lose economic profit.

00:07:01.214 --> 00:07:04.665
Now you might say what if
they produced beyond 37.5?

00:07:04.665 --> 00:07:07.858
Why can't they keep producing
and go beyond there?

00:07:07.858 --> 00:07:12.469
Holding A constant, if B were
to produce more than 37.5

00:07:12.469 --> 00:07:15.591
from this state right
over here, then the total

00:07:15.591 --> 00:07:17.716
pie will get negative
and it doesn't matter

00:07:17.716 --> 00:07:20.176
if B's getting a larger or
smaller chunk of that pie.

00:07:20.176 --> 00:07:21.869
B's chunk is going to be negative.

00:07:21.869 --> 00:07:24.057
He's going to drive down
the price even more.

00:07:24.057 --> 00:07:25.745
You can see it over here.

00:07:25.745 --> 00:07:27.744
If they increase quantity beyond

00:07:27.744 --> 00:07:31.416
this market quantity of 75, 37.5 each,

00:07:31.416 --> 00:07:36.592
if we go beyond that,
the price that they would

00:07:36.592 --> 00:07:39.124
be selling at, at that
quantity over there,

00:07:39.124 --> 00:07:42.328
is lower than the average total cost.

00:07:42.328 --> 00:07:44.665
You're going to be, the total economic,

00:07:44.665 --> 00:07:47.392
the average economic profit per unit

00:07:47.392 --> 00:07:49.414
is going to be negative.
There will be a total

00:07:49.414 --> 00:07:51.455
of negative economic profit.

00:07:51.455 --> 00:07:53.916
Neither of them will want to produce more

00:07:53.916 --> 00:07:56.085
from this state either. All of a sudden

00:07:56.085 --> 00:07:57.120
in this top-left

00:07:57.120 --> 00:07:59.126
state,
holding others constant;

00:07:59.126 --> 00:08:01.660
if you hold A constant, B can't gain by

00:08:01.660 --> 00:08:04.512
changing his strategy,
and if you hold B constant

00:08:04.512 --> 00:08:06.994
A can't gain by changing his strategy,

00:08:06.994 --> 00:08:12.952
so we are, up here, in a Nash equilibrium.

00:08:12.952 --> 00:08:14.582
This is a Nash equilibrium.

00:08:14.582 --> 00:08:18.933
Like the prisoner's dilemma, it was not

00:08:18.933 --> 00:08:21.688
the optimal state. The
optimal state was here,

00:08:21.688 --> 00:08:23.439
but because they both wanted to cheat,

00:08:23.439 --> 00:08:25.281
they both wanted to do this one-upmanship,

00:08:25.281 --> 00:08:26.800
they both broke their contracts,

00:08:26.800 --> 00:08:29.192
they could end up in this state over here.

00:08:29.192 --> 00:08:31.367
But this state is stable.

00:08:31.367 --> 00:08:33.023
There's nothing holding
the other party equal.

00:08:33.023 --> 00:08:36.941
There's nothing that they could
do to change, to optimize.

00:08:36.941 --> 00:08:38.922
What they could do, and
this is not what Nash

00:08:38.922 --> 00:08:40.396
applies to, they could say okay,

00:08:40.396 --> 00:08:42.698
we've been really ruining
each others' business.

00:08:42.698 --> 00:08:45.730
Let's go coordinate again
and I'm going to decrease

00:08:45.730 --> 00:08:47.993
production if you decrease production.

00:08:47.993 --> 00:08:50.352
That is not, and they
could maybe try to go back

00:08:50.352 --> 00:08:52.798
to this state, and that does
not mean that this is not

00:08:52.798 --> 00:08:56.436
a Nash equilibrium because
by coordinating again

00:08:56.436 --> 00:08:58.525
we're not holding the others constant.

00:08:58.525 --> 00:09:01.103
We're saying I'm changing
my strategy while

00:09:01.103 --> 00:09:03.590
you're changing your strategy. Maybe only

00:09:03.590 --> 00:09:06.153
through another agreement
they could go over here.

00:09:06.153 --> 00:09:08.357
That still doesn't mean that this is not

00:09:08.357 --> 00:09:10.796
a Nash equilibrium. This
is a Nash equilibrium.

00:09:10.796 --> 00:09:13.062
If there's no coordination,
if you hold one player

00:09:13.062 --> 00:09:16.191
constant, the other player
cannot change their strategy,

00:09:16.191 --> 00:09:20.000
or change their production, for a gain.


Why parties to cartels cheat

WEBVTT
Kind: captions
Language: en

00:00:00.350 --> 00:00:01.770
What I want to do
in this video is

00:00:01.770 --> 00:00:05.280
analyze why it makes sense
for two companies that

00:00:05.280 --> 00:00:10.050
make up a duopoly to coordinate.

00:00:10.050 --> 00:00:12.870
To get into an agreement,
which may or may not be legal--

00:00:12.870 --> 00:00:16.170
probably would be illegal--
and restrict quantity.

00:00:16.170 --> 00:00:19.010
But also think about why
there's a strong incentive

00:00:19.010 --> 00:00:21.010
for either or both
of the parties

00:00:21.010 --> 00:00:24.170
to cheat their agreement
and produce more quantity

00:00:24.170 --> 00:00:26.010
than they agreed to produce.

00:00:26.010 --> 00:00:29.870
So let's say that both of
our players in our duopoly--

00:00:29.870 --> 00:00:32.204
and this would actually apply
to an oligopoly generally,

00:00:32.204 --> 00:00:34.661
but the analysis would be a
little bit more difficult if we

00:00:34.661 --> 00:00:36.640
had more than two
players-- but let's say

00:00:36.640 --> 00:00:40.060
each player has an identical--
they're identical companies.

00:00:40.060 --> 00:00:42.340
And they both have a
marginal cost curve

00:00:42.340 --> 00:00:44.350
that looks something like that.

00:00:44.350 --> 00:00:48.100
So they both have an
individual marginal cost

00:00:48.100 --> 00:00:49.430
curve that looks like that.

00:00:49.430 --> 00:00:51.520
And they both have an
average total cost curve

00:00:51.520 --> 00:00:53.765
that looks something like this.

00:01:01.290 --> 00:01:02.327
And they are identical.

00:01:02.327 --> 00:01:03.410
So I'll just draw it once.

00:01:03.410 --> 00:01:05.519
This is the marginal
cost and average total

00:01:05.519 --> 00:01:07.040
cost for both firms.

00:01:07.040 --> 00:01:10.410
Now let's think about what it
would look like for the market.

00:01:10.410 --> 00:01:13.220
Well, one way to
think about it--

00:01:13.220 --> 00:01:17.190
pick an arbitrary marginal cost.

00:01:17.190 --> 00:01:19.700
So for one firm, what
can they produce,

00:01:19.700 --> 00:01:22.176
or what quantity will they
be at that marginal cost?

00:01:22.176 --> 00:01:23.550
Well, they'll be
at this quantity

00:01:23.550 --> 00:01:24.740
for that marginal cost.

00:01:24.740 --> 00:01:27.110
But if you have two firms
that are just like that,

00:01:27.110 --> 00:01:29.670
they could have twice
as much quantity

00:01:29.670 --> 00:01:32.200
to be at that point
in marginal cost.

00:01:32.200 --> 00:01:34.210
So two firms will be over there.

00:01:34.210 --> 00:01:36.790
And if you picked
this marginal cost,

00:01:36.790 --> 00:01:38.850
one firm would
produce that quantity

00:01:38.850 --> 00:01:40.470
to be right at
that marginal cost,

00:01:40.470 --> 00:01:42.210
for that next incremental good.

00:01:42.210 --> 00:01:44.670
But two firms could
produce two, especially

00:01:44.670 --> 00:01:47.037
if they have the exact
same cost structure.

00:01:47.037 --> 00:01:48.620
So what you're going
to have is you're

00:01:48.620 --> 00:01:51.300
essentially adding
this curve to itself

00:01:51.300 --> 00:01:53.330
in the horizontal direction.

00:01:53.330 --> 00:01:55.974
So if you look at the marginal
cost curve for both firms

00:01:55.974 --> 00:01:57.390
together, you're
essentially going

00:01:57.390 --> 00:02:00.800
to get a curve that is twice
is fat as the marginal cost

00:02:00.800 --> 00:02:02.680
curve for one firm.

00:02:02.680 --> 00:02:04.290
So it will look
something like this.

00:02:04.290 --> 00:02:06.400
And I'll do it in yellow.

00:02:06.400 --> 00:02:09.270
So it will look
something like that.

00:02:09.270 --> 00:02:13.570
So that is the marginal
cost for the market, where

00:02:13.570 --> 00:02:17.310
the market in this example
is both of these firms.

00:02:17.310 --> 00:02:22.070
And that will also be true
for the average total cost.

00:02:22.070 --> 00:02:25.740
If at this price--
or actually, I

00:02:25.740 --> 00:02:28.190
should say, if the average
total cost is up here

00:02:28.190 --> 00:02:30.400
for one firm-- that
means that they

00:02:30.400 --> 00:02:32.160
are producing this quantity.

00:02:32.160 --> 00:02:35.380
But two firms together could
produce twice the quantity

00:02:35.380 --> 00:02:37.070
of that average total cost.

00:02:37.070 --> 00:02:38.915
So two firms would
produce twice.

00:02:38.915 --> 00:02:41.540
And so what you're going to have
is an average total cost curve

00:02:41.540 --> 00:02:44.160
that is twice as fat as
the average total cost

00:02:44.160 --> 00:02:46.640
curve for one firm, if
you talk about the market.

00:02:46.640 --> 00:02:49.310
So the market's average
total cost curve

00:02:49.310 --> 00:02:50.980
is going to look
something like this.

00:02:50.980 --> 00:02:52.340
It's going to be twice as fat.

00:02:52.340 --> 00:02:54.390
It's the exact same logic.

00:02:54.390 --> 00:02:58.970
It's going to look
something like that.

00:02:58.970 --> 00:03:04.005
So that is the average total
cost curve for the market.

00:03:04.005 --> 00:03:06.570
So, so far, the convention
that I've ended up using

00:03:06.570 --> 00:03:09.020
is orange for an
individual firm,

00:03:09.020 --> 00:03:14.050
and then this dotted yellow
line for the market as a whole.

00:03:14.050 --> 00:03:17.580
Now let's think about
what a good equilibrium--

00:03:17.580 --> 00:03:20.490
or what the right
price should be

00:03:20.490 --> 00:03:24.854
if they were able to
coordinate together.

00:03:24.854 --> 00:03:27.270
If they were to essentially
combine their firms and almost

00:03:27.270 --> 00:03:28.701
behave like a monopoly.

00:03:28.701 --> 00:03:30.200
And to think about
that, we're going

00:03:30.200 --> 00:03:32.050
to have to draw a demand curve.

00:03:32.050 --> 00:03:34.500
So let me draw the
market demand curve.

00:03:34.500 --> 00:03:36.200
Let's say the
market demand curve

00:03:36.200 --> 00:03:38.909
looks something like that.

00:03:38.909 --> 00:03:40.450
It's really big, so
it's hard for me.

00:03:40.450 --> 00:03:42.410
And we'll assume
that this is a line.

00:03:42.410 --> 00:03:45.600
So it's not-- well,
that's pretty good.

00:03:45.600 --> 00:03:47.350
So this is the
market demand curve.

00:03:52.220 --> 00:03:57.640
So if both of these firms
operated together, if they--

00:03:57.640 --> 00:03:59.440
I drew the market demand curve.

00:03:59.440 --> 00:04:01.770
I also want to draw the
market marginal revenue curve.

00:04:01.770 --> 00:04:04.270
Now remember, we're going to
assume that both of these firms

00:04:04.270 --> 00:04:05.760
are acting together.

00:04:05.760 --> 00:04:08.590
If they perfectly coordinate,
they can join their capacities

00:04:08.590 --> 00:04:11.220
and act essentially
like a monopoly.

00:04:11.220 --> 00:04:13.660
So if they did act
like a monopoly,

00:04:13.660 --> 00:04:15.800
their marginal
revenue curve would

00:04:15.800 --> 00:04:18.880
be twice the slope of
this market demand curve.

00:04:18.880 --> 00:04:22.660
So it would hit the horizontal
axis right over there.

00:04:22.660 --> 00:04:24.400
And so it would look
something like this.

00:04:27.200 --> 00:04:38.430
So this right over here is the
market marginal revenue curve.

00:04:38.430 --> 00:04:40.280
So if they were to
behave like a monopoly,

00:04:40.280 --> 00:04:43.810
you could view this dotted line
as their marginal cost curve.

00:04:43.810 --> 00:04:45.490
This would be their
average total cost.

00:04:45.490 --> 00:04:47.530
And now this is their
marginal revenue.

00:04:47.530 --> 00:04:49.090
If they were to
behave as a monopoly,

00:04:49.090 --> 00:04:50.548
what would be the
optimal quantity?

00:04:50.548 --> 00:04:53.380
Well, it would be right there,
right where marginal revenue is

00:04:53.380 --> 00:04:55.000
equal to marginal cost.

00:04:55.000 --> 00:04:56.500
Before that, they
would keep wanting

00:04:56.500 --> 00:05:01.070
to produce because
marginal revenue is

00:05:01.070 --> 00:05:02.261
higher than marginal cost.

00:05:02.261 --> 00:05:04.260
And then after that, they
don't want to produce,

00:05:04.260 --> 00:05:06.922
because marginal cost is
higher than marginal revenue,

00:05:06.922 --> 00:05:08.630
and they're going to
take economic losses

00:05:08.630 --> 00:05:11.350
on each of those
incremental units.

00:05:11.350 --> 00:05:13.760
And so this is the quantity
that they would produce.

00:05:13.760 --> 00:05:15.870
And the price they would
get for that-- they just

00:05:15.870 --> 00:05:17.790
have to go to the
market demand curve--

00:05:17.790 --> 00:05:22.200
they would get this
price right over here.

00:05:22.200 --> 00:05:25.150
Let's say they would get
that price right over there.

00:05:25.150 --> 00:05:29.200
And the actual-- their average
total cost per unit-- once

00:05:29.200 --> 00:05:32.380
again, we have to go
to the market here.

00:05:32.380 --> 00:05:34.230
It's this dotted
line right over here.

00:05:34.230 --> 00:05:36.820
That is their average
total cost per unit.

00:05:36.820 --> 00:05:39.570
So their average
economic profit per unit

00:05:39.570 --> 00:05:41.520
is going to be their
revenue per unit,

00:05:41.520 --> 00:05:44.190
minus their average
total cost per unit.

00:05:44.190 --> 00:05:49.930
So this height is their
economic profit per unit.

00:05:49.930 --> 00:05:53.660
And if we multiply that times
the total number of units,

00:05:53.660 --> 00:05:57.310
you would get their
total economic profit

00:05:57.310 --> 00:06:01.960
if they coordinate perfectly,
essentially behaving

00:06:01.960 --> 00:06:03.110
like a monopoly.

00:06:03.110 --> 00:06:05.490
And let's just say for
argument that this height

00:06:05.490 --> 00:06:08.170
right over here-- let's
say that that is 10.

00:06:08.170 --> 00:06:11.660
And let's say that
this quantity that they

00:06:11.660 --> 00:06:15.430
would want to produce
as a monopolist is 50.

00:06:15.430 --> 00:06:18.120
So what is the total
economic profit here?

00:06:18.120 --> 00:06:21.300
Well, their total
economic profit is 500.

00:06:21.300 --> 00:06:32.160
Total economic profit if
they coordinate is 500.

00:06:32.160 --> 00:06:35.270
And so they see this, and
they say, look, why don't we

00:06:35.270 --> 00:06:38.860
agree to each produce
exactly half of this,

00:06:38.860 --> 00:06:42.420
and we would split
the economic profit.

00:06:42.420 --> 00:06:45.340
And to see that, let's
just say one firm says, OK.

00:06:45.340 --> 00:06:48.180
They both decide that
they're going to produce 25.

00:06:48.180 --> 00:06:49.810
They're going to get
this price for it

00:06:49.810 --> 00:06:51.720
up here, which was
the market price.

00:06:51.720 --> 00:06:54.090
They're going to get
that price for it,

00:06:54.090 --> 00:06:56.520
and their costs are right here.

00:06:56.520 --> 00:06:58.530
Now we're going on
each individual firm.

00:06:58.530 --> 00:07:01.130
And that makes sense,
because this cost is just

00:07:01.130 --> 00:07:02.860
twice as far away as this cost.

00:07:02.860 --> 00:07:05.850
And the dotted line
yellow average total cost

00:07:05.850 --> 00:07:08.600
for the market is just a
fatter version, twice as fat

00:07:08.600 --> 00:07:10.310
as the orange line.

00:07:10.310 --> 00:07:14.210
And so each firm will make
this much economic profit

00:07:14.210 --> 00:07:17.090
per unit, times 25 units.

00:07:17.090 --> 00:07:19.850
And so each firm would
make this orange area

00:07:19.850 --> 00:07:24.080
in terms of economic profit,
or half of the entire 500,

00:07:24.080 --> 00:07:27.950
or 250 per firm.

00:07:30.650 --> 00:07:34.640
Now let's think about why
there is an incentive for one

00:07:34.640 --> 00:07:37.020
or both of the firms to cheat.

00:07:37.020 --> 00:07:39.560
Let's say one firm
in particular--

00:07:39.560 --> 00:07:42.920
so the other firm
holds at 25 units.

00:07:42.920 --> 00:07:45.130
But the other firm says,
hey, I like this price.

00:07:45.130 --> 00:07:46.970
I'm already making
economic profit.

00:07:46.970 --> 00:07:49.704
Let me produce 10 more units.

00:07:49.704 --> 00:07:51.870
So the other firm says, I'm
not going to produce 25.

00:07:51.870 --> 00:07:57.010
I'm going to produce 35 units.

00:07:57.010 --> 00:07:59.310
And if that guy
produces 35 units,

00:07:59.310 --> 00:08:03.910
and the other firm in the
market-- the other duopolist,

00:08:03.910 --> 00:08:07.260
I guess we could say it--
continues to produce at 25,

00:08:07.260 --> 00:08:10.325
then the total market production
is now going to be 60.

00:08:14.520 --> 00:08:16.910
Now what is the total
economic profit?

00:08:16.910 --> 00:08:21.870
So we can go up the demand
curve right over there.

00:08:21.870 --> 00:08:23.530
That's the new price.

00:08:23.530 --> 00:08:26.340
That right over there
is the new price.

00:08:26.340 --> 00:08:31.060
The cost per unit is
this right over here,

00:08:31.060 --> 00:08:34.030
and then the number of units
that they're producing is 60.

00:08:34.030 --> 00:08:39.330
So the new economic
profit is this area,

00:08:39.330 --> 00:08:43.850
in this bluish purplish
color that I just drew.

00:08:43.850 --> 00:08:47.029
And even visually this is true--
looks like the demand curve

00:08:47.029 --> 00:08:49.570
and the average total cost curve
have gotten closer together.

00:08:49.570 --> 00:08:53.306
So let's say that this
height right over here is 8.

00:08:53.306 --> 00:08:58.850
And it's going to be $8 of
economic profit per unit,

00:08:58.850 --> 00:09:00.512
times 60 units.

00:09:00.512 --> 00:09:01.970
So if they cheat--
let's talk about

00:09:01.970 --> 00:09:05.140
the cheating circumstance.

00:09:05.140 --> 00:09:08.100
This was coordinate, now let's
think about if they cheat.

00:09:08.100 --> 00:09:11.190
Now we have 60 units
for the whole market

00:09:11.190 --> 00:09:14.430
times $8 of economic
profit per unit.

00:09:14.430 --> 00:09:23.310
You're going to have total
economic profit of 480.

00:09:23.310 --> 00:09:25.550
Your total economic
profit went down.

00:09:25.550 --> 00:09:27.990
And that makes sense,
because now as a market,

00:09:27.990 --> 00:09:29.770
you're producing
beyond the point

00:09:29.770 --> 00:09:32.410
where marginal revenue is
equal to marginal cost.

00:09:32.410 --> 00:09:36.800
Now marginal cost as a market
is higher than marginal revenue.

00:09:36.800 --> 00:09:39.950
And so all of this
is essentially,

00:09:39.950 --> 00:09:42.080
you're creating economic
loss because each

00:09:42.080 --> 00:09:45.110
of these incremental
units as a market--

00:09:45.110 --> 00:09:47.560
The cost is higher
than the revenue,

00:09:47.560 --> 00:09:49.620
and you have an economic loss.

00:09:49.620 --> 00:09:52.160
And so that's why your total
economic profit as a market

00:09:52.160 --> 00:09:55.260
went down from 500 to 480.

00:09:55.260 --> 00:09:59.570
But how much is this
character going to be making?

00:09:59.570 --> 00:10:01.710
The one that decided to cheat?

00:10:01.710 --> 00:10:03.990
Well, he now has 35 units.

00:10:03.990 --> 00:10:06.780
He's producing 35
units, and he's

00:10:06.780 --> 00:10:10.430
getting an economic
profit of $8 per unit.

00:10:10.430 --> 00:10:14.000
So he gets this entire
area right over here.

00:10:14.000 --> 00:10:16.896
So let's multiply 35 times 8.

00:10:16.896 --> 00:10:18.020
I'll do it right over here.

00:10:18.020 --> 00:10:20.720
35 times 8.

00:10:20.720 --> 00:10:27.260
5 times 8 is 40, 3 times
8 is 24, plus 4 is 280.

00:10:27.260 --> 00:10:32.110
So now the cheating
firm, Cheat, has

00:10:32.110 --> 00:10:36.100
$280 of economic
profit in this period.

00:10:36.100 --> 00:10:38.970
And then the honest firm, or the
fair firm-- what they're both

00:10:38.970 --> 00:10:41.750
doing might be illegal by even
attempting to coordinate--

00:10:41.750 --> 00:10:44.490
the non-cheater, I guess
I could call them--

00:10:44.490 --> 00:10:46.155
the non-cheater
will have the rest.

00:10:49.820 --> 00:10:51.710
The non-cheater is going
to have the balance

00:10:51.710 --> 00:10:53.280
of the economic profit.

00:10:53.280 --> 00:10:55.410
And the total economic
profit was 480.

00:10:55.410 --> 00:10:56.690
The cheater's getting 280.

00:10:56.690 --> 00:11:00.060
The non-cheater is
only going to get 200.

00:11:00.060 --> 00:11:02.260
So the cheater
definitely benefited

00:11:02.260 --> 00:11:04.850
by increasing quantity
past that optimal one.

00:11:04.850 --> 00:11:08.090
He went from 250 to 280.

00:11:08.090 --> 00:11:09.720
So it made sense for him.

00:11:09.720 --> 00:11:11.930
It reduced the total
economic profit,

00:11:11.930 --> 00:11:18.120
and it really hurt the
non-cheat right over there.


Monopolistic competition and economic profit

WEBVTT
Kind: captions
Language: en

00:00:00.470 --> 00:00:01.777
Narrator: What I want to do in this video

00:00:01.777 --> 00:00:03.869
is think about why it's so hard for

00:00:03.869 --> 00:00:08.473
a monopolistic competitor to make money

00:00:08.473 --> 00:00:11.480
in the long run.

00:00:11.480 --> 00:00:12.917
Just as a reminder, a
monopolistic competitor

00:00:12.917 --> 00:00:15.420
is much closer to perfect
competition then it is

00:00:15.420 --> 00:00:16.362
to a monopoly.

00:00:16.362 --> 00:00:17.571
What it means is that you have a monopoly

00:00:17.571 --> 00:00:19.888
in your differentiated product,

00:00:19.888 --> 00:00:21.728
but eventually other
people are going to make

00:00:21.728 --> 00:00:22.886
substitute products.

00:00:22.886 --> 00:00:24.328
They can't make exactly your product,

00:00:24.328 --> 00:00:26.398
it can't be identical and it might eat

00:00:26.398 --> 00:00:27.599
into your demand.

00:00:27.599 --> 00:00:30.995
To understand that, let
us draw the demand curve

00:00:30.995 --> 00:00:37.330
for a market in which
monopolistic competition

00:00:37.330 --> 00:00:38.933
is going on.

00:00:38.933 --> 00:00:40.530
I will draw it nice and big.

00:00:40.530 --> 00:00:42.576
In this axis right over
here I'm going to plot

00:00:42.576 --> 00:00:47.536
dollars per unit and so price is revenue

00:00:47.536 --> 00:00:49.198
per unit and we'll have cost per unit

00:00:49.198 --> 00:00:50.534
and things like that.

00:00:50.534 --> 00:00:52.697
And in this axis I'm going
to have quantity produced

00:00:52.697 --> 00:00:54.203
in an given period of time.

00:00:54.203 --> 00:00:55.864
We're going to speak
in fairly general terms

00:00:55.864 --> 00:00:56.795
over here.

00:00:56.795 --> 00:01:01.125
Now, let's assume that our
monopolistic competitor

00:01:01.125 --> 00:01:05.160
right over here is Apple and it's iPad's.

00:01:05.160 --> 00:01:06.705
(writing) Apple, iPad's.

00:01:06.705 --> 00:01:09.737
I want to emphasize, I'm
not making any accusations

00:01:09.737 --> 00:01:12.210
that Apple is a monopolist here.

00:01:12.210 --> 00:01:14.134
They just have a differentiated product

00:01:14.134 --> 00:01:16.625
and so they are monopolistic
competitors here,

00:01:16.625 --> 00:01:18.930
they have a monopoly in iPad's.

00:01:18.930 --> 00:01:20.333
They don't have a monopoly
in Tablet computers

00:01:20.333 --> 00:01:23.332
or computers in general, but only they can

00:01:23.332 --> 00:01:24.869
sell iPad's.

00:01:24.869 --> 00:01:26.961
So, let's draw the demand
curve in the short run

00:01:26.961 --> 00:01:29.406
for iPad's and I'll make it linear to

00:01:29.406 --> 00:01:31.467
make things simple.

00:01:31.467 --> 00:01:32.735
Let me draw a little bit better than that.

00:01:32.735 --> 00:01:34.570
Let's say the demand curve looks something

00:01:34.570 --> 00:01:35.521
like that.

00:01:35.521 --> 00:01:39.588
That is our demand curve
and we know that if that's

00:01:39.588 --> 00:01:42.250
the demand curve and
remember we're talking about

00:01:42.250 --> 00:01:44.258
the market for iPad's,
not the market for Tablet

00:01:44.258 --> 00:01:47.059
computers, Apple is the
monopolist in the market

00:01:47.059 --> 00:01:50.408
for iPad's, so it's
marginal revenue will have

00:01:50.408 --> 00:01:53.660
twice the slope of this demand curve.

00:01:53.660 --> 00:01:56.576
So, it will look something like that.

00:01:56.576 --> 00:01:59.668
That is Apple's marginal revenue curve

00:01:59.668 --> 00:02:02.185
and then think about its
short run economic profit

00:02:02.185 --> 00:02:03.854
in a given period of time,
whatever this quantity

00:02:03.854 --> 00:02:05.784
per period of time is.

00:02:05.784 --> 00:02:09.084
Let's draw its cost,
so first I'll draw ...

00:02:09.084 --> 00:02:11.498
Let me draw its marginal cost,

00:02:11.498 --> 00:02:14.587
so its marginal cost might
look something like this.

00:02:14.587 --> 00:02:18.582
That is their marginal
cost and then to do average

00:02:18.582 --> 00:02:22.166
total cost, up here when
you have very low quantity,

00:02:22.166 --> 00:02:24.165
most of your costs are fixed cost,

00:02:24.165 --> 00:02:26.076
but you're dividing it
by a very small quantity

00:02:26.076 --> 00:02:27.787
so you're going to have a very high

00:02:27.787 --> 00:02:29.061
average total cost.

00:02:29.061 --> 00:02:30.743
It's going to get lower
and lower and lower

00:02:30.743 --> 00:02:32.826
as long as the cost on
each incremental unit

00:02:32.826 --> 00:02:34.779
is lower than the average

00:02:34.779 --> 00:02:36.591
and the cost on each incremental unit is

00:02:36.591 --> 00:02:38.716
a marginal cost curve.

00:02:38.716 --> 00:02:41.332
As long as an average total cost is higher

00:02:41.332 --> 00:02:46.526
than the marginal cost
curve, that's going to be

00:02:46.526 --> 00:02:48.856
downward sloping, and at
some point they're going

00:02:48.856 --> 00:02:50.254
to be equal to each other.

00:02:50.254 --> 00:02:52.794
Now, each incremental unit that you add on

00:02:52.794 --> 00:02:54.123
is going to increase the average

00:02:54.123 --> 00:02:56.394
because each incremental
unit's cost is more

00:02:56.394 --> 00:02:58.856
than the average, so it's
going to cause everything

00:02:58.856 --> 00:03:01.787
to average up.

00:03:01.787 --> 00:03:03.510
This actually right
over here should be the

00:03:03.510 --> 00:03:07.258
minimum point on our
average total cost curve.

00:03:07.258 --> 00:03:09.818
Given the way I've drawn
things, what is Apple's

00:03:09.818 --> 00:03:12.524
short run economic profit?

00:03:12.524 --> 00:03:14.821
We just have to think
of its optimal quantity

00:03:14.821 --> 00:03:16.186
to produce.

00:03:16.186 --> 00:03:18.071
It's definitely going to produce one,

00:03:18.071 --> 00:03:20.080
so the marginal revenue
much higher than the

00:03:20.080 --> 00:03:21.531
marginal cost is going
to make economic profit

00:03:21.531 --> 00:03:23.132
on that unit, it's going to keep producing

00:03:23.132 --> 00:03:25.932
because that continues
to be true all the way

00:03:25.932 --> 00:03:27.731
until this point right over here.

00:03:27.731 --> 00:03:29.824
It doesn't want to produce
more than that because

00:03:29.824 --> 00:03:33.455
the opportunity cost on
each incremental unit

00:03:33.455 --> 00:03:35.595
is higher than the revenue on that,

00:03:35.595 --> 00:03:37.479
so you're going to take an economic loss.

00:03:37.479 --> 00:03:39.594
So, you're going to
produce right over there

00:03:39.594 --> 00:03:43.396
and at that quantity, I'll call that Q*

00:03:43.396 --> 00:03:44.481
right over there.

00:03:44.481 --> 00:03:46.325
At that quantity this
is the price that they

00:03:46.325 --> 00:03:47.731
can charge in the market going in to

00:03:47.731 --> 00:03:48.792
the demand curve.

00:03:48.792 --> 00:03:50.421
I just went straight
up to the demand curve

00:03:50.421 --> 00:03:51.198
over there.

00:03:51.198 --> 00:03:53.696
This is the price that they can charge

00:03:53.696 --> 00:03:56.803
in the market and there
average or you could view

00:03:56.803 --> 00:03:59.034
that as their average revenue per unit.

00:03:59.034 --> 00:04:01.467
Then we have our average cost per unit

00:04:01.467 --> 00:04:04.099
right over here, an average total cost.

00:04:04.099 --> 00:04:07.465
This is their average
economic profit per unit.

00:04:07.465 --> 00:04:10.891
If we multiply that times
the total number of units.

00:04:10.891 --> 00:04:13.603
If we multiply times the
total number of units

00:04:13.603 --> 00:04:16.640
the area of this rectangle right over here

00:04:16.640 --> 00:04:18.969
is going to give total economic profit.

00:04:18.969 --> 00:04:23.665
(writing) total, total,
economic, economic,

00:04:23.665 --> 00:04:25.935
economic profit.

00:04:25.935 --> 00:04:29.005
Now, in all things, if
the rest of the world sees

00:04:29.005 --> 00:04:30.804
economic profit they're just like,

00:04:30.804 --> 00:04:33.225
wow that's a good ...
people are doing better

00:04:33.225 --> 00:04:35.640
in that market than
their opportunity cost.

00:04:35.640 --> 00:04:37.736
So other competitors say
well I can't produce iPad's

00:04:37.736 --> 00:04:40.205
but I can start making
competitive products,

00:04:40.205 --> 00:04:43.326
so you'll see players like Samsung

00:04:43.326 --> 00:04:46.144
and we are seeing this,
sitting here in 2012

00:04:46.144 --> 00:04:48.470
and this is a work in progress for these

00:04:48.470 --> 00:04:49.933
competitors right over here.

00:04:49.933 --> 00:04:54.970
Samsung htc, HP, all the
tablet manufacturers,

00:04:54.970 --> 00:04:56.400
all the computer manufacturers
and they're pairing

00:04:56.400 --> 00:04:58.640
up, they're pairing up
with the operating system

00:04:58.640 --> 00:05:05.341
manufacturers like Microsoft
and Google's Android

00:05:05.341 --> 00:05:07.302
and they're making competitive products.

00:05:07.302 --> 00:05:10.325
And on top of it they are marketing it,

00:05:10.325 --> 00:05:12.403
they are marketing it heavily.

00:05:12.403 --> 00:05:14.133
(writing)they are marketing.

00:05:14.133 --> 00:05:15.604
They are trying to market the products

00:05:15.604 --> 00:05:17.139
as aggressively as possible.

00:05:17.139 --> 00:05:19.602
So, as their products become more and more

00:05:19.602 --> 00:05:21.600
comparable to an iPad,
or maybe even better

00:05:21.600 --> 00:05:23.553
in certain dimensions,
either cost or features

00:05:23.553 --> 00:05:25.182
and they market heavily.

00:05:25.182 --> 00:05:26.967
In the long run what's going to happen to

00:05:26.967 --> 00:05:28.809
Apple's demand curve?

00:05:28.809 --> 00:05:31.403
Well, at any given price
less will be demanded

00:05:31.403 --> 00:05:34.127
and so the demand curve will shift.

00:05:34.127 --> 00:05:36.143
The demand curve will shift to the left

00:05:36.143 --> 00:05:38.894
and so we could end up
with a new demand curve.

00:05:38.894 --> 00:05:40.554
I'll do it in a different shade of blue,

00:05:40.554 --> 00:05:44.516
that looks something ...
that looks something like,

00:05:44.516 --> 00:05:46.207
(writing) That looks something like that.

00:05:46.207 --> 00:05:49.376
This is our new demand curve,

00:05:49.376 --> 00:05:51.754
or we should say, maybe
our long run demand curve

00:05:51.754 --> 00:05:53.465
after these people have
made their products

00:05:53.465 --> 00:05:55.525
better and have marketed heavily.

00:05:55.525 --> 00:05:57.794
If that's the new long run demand curve

00:05:57.794 --> 00:06:00.528
then our long run marginal revenue curve

00:06:00.528 --> 00:06:02.926
was going to have twice the slope of that,

00:06:02.926 --> 00:06:04.857
so it's going to look something like this.

00:06:04.857 --> 00:06:06.501
If it's twice the slope it's going to hit

00:06:06.501 --> 00:06:10.667
right about ... it's going to look ...

00:06:10.667 --> 00:06:12.260
I can do a better job than that.

00:06:12.260 --> 00:06:14.292
Our new marginal revenue
... let me do it in a

00:06:14.292 --> 00:06:16.061
slightly different color,
I'll do it in pink.

00:06:16.061 --> 00:06:19.061
Our new marginal revenue curve will look

00:06:19.061 --> 00:06:20.453
something like that.

00:06:20.453 --> 00:06:22.984
This is long run marginal revenue.

00:06:22.984 --> 00:06:26.359
(writing) long run marginal revenue curve.

00:06:26.359 --> 00:06:29.609
Now what is the optimal quantity for Apple

00:06:29.609 --> 00:06:30.858
to produce?

00:06:30.858 --> 00:06:33.785
Now it's going to make economic profit,

00:06:33.785 --> 00:06:36.277
economic profit, economic
profit, all the way until

00:06:36.277 --> 00:06:38.453
this point right over here.

00:06:38.453 --> 00:06:41.118
Now we have this new,
I'll call it long run,

00:06:41.118 --> 00:06:43.532
long run quantity.

00:06:43.532 --> 00:06:45.387
Maybe I'll call it ... let me
do it in a different color.

00:06:45.387 --> 00:06:46.910
I'm using that pink too much.

00:06:46.910 --> 00:06:49.847
Long run quantity right over there

00:06:49.847 --> 00:06:52.066
and to figure out the revenue per unit

00:06:52.066 --> 00:06:55.149
or the price at that
quantity we just go up to

00:06:55.149 --> 00:06:57.117
the demand curve, our new demand curve.

00:06:57.117 --> 00:06:58.512
Remember our long run demand curve,

00:06:58.512 --> 00:06:59.989
it's right over there.

00:06:59.989 --> 00:07:01.399
It looks like, at least
the way I've drawn it,

00:07:01.399 --> 00:07:03.245
that the price hasn't changed much.

00:07:03.245 --> 00:07:05.580
We've got the same price,
but now what is our

00:07:05.580 --> 00:07:07.785
average economic profit per unit?

00:07:07.785 --> 00:07:10.583
The way I've drawn it,
the average total cost

00:07:10.583 --> 00:07:14.117
right over there are right
about what that price is.

00:07:14.117 --> 00:07:17.513
So, our average economic profit per unit

00:07:17.513 --> 00:07:19.180
goes down to zero.

00:07:19.180 --> 00:07:21.736
Over here we had this nice green height

00:07:21.736 --> 00:07:23.369
and now we have no height anymore.

00:07:23.369 --> 00:07:24.718
Even though we're selling
a good number of units

00:07:24.718 --> 00:07:27.784
our average economic
profit per unit is zero.

00:07:27.784 --> 00:07:29.715
Instead of an area over there,

00:07:29.715 --> 00:07:31.522
we're going to have the area of a line,

00:07:31.522 --> 00:07:33.282
which is essentially zero.

00:07:33.282 --> 00:07:36.936
Now we have zero economic,

00:07:36.936 --> 00:07:39.446
(writing) zero economic, economic,

00:07:39.446 --> 00:07:41.782
zero economic profit.

00:07:41.782 --> 00:07:43.364
The important thing to
realize for a monopolistic

00:07:43.364 --> 00:07:45.694
competitor and this wont
happen over night ...

00:07:45.694 --> 00:07:47.859
some would argue that
sitting here in 2012,

00:07:47.859 --> 00:07:50.857
early 2012, Apple is still
generating economic profit

00:07:50.857 --> 00:07:52.570
and it's always important to realize

00:07:52.570 --> 00:07:55.004
economic profit is different
than accounting profit.

00:07:55.004 --> 00:07:56.534
Accounting profit can be positive,

00:07:56.534 --> 00:08:00.003
economic profit can be
zero when accounting profit

00:08:00.003 --> 00:08:01.142
is positive.

00:08:01.142 --> 00:08:05.055
You can even have an economic loss

00:08:05.055 --> 00:08:06.936
and still have accounting profit.

00:08:06.936 --> 00:08:08.871
Some people would argue that right now

00:08:08.871 --> 00:08:10.870
Apple is still making
profits above and beyond

00:08:10.870 --> 00:08:13.571
even their opportunity
cost and this is actually

00:08:13.571 --> 00:08:15.936
a work in progress right now in 2012,

00:08:15.936 --> 00:08:18.582
that the demand curve
is shifting to the left,

00:08:18.582 --> 00:08:21.870
but eventually all of the
economic profit will be

00:08:21.870 --> 00:08:23.811
eaten up and there will be less incentive

00:08:23.811 --> 00:08:26.471
for all of these players
to be as aggressive.

00:08:26.471 --> 00:08:28.070
The important thing to realize with a

00:08:28.070 --> 00:08:32.277
monopolistic competitor is
sure, they're curves look

00:08:32.277 --> 00:08:34.806
like a monopolist, but the competition

00:08:34.806 --> 00:08:37.773
doesn't happen in terms
of supply of iPad's.

00:08:37.773 --> 00:08:39.869
None of these players can supply iPad's

00:08:39.869 --> 00:08:42.609
the competitive part happens
with all of these people

00:08:42.609 --> 00:08:44.607
producing substitutes and being aggressive

00:08:44.607 --> 00:08:47.357
about it and eating in to the monopolistic

00:08:47.357 --> 00:08:49.902
competitor's demand.


More on Nash equilibrium

WEBVTT
Kind: captions
Language: en

00:00:00.570 --> 00:00:03.260
The idea of a Nash equilibrium
is important enough

00:00:03.260 --> 00:00:05.896
that I think it
deserves its own video.

00:00:05.896 --> 00:00:07.270
And you may or
may not know, it's

00:00:07.270 --> 00:00:09.700
named for John
Nash, who was played

00:00:09.700 --> 00:00:12.440
by Russell Crowe in the
movie "A Beautiful Mind."

00:00:12.440 --> 00:00:14.940
And it's a game
theoretical concept.

00:00:14.940 --> 00:00:16.730
And game theory
sounds very fancy,

00:00:16.730 --> 00:00:18.791
but it really is just
the theory of games.

00:00:18.791 --> 00:00:20.790
And this prisoner's dilemma
that we talked about

00:00:20.790 --> 00:00:23.631
in the previous video
really is a game.

00:00:23.631 --> 00:00:25.630
The different players
have different strategies,

00:00:25.630 --> 00:00:27.830
and based on their
interacting strategies,

00:00:27.830 --> 00:00:29.390
you end up in different states.

00:00:29.390 --> 00:00:31.280
You end up with
different outcomes.

00:00:31.280 --> 00:00:34.354
And here's a definition of Nash
equilibrium from Princeton.

00:00:34.354 --> 00:00:36.270
And that's a good place
to get the definition,

00:00:36.270 --> 00:00:39.419
because that's where John Nash
spent a good bit of his career.

00:00:39.419 --> 00:00:41.210
And it is defined, or
this definition says,

00:00:41.210 --> 00:00:43.610
it's a stable state
of a system that

00:00:43.610 --> 00:00:45.770
involves several
interacting participants--

00:00:45.770 --> 00:00:48.630
in our prisoners' dilemma,
we had two participants--

00:00:48.630 --> 00:00:54.410
in which no participant can
gain by a change of strategy

00:00:54.410 --> 00:00:59.510
as long as all the other
participants remain unchanged.

00:00:59.510 --> 00:01:02.260
So let's think about the
different states of this system

00:01:02.260 --> 00:01:05.640
right over here and think
of whether any of them

00:01:05.640 --> 00:01:07.620
meet this criteria.

00:01:07.620 --> 00:01:09.590
So let's say, let me
number this one-- let's

00:01:09.590 --> 00:01:11.000
say that is state 1.

00:01:11.000 --> 00:01:12.340
This is state 2.

00:01:12.340 --> 00:01:16.690
This is state 3, and this
is state 4 right over here.

