WEBVTT

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So far, we've been
focused on the elasticity

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of demand for only one good.

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We've thought about how
changes in the price

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of that good affect
changes in its quantity.

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Now what we're going to explore
is how we can go across goods.

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So we're going to talk about
the cross elasticity of demand.

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And there's multiple different
scenarios we could think about,

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but it's really thinking about
how a price change in one good

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might affect the quantity
demanded in another good.

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And to see an example of this,
think about two airlines--

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two competing airlines-- maybe
it's the same exact route going

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at the exact same time, maybe
between New York and London.

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So airline one, right
over here-- airline two,

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very competitive,
price right over here

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is $1,000 for a round trip.

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Quantity demanded
is 200 tickets,

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let's say, in a given week.

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Airline two, price is
$1,000 for the round trip,

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and the quantity demanded
is 200 tickets as well.

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Now let's think about
what will happen.

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What will happen if
airline one raises

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its price from $1,000 to $1,100?

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In fact, we could
even do something

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less dramatic than that,
to $1,050-- so a relatively

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small increase in price.

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And remember, when we think
about the percentage price

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increase, when we're thinking
about elasticities in general,

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we don't just say,
OK, $50 on top

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of $1,000, that's a
5% price increase.

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That's what we would do
in everyday thinking.

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If you said you went
from $1,000 to $1,050,

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you would say that's a $50
increase on a base of $1,000

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or that is a 5% increase.

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But when you think
about elasticities,

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because we want to have the same
percent change between-- if you

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go from $1,000 to $1,050,
or if you go from $1,050

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down to 1,000-- we actually use
the average point as a base.

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So the percent change
in this scenario--

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let me write it right over here.

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So our percent change--
and I'll write it

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in quotes, because
it's a little bit

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different than what you do
in traditional mathematics

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when you think about
percent changes-- is

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you had a 50 change in price.

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Your price went up by
50, and on our base

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we will use 1,025, which is
the average of 1,000 and 1,050.

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And so that gives us a
change of 50 divided by 1,025

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is equal to, let's
say, roughly 4.9%.

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So this is approximately 4.9%,
we'll say, "increase" in price,

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although we're going to put
that increase in quotes,

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because we're using
it on the average.

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And we do that so that if we
said it was 1,050 to 1,000,

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it would still be a 4.9%
decrease using this same idea--

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using the midpoint as the base.

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Now, when that happens--
Everyone today,

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they use these
travel sites where

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you can compare
prices-- If these really

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are the exact same route, going
from the exact same airport

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to the exact same other
airport in London,

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leaving at the exact
same time, everyone

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is going to gravitate
to this one now,

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because it's only $1,000--
even just to save $50.

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Why would they ride
on this airline?

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So this quantity demand
is going to go to 0.

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And this quantity demanded
is going to go to 400.

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And we're not going to think
about the actual capacity

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of the planes and all that.

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We're going to have a
very simple model here.

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So what was the percent
change in quantity for airline

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two right over here?

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Well, once again, our change
in quantity is 200, not 400.

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We went from 200 to 400.

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So we gained 200.

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And our base, we want to use
the average of 200 and 400,

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which is 300.

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And so this is
approximately 67%.

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So we have, all of a
sudden, our cross elasticity

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of demand for airline
two's tickets,

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relative to a1's price.

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And we get the percent
change in the quantity

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demanded for a2's tickets, which
is 67% over the percent change,

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not in a2's price change,
but in a1's price change.

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That's why we call
it cross elasticity.

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We're going from
one good to another.

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So let's just say, for
simplicity, roughly 5%.

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And so you do the math.

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So if you have 67% divided by
5%, you get to roughly 13.4.

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So this is approximately 13.4.

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So you have a very high
cross elasticity of demand.

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In fact, if you even
increase this, maybe by $5,

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you might have had
the same effect.

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And so you would have had
a very large number here.

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And that situation right here,
for this cross elasticity

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of demand-- it's
because these things

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are near perfect substitutes.

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The way that we set up
this problem, we said,

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well, people don't care
which one they take.

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They're just going to
go for the cheapest one.

