WEBVTT

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So let's just review what
we've seen with budget lines.

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Let's say I'm
making $20 a month.

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So my income is $20 per month.

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Let's say per month.

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The price of chocolate
is $1 per bar.

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And the price of
fruit is $2 per pound.

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And we've already
done this before,

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but I'll just redraw
a budget line.

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So this axis, let's say this
is the quantity of chocolate.

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I could have picked
it either way.

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And that is the
quantity of fruit.

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If I spend all my
money on chocolate,

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I could buy 20 bars
of chocolate a month.

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So that is 20.

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This is 10 right over here.

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At these prices, if I
spent all my money on fruit

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I could buy 10 pounds per month.

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So this is 10.

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So that's 10 pounds per month.

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That would be 20.

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And so I have a budget
line that looks like this.

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And the equation of this budget
line is going to be-- well,

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I could write it like this.

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My budget, 20, is going
to be equal to the price

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of chocolate, which is 1, times
the quantity of chocolate.

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So this is 1 times the
quantity of chocolate,

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plus the price of
fruit, which is

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2 times the quantity of fruit.

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And if I want to
write this explicitly

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in terms of my
quantity of chocolate,

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since I put that
on my vertical axis

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and that tends to be
the more dependent axis,

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I can just subtract 2
times the quantity of fruit

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from both sides.

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And I can flip them.

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And I get my
quantity of chocolate

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is equal to 20 minus 2
times my quantity of fruit.

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And I get this budget
line right over there.

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We've also looked at the idea
of an indifference curve.

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So for example,
let's say I'm sitting

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at some point on my
budget line where

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I have-- let's say I am
consuming 18 bars of chocolate

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and 1 pound of fruit.

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18-- and you can
verify that make sense,

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it's going to be $18
plus $2, which is $20.

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So let's say I'm at this
point on my budget line.

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18 bars of chocolate,
so this is in bars,

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and 1 pound of fruit per month.

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So that is 1.

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And this is in pounds.

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And this is chocolate, and
this is fruit right over here.

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Well, we know we have this
idea of an indifference curve.

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There's different combinations
of chocolate and fruit

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to which we are
indifferent, to which

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we would get the same
exact total utility.

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And so we can plot
all of those points.

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I'll do it in white.

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It could look
something like this.

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I'll do it as a dotted line, it
makes it a little bit easier.

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So let me draw it like this.

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So let's say I'm
indifferent between any

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of these points, any of those
points right over there.

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Let me draw it a
little bit better.

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So between any of these
points right over there.

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So for example, I could
have 18 bars of chocolate

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and 1 pound of fruit,
or I could have--

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let's say that is
4 bars of chocolate

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and roughly 8 pounds of fruit.

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I'm indifferent.

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I get the same
exact total utility.

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Now, am I maximizing
my total utility

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at either of those points?

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Well, we've already
seen that anything

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to the top right
of our indifference

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curve of this white curve right
over here-- let me label this.

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This is our indifference curve.

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Everything to the top right
of our indifference curve

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is preferable.

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We're going to get
more total utility.

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So let me color that in.

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So everything to the top right
of our indifference curve

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is going to be preferable.

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So all of these other
points on our budget

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line, even a few points
below or budget line,

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where we would actually
save money, are preferable.

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So either of these
points are not

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going to maximize
our total utility.

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We can maximize or total utility
at all of these other points

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in between, along
our budget line.

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So to actually maximize
our total utility

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what we want to do is find
a point on our budget line

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that is just tangent, that
exactly touches at exactly one

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point one of our
indifference curves.

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We could have an infinite
number of indifference curves.

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There could be another
indifference curve

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that looks like that.

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There could be another
indifferent curve

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that looks like that.

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All that says is that we are
indifferent between any points

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on this curve.

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And so there is an indifference
curve that touches exactly

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this budget line, or exactly
touches the line at one point.

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And so I might have
an indifference curve

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that looks like this.

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Let me do this in a
vibrant color, in magenta.

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So I could have an indifference
curve that looks like this.

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And because it's tangent, it
touches at exactly