00:01:16.690 --> 00:01:22.460
So if we are sitting, if
we are sitting in state 1,

00:01:22.460 --> 00:01:25.890
can any of the
participants change

00:01:25.890 --> 00:01:28.490
their strategy-- can gain
by changing their strategy,

00:01:28.490 --> 00:01:30.970
assuming the other
participant is constant?

00:01:30.970 --> 00:01:33.810
So if we are sitting here in
state one right over here,

00:01:33.810 --> 00:01:37.390
so Al is denying and
Bill is denying-- well,

00:01:37.390 --> 00:01:43.990
Al can improve his situation
by changing his strategy.

00:01:43.990 --> 00:01:47.160
He can go from denying,
which is the scenario here,

00:01:47.160 --> 00:01:48.450
to confessing.

00:01:48.450 --> 00:01:51.337
So Al can change his
strategy and gain.

00:01:51.337 --> 00:01:52.420
Or you could go the other.

00:01:52.420 --> 00:01:55.110
Assuming Bill was
constant in the denial--

00:01:55.110 --> 00:01:56.360
or you could go the other way.

00:01:56.360 --> 00:02:02.880
If we're sitting here in state
4 and we assume Al is constant,

00:02:02.880 --> 00:02:06.170
Bill can improve his situation
by going from a denial

00:02:06.170 --> 00:02:06.870
to a confession.

00:02:06.870 --> 00:02:09.770
He can go from two
year to one year.

00:02:09.770 --> 00:02:12.480
So for both of those reasons--
if either of those were true,

00:02:12.480 --> 00:02:14.095
this would not be
a Nash equilibrium.

00:02:14.095 --> 00:02:15.220
But both of those are true.

00:02:15.220 --> 00:02:17.350
So this is definitely
not a Nash equilibrium.

00:02:21.490 --> 00:02:24.960
I gave two examples in
which a participant can

00:02:24.960 --> 00:02:28.250
gain by a change of strategy as
long as the other participant

00:02:28.250 --> 00:02:29.960
remains unchanged.

00:02:29.960 --> 00:02:33.200
This move was one example,
and this was a move by Al,

00:02:33.200 --> 00:02:35.340
with Bill's denial constant.

00:02:35.340 --> 00:02:39.340
This was a move by Bill,
with Al's denial constant.

00:02:39.340 --> 00:02:41.410
Not a Nash equilibrium.

00:02:41.410 --> 00:02:44.900
Now let's think about--
let's think about state 2.

00:02:44.900 --> 00:02:52.360
If we are sitting in state
2, assuming Bill is constant,

00:02:52.360 --> 00:02:55.670
can Al change to
improve his outcome?

00:02:55.670 --> 00:02:57.560
So can Al change to
improve his outcome?

00:02:57.560 --> 00:03:00.820
In state 2, Al was
only getting one year.

00:03:00.820 --> 00:03:03.520
If Al goes from a
confession to a denial

00:03:03.520 --> 00:03:05.230
he's going to get two years.

00:03:05.230 --> 00:03:10.740
So Al cannot change his
strategy and get a gain here.

00:03:10.740 --> 00:03:12.250
So far it's looking good.

00:03:12.250 --> 00:03:14.780
But let's think of it
from Bill's point of view.

00:03:14.780 --> 00:03:19.370
So if we are in state 2, if we
are in state 2 right over here,

00:03:19.370 --> 00:03:22.060
and we assume Al is
constant, can Bill

00:03:22.060 --> 00:03:24.000
do something that
changes things?

00:03:24.000 --> 00:03:27.430
Well, sure, Bill can go
from denying to confessing.

00:03:27.430 --> 00:03:29.480
If he goes from denying
to confessing he

00:03:29.480 --> 00:03:33.200
goes from 10 years in prison
to three years in prison.

00:03:33.200 --> 00:03:35.470
So I've given an example
of a participant who

00:03:35.470 --> 00:03:38.320
can gain by a change of
strategy as long as all

00:03:38.320 --> 00:03:40.190
of the other participants
remain unchanged.

00:03:40.190 --> 00:03:41.930
Both of them don't have
to be able to do this.

00:03:41.930 --> 00:03:43.370
You just need to
have one of them

00:03:43.370 --> 00:03:45.400
for it to not be a
Nash equilibrium.

00:03:45.400 --> 00:03:49.110
Because Bill can have a
gain by a change of strategy

00:03:49.110 --> 00:03:52.220
holding Al's strategy
constant, so holding

00:03:52.220 --> 00:03:55.220
Al's strategy in the
confession, then this

00:03:55.220 --> 00:03:57.360
is not a Nash equilibrium.

00:03:57.360 --> 00:04:00.160
So this is not Nash,
because you have

00:04:00.160 --> 00:04:03.640
this movement can occur to a
more favorable state for Bill

00:04:03.640 --> 00:04:05.480
holding Al constant.

00:04:05.480 --> 00:04:08.210
Now, let's go to state 3.

00:04:08.210 --> 00:04:09.850
Let's think about this.

00:04:09.850 --> 00:04:13.940
So if we're in state 3,
so this is Bill confessing

00:04:13.940 --> 00:04:18.070
and Al denying-- so let's first
think about Al's point of view.

00:04:18.070 --> 00:04:21.339
If we assume Bill is
constant in his confession,

00:04:21.339 --> 00:04:23.550
can Al improve his scenario?

00:04:23.550 --> 00:04:24.480
Well, sure.

00:04:24.480 --> 00:04:26.230
He can go from
denying, which is what

00:04:26.230 --> 00:04:28.750
would have to be in
state 3, to confessing.

00:04:28.750 --> 00:04:32.990
So he could move in this
direction right over here.

00:04:32.990 --> 00:04:34.700
And that by itself
is enough evidence

00:04:34.700 --> 00:04:36.516
that this is not a
Nash equilibrium.

00:04:36.516 --> 00:04:38.140
We don't even have
to think about Bill.

00:04:38.140 --> 00:04:38.980
And it's symmetric.

00:04:38.980 --> 00:04:41.521
There's actually nothing that
Bill could do in this scenario,

00:04:41.521 --> 00:04:43.530
holding Al constant, that
could improve things.

00:04:43.530 --> 00:04:45.680
Bill would not want to
go from here to here.

00:04:45.680 --> 00:04:48.100
But just by the fact that Al
could go from here to here,

00:04:48.100 --> 00:04:52.140
holding Bill constant,
tells you that this is not

00:04:52.140 --> 00:04:54.300
a Nash equilibrium.

00:04:54.300 --> 00:04:55.985
Now let's go to scenario 4.

00:04:55.985 --> 00:04:57.360
And you know where
this is going,

00:04:57.360 --> 00:04:58.964
because you watched
the last video.

00:04:58.964 --> 00:05:00.630
But it's a little--
I'm going through it

00:05:00.630 --> 00:05:02.860
in a little bit in more detail.

00:05:02.860 --> 00:05:05.990
In state 4, they
are both confessing.

00:05:05.990 --> 00:05:08.320
Now let's look at it
from Al's point of view.

00:05:08.320 --> 00:05:10.130
And we're going to
hold Bill constant.

00:05:10.130 --> 00:05:11.589
We're going to hold
Bill unchanged.

00:05:11.589 --> 00:05:13.505
So we're going to have
to stay in this column.

00:05:13.505 --> 00:05:15.880
We're going to say that,
assume that Bill's confessing.

00:05:15.880 --> 00:05:18.720
From Al's point of view,
if we are in state 1,

00:05:18.720 --> 00:05:21.907
can he change his strategy
to get a better outcome?

00:05:21.907 --> 00:05:24.240
Well, the only thing he could
do is go from a confession

00:05:24.240 --> 00:05:24.897
to a denial.

00:05:24.897 --> 00:05:26.230
But that's not going to do good.

00:05:26.230 --> 00:05:28.146
He's going to go from
three years to 10 years.

00:05:28.146 --> 00:05:32.120
So Al cannot gain by
a change of strategy,

00:05:32.120 --> 00:05:34.965
as long as all the
participants remain unchanged.

00:05:34.965 --> 00:05:37.090
Now let's think about it
from Bill's point of view.

00:05:37.090 --> 00:05:38.910
We're in this state
right over here.

00:05:38.910 --> 00:05:40.710
We're going to assume
that Al is constant,

00:05:40.710 --> 00:05:43.990
that Al is in the
confession mode.

00:05:43.990 --> 00:05:47.080
So Bill, right now, in
state 4, is confessing.

00:05:47.080 --> 00:05:48.990
His only option is to deny.

00:05:48.990 --> 00:05:51.470
But by doing that, he'll go
from three years in prison

00:05:51.470 --> 00:05:52.570
to 10 years in prison.

00:05:52.570 --> 00:05:54.020
So he's not going to gain.

00:05:54.020 --> 00:05:55.960
So he, too, cannot gain.

00:05:55.960 --> 00:05:57.790
So we've just found
a state in state 4

00:05:57.790 --> 00:06:01.860
which no participant can
gain by a change of strategy

00:06:01.860 --> 00:06:05.300
as long as all other
participants remain unchanged.

00:06:05.300 --> 00:06:06.870
And this part is important.

00:06:06.870 --> 00:06:10.020
Because we're not saying that
both can change simultaneously.

00:06:10.020 --> 00:06:12.280
You are not, in
this payoff matrix,

00:06:12.280 --> 00:06:14.270
allowing a diagonal move.

00:06:14.270 --> 00:06:17.910
And so no participant can
gain, neither Al nor Bill,

00:06:17.910 --> 00:06:19.540
holding the other one constant.

00:06:19.540 --> 00:06:22.596
This is a Nash equilibrium.

00:06:26.150 --> 00:06:27.500
This one right here.

00:06:27.500 --> 00:06:30.840
And this is a stable state.


Prisoners' dilemma and Nash equilibrium

WEBVTT
Kind: captions
Language: en

00:00:00.820 --> 00:00:03.540
On the same day,
police have made two

00:00:03.540 --> 00:00:06.150
at first unrelated arrests.

00:00:06.150 --> 00:00:08.560
They arrest a
gentleman named Al.

00:00:08.560 --> 00:00:11.450
And they caught him red
handed selling drugs.

00:00:11.450 --> 00:00:13.070
So it's an open and shut case.

00:00:13.070 --> 00:00:16.820
And the same day, they catch
a gentleman named Bill.

00:00:16.820 --> 00:00:20.120
And he is also caught red
handed, stealing drugs.

00:00:20.120 --> 00:00:22.840
And they bring them separately
to the police station.

00:00:22.840 --> 00:00:25.670
And they tell them, look,
this is an open and shut case.

00:00:25.670 --> 00:00:27.784
You're going to get
convicted for drug dealing

00:00:27.784 --> 00:00:29.200
and you're going
to get two years.

00:00:29.200 --> 00:00:30.900
And they tell this to
each of them individually.

00:00:30.900 --> 00:00:32.400
They were selling the
same type of drugs,

00:00:32.400 --> 00:00:33.441
just happened to be that.

00:00:33.441 --> 00:00:35.510
But they were doing it
completely independently.

00:00:35.510 --> 00:00:39.270
Two years for drugs
is what's going

00:00:39.270 --> 00:00:41.829
to happen assuming nothing else.

00:00:41.829 --> 00:00:43.620
But then the district
attorney has a chance

00:00:43.620 --> 00:00:46.080
to chat with each of
these gentleman separately

00:00:46.080 --> 00:00:47.690
and while he's
chatting with them

00:00:47.690 --> 00:00:50.145
he reinforces the idea this
is an open and shut case

00:00:50.145 --> 00:00:51.020
for the drug dealing.

00:00:51.020 --> 00:00:54.050
They're each going to get two
years, if nothing else happens.

00:00:54.050 --> 00:00:58.280
But then he starts to realize
that these two characters look

00:00:58.280 --> 00:01:00.760
like-- he starts to have a
suspicion, for whatever reason,

00:01:00.760 --> 00:01:02.760
that these were the two
characters that actually

00:01:02.760 --> 00:01:04.599
committed a much
more serious offense.

00:01:04.599 --> 00:01:09.010
That they had committed a major
armed robbery a few weeks ago.

00:01:09.010 --> 00:01:13.160
And all the district
attorney has to go on

00:01:13.160 --> 00:01:15.770
is his hunch, his suspicion.

00:01:15.770 --> 00:01:17.710
He has no hard evidence.

00:01:17.710 --> 00:01:20.520
So what he wants to do is
try to get a deal with each

00:01:20.520 --> 00:01:22.910
of these guys so that
they have an incentive

00:01:22.910 --> 00:01:25.410
to essentially
snitch on each other.

00:01:25.410 --> 00:01:27.222
So what he tells each
of them is, look,

00:01:27.222 --> 00:01:29.180
you're going to get two
years for drug dealing.

00:01:29.180 --> 00:01:32.220
That's kind of guaranteed.

00:01:32.220 --> 00:01:39.960
But he says, look,
if you confess

00:01:39.960 --> 00:01:47.040
and the other doesn't
then you will get 1 year.

00:01:50.560 --> 00:01:56.880
And the other guy
will get 10 years.

00:01:56.880 --> 00:02:00.050
So he's telling Al, look,
we caught Bill, too, just

00:02:00.050 --> 00:02:00.820
randomly today.

00:02:00.820 --> 00:02:02.810
If you confess that
it was you and Bill

00:02:02.810 --> 00:02:05.217
who performed that
armed robbery your term

00:02:05.217 --> 00:02:07.550
is actually going to go down
from two years to one year.

00:02:07.550 --> 00:02:09.110
But Bill is obviously
going to have

00:02:09.110 --> 00:02:10.880
to spend a lot
more time in jail.

00:02:10.880 --> 00:02:14.340
Especially because he is
not cooperating with us.

00:02:14.340 --> 00:02:16.080
He is not confessing.

00:02:16.080 --> 00:02:19.410
But then, the other
statement is also true.

00:02:19.410 --> 00:02:28.770
If you deny and the
other confesses now

00:02:28.770 --> 00:02:29.750
it switches around.

00:02:29.750 --> 00:02:33.180
You will get 10 years, because
you're not cooperating.

00:02:33.180 --> 00:02:36.060
And the other, your
co-conspirator,

00:02:36.060 --> 00:02:39.335
will get a reduced sentence--
will get the one year.

00:02:39.335 --> 00:02:40.710
So this is like
telling Al, look,

00:02:40.710 --> 00:02:43.370
if you deny that you
were the armed robber

00:02:43.370 --> 00:02:45.850
and Bill snitches
you out, then you're

00:02:45.850 --> 00:02:47.660
going to get 10 years in prison.

00:02:47.660 --> 00:02:50.630
And Bill's only going to
get one year in prison.

00:02:50.630 --> 00:02:57.830
And if both of you
essentially confess,

00:02:57.830 --> 00:02:59.770
you will both get three years.

00:03:02.700 --> 00:03:06.250
So this scenario is called
the prisoner's dilemma.

00:03:06.250 --> 00:03:08.000
Because we'll see
in a second there

00:03:08.000 --> 00:03:13.130
is a globally optimal scenario
for them where they both deny

00:03:13.130 --> 00:03:14.970
and they both get two years.

00:03:14.970 --> 00:03:16.850
But we'll see, based
on their incentives,

00:03:16.850 --> 00:03:20.427
assuming they don't have any
unusual loyalty to each other--

00:03:20.427 --> 00:03:22.010
and these are hardened
criminals here.

00:03:22.010 --> 00:03:24.385
They're not brothers or related
to each other in any way.

00:03:24.385 --> 00:03:26.160
They don't have any
kind of loyalty pact.

00:03:26.160 --> 00:03:29.400
We'll see that they
will rationally pick,

00:03:29.400 --> 00:03:33.200
or they might rationally
pick, a non-optimal scenario.

00:03:33.200 --> 00:03:35.390
And to understand that I'm
going to draw something

00:03:35.390 --> 00:03:36.570
called a payoff matrix.

00:03:39.630 --> 00:03:42.090
So let me do it
right here for Bill.

00:03:42.090 --> 00:03:45.600
So Bill has two options.

00:03:45.600 --> 00:03:49.610
He can confess to
the armed robbery

00:03:49.610 --> 00:03:51.670
or he can deny that
he had anything--

00:03:51.670 --> 00:03:55.190
that he knows anything
about the armed robbery.

00:03:55.190 --> 00:03:57.020
And Al has the same two options.

00:03:57.020 --> 00:04:03.950
Al can confess and Al can deny.

00:04:03.950 --> 00:04:05.950
And since it's called
a payoff matrix,

00:04:05.950 --> 00:04:09.250
let me draw some grids here.

00:04:09.250 --> 00:04:11.380
Let me draw some grids
and let's think about all

00:04:11.380 --> 00:04:14.340
of the different scenarios
and what the payoffs would be.

00:04:14.340 --> 00:04:17.720
If Al confesses and
Bill confesses then

00:04:17.720 --> 00:04:19.070
we're in scenario four.

00:04:19.070 --> 00:04:23.100
They both get three
years in jail.

00:04:23.100 --> 00:04:29.560
So they both will get three
for Al and three for Bill.

00:04:29.560 --> 00:04:35.670
Now, if Al confesses
and Bill denies,

00:04:35.670 --> 00:04:38.940
then we are in scenario two
from Al's point of view.

00:04:38.940 --> 00:04:40.580
Al is only going
to get one year.

00:04:43.370 --> 00:04:45.070
But Bill is going
to get 10 years.

00:04:47.942 --> 00:04:49.400
Now, if the opposite
thing happens,

00:04:49.400 --> 00:04:51.360
if Bill confesses and
Al denies, then it

00:04:51.360 --> 00:04:52.800
goes the other way around.

00:04:52.800 --> 00:04:55.114
Al's going to get 10
years for not cooperating.

00:04:55.114 --> 00:04:56.530
And Bill's going
to have a reduced

00:04:56.530 --> 00:04:59.490
sentence of one year
for cooperating.

00:04:59.490 --> 00:05:05.861
And then if they both deny,
they're in scenario one,

00:05:05.861 --> 00:05:08.360
where they're both just going
to get their time for the drug

00:05:08.360 --> 00:05:09.270
dealing.

00:05:09.270 --> 00:05:15.690
So Al will get two years,
and Bill will get two years.

00:05:15.690 --> 00:05:17.830
Now, I alluded to this
earlier in the video.

00:05:17.830 --> 00:05:21.160
What is the globally
optimal scenario for them?

00:05:21.160 --> 00:05:23.340
Well, it's this scenario,
where they both deny

00:05:23.340 --> 00:05:25.610
having anything to do
with the armed robbery.

00:05:25.610 --> 00:05:28.060
Then they both get two years.

00:05:28.060 --> 00:05:31.210
But what we'll see is
actually somewhat rational,

00:05:31.210 --> 00:05:33.520
assuming that they don't
have any strong loyalties

00:05:33.520 --> 00:05:36.180
to each other, or strong level
of trust with the other party,

00:05:36.180 --> 00:05:37.200
to not go there.

00:05:37.200 --> 00:05:39.720
And it's actually rational
for both of them to confess.

00:05:39.720 --> 00:05:42.780
And the confession is
actually a Nash equilibrium.

00:05:42.780 --> 00:05:45.800
And we'll talk more about
this, but a Nash equilibrium

00:05:45.800 --> 00:05:49.750
is where each party has
picked a choice given

00:05:49.750 --> 00:05:52.230
the choices of the other party.

00:05:52.230 --> 00:05:53.896
So when we think
of, or each party

00:05:53.896 --> 00:05:58.620
has to pick the optimal
choice, given whatever choice

00:05:58.620 --> 00:06:00.090
the other party picks.

00:06:00.090 --> 00:06:03.210
And so from Al's point of
view, he says, well, look,

00:06:03.210 --> 00:06:06.430
I don't know whether Bill
is confessing or denying.

00:06:06.430 --> 00:06:08.300
So let's say he confesses.

00:06:08.300 --> 00:06:10.200
What's better for me to do?

00:06:10.200 --> 00:06:12.910
If he confesses, and I confess,
then I get three years.

00:06:12.910 --> 00:06:15.820
If he confesses and I
deny I get 10 years.

00:06:15.820 --> 00:06:19.370
So if he confesses, it's better
for me to confess as well.

00:06:19.370 --> 00:06:23.237
So this is a preferable
scenario to this one down here.

00:06:23.237 --> 00:06:24.820
Now, I don't know
that Bill confessed.

00:06:24.820 --> 00:06:26.070
He might deny.

00:06:26.070 --> 00:06:28.210
If I assume Bill
denied, is it better

00:06:28.210 --> 00:06:32.510
for me to confess and get one
year or deny and get two years?

00:06:32.510 --> 00:06:35.390
Well, once again, it's
better for me to confess.

00:06:35.390 --> 00:06:38.790
And so regardless of whether
Bill confesses or denies,

00:06:38.790 --> 00:06:42.390
so this once again, the
optimal choice for Al to pick,

00:06:42.390 --> 00:06:46.020
taking into account Bill's
choices, is to confess.

00:06:46.020 --> 00:06:48.550
If Bill confesses, Al is
better off confessing.

00:06:48.550 --> 00:06:50.996
And if Bill denies, Al
is better off confessing.

00:06:50.996 --> 00:06:52.870
Now, we look at it from
Bill's point of view.

00:06:52.870 --> 00:06:54.500
And it's completely symmetric.

00:06:54.500 --> 00:06:58.220
If Bill says, well, I don't know
if Al is confessing or denying.

00:06:58.220 --> 00:07:01.950
If Al confesses, I can
confess and get three years

00:07:01.950 --> 00:07:03.890
or I can deny and get 10 years.

00:07:03.890 --> 00:07:06.300
Well, three years in
prison is better than 10.

00:07:06.300 --> 00:07:09.020
So I will go-- I would
go for the three years

00:07:09.020 --> 00:07:10.750
if I know Al is confessing.

00:07:10.750 --> 00:07:12.860
But I don't know that Al
is definitely confessing.

00:07:12.860 --> 00:07:14.030
He might deny.

00:07:14.030 --> 00:07:17.840
If Al is denying, I could
confess and get one year

00:07:17.840 --> 00:07:19.580
or I could deny
and get two years.

00:07:19.580 --> 00:07:23.050
Well, once again, I
would want to confess

00:07:23.050 --> 00:07:24.470
and get the one year.

00:07:24.470 --> 00:07:27.100
So Bill, taking into account
each of the scenarios

00:07:27.100 --> 00:07:33.280
that Al might take, it's always
better for him to confess.

00:07:33.280 --> 00:07:35.027
And so this is interesting.

00:07:35.027 --> 00:07:36.610
They are rationally
deducing that they

00:07:36.610 --> 00:07:40.990
should get to this scenario,
this Nash equilibrium state,

00:07:40.990 --> 00:07:43.590
as opposed to this
globally optimal state.

00:07:43.590 --> 00:07:46.360
They're both getting three years
by both confessing as opposed

00:07:46.360 --> 00:07:49.490
to both of them getting
two years by both denying.

00:07:49.490 --> 00:07:54.290
The problem with this one is
this is an unstable state.

00:07:54.290 --> 00:07:58.140
If one of them assumes that the
other one has-- if one of them

00:07:58.140 --> 00:08:00.810
assumes that they're somehow
in that state temporarily,

00:08:00.810 --> 00:08:04.370
they say, well, I can
always improve my scenario

00:08:04.370 --> 00:08:07.630
by changing what I want to do.

00:08:07.630 --> 00:08:10.130
If Al thought that Bill
was definitely denying,

00:08:10.130 --> 00:08:12.110
Al could improve
his circumstance

00:08:12.110 --> 00:08:14.770
by moving out of that state
and confessing and only

00:08:14.770 --> 00:08:15.950
getting one here.

00:08:15.950 --> 00:08:20.140
Likewise, if Bill thought that
maybe Al is likely to deny,

00:08:20.140 --> 00:08:23.572
he realizes that he can optimize
by moving in this direction.

00:08:23.572 --> 00:08:25.280
Instead of denying,
getting, two and two,

00:08:25.280 --> 00:08:28.290
he could move in that
direction right over there.

00:08:28.290 --> 00:08:31.270
So this is an unstable
optimal scenario.

00:08:31.270 --> 00:08:34.000
But this Nash equilibrium,
this state right over here,

00:08:34.000 --> 00:08:36.280
is actually very,
very, very stable.

00:08:36.280 --> 00:08:40.490
If they assume, it's
better for each of them

00:08:40.490 --> 00:08:43.490
to confess regardless of
what the other ones does.

00:08:43.490 --> 00:08:45.890
And assuming all
of the other actors

00:08:45.890 --> 00:08:50.480
have chosen their strategy,
there's no incentive for Bill.

00:08:50.480 --> 00:08:53.800
So if assuming everyone else
has changed their strategy,

00:08:53.800 --> 00:08:56.670
you can only move
in that direction.

00:08:56.670 --> 00:08:59.310
If you're Bill, you can go
from the Nash equilibrium

00:08:59.310 --> 00:09:02.380
of confessing to denying,
but you're worse off.

00:09:02.380 --> 00:09:03.760
So you won't want to do that.

00:09:03.760 --> 00:09:06.100
Or you could move in
this direction, which

00:09:06.100 --> 00:09:08.020
would be Al changing
his decision.

00:09:08.020 --> 00:09:10.950
But once again, that gives
a worse outcome for Al.

00:09:10.950 --> 00:09:13.090
You're going from three
years to 10 years.

00:09:13.090 --> 00:09:15.830
So this is the equilibrium
state, the stable state,

00:09:15.830 --> 00:09:18.870
that both people will pick
something that is not optimal

00:09:18.870 --> 00:09:19.935
globally.