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And so when you have
near substitutes,

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or nearly perfect
substitutes, for each other,

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like this example right here,
the cross elasticity of demand

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approaches infinity.

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It gets higher and
higher and higher.

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In theory, if these are really,
really, really identical,

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even if you raise this a
penny, people will say, well,

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why would I waste a penny?

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I would just use airline two.

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And so this number would be
even lower right over here.

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And so this thing might
approach infinity.

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And notice this was a positive.

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When we just did regular
price elasticity of demand,

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the only way that you
would increase quantity

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for a traditional goods
was by lowering price.

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But here, we raise price on a
substitute competitive product,

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and we raise the demand
for airline two's

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product, which actually
made a lot of sense.

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So it wasn't a
negative relationship.

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It's actually a positive
value right over here.

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But you could have
things in other--

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you could have that
negative relationship using

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cross elasticity of demand.

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This is an example
of a substitute.

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We could think about the
example of a complement.

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So what if we're
talking about e-books?

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So let's say I have
some type of an e-book,

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and the current quantity
demanded in a given week

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is 1,000.

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And let's say that the price
of an e-reader that you

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would need for my
e-book is $100.

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But let's say that
price of the e-reader

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goes down from $100 to $80.

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So you had a $20
decrease in price.

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Well, what's going to happen to
my e-book, assuming its price

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does not change?

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Well, then the quantity demanded
for my e-book will go up.

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So let's say the quantity
demanded for my e-book goes up

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by 100, because more
people are going

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to be able to afford
this, or they're

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going to have money
left over when

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they buy this to
buy more e-books.

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And so I don't even know what
the price for my e-book is,

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but at a given price point, the
quantity demanded will go up.

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And so this goes to 1,100.

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And so I'll leave it
to you to calculate

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this price elasticity of demand.

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But you will see that you will
actually get a negative value,

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like we're used to
seeing for regular price

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elasticity of demand.

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And when you do
calculate it, remember,

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you want to do your
percent price change

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in e-book quantity over percent
change in e-reader price.

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And the other thing
you have to remember,

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you don't just take
negative 20 over 100.

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You take negative 20 over
the average of these two,

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when you're thinking of it
in the elasticity context.

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So this right over
here-- actually,

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maybe we'll just
work it through.

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Pause it, and try
to do it yourself.

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So this value right over
here is negative 20 over 90--

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the average of those two--
and this value right over here

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is going to be plus 100 over
the average of these two.

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So the average of
those two is 1,050.

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And so this is 100
divided by 1,050,

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which gets you to about 0.95.

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So about 9 and 1/2% change in
quantity demanded for my book.

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And then this
denominator right here

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is negative 20 divided by 90.

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So you get a drop of 22%.

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And so if you divide the
numerator by the denominator,

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you get 0.952 divided
by negative 0.22222--

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I'll just put couple
of 2's there--

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and you get a negative 0.43.

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So this is equal
to negative 0.43.

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And this makes sense.

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If you lower the
price of an e-reader--

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this complement product,
a product that goes along

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with my e-book-- it
increases the demand.

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So just like you get with
price elasticity of demand,

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you get a negative
value over here.

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And what about completely
two unrelated products?

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So let's say that
I have basketballs,

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and the price of basketballs
goes from, let's say,

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$20 to $30.

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What's going to
happen to my e-book?

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Well, my e-book's
not going to change.

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It's going to stay at $1,000.

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So my percent change in the
quantity demanded of my e-book

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is going to be 0
in this example.

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So we're going to
have 0, when we

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want to do this cross
elasticity of demand,

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over my percent
change in basketballs,

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which would be 30 over 25.

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So whatever that
is-- 30 over 25 would

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be 10 over 25-- which
is a 40% increase.

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So that would be 0 over
40%, which equals 0.

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So for unrelated
products, products

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where the price of
change in one of them

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does not affect the quantity
demanded in the other,

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it makes complete
sense that you have

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a 0 cross elasticity of demand.

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If they're complements, you
would have a negative cross

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elasticity of demand.

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And if they're substitutes,
you would have a positive one.

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And the closer the substitutes
they are, the more positive

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your cross elasticity of
demand is going to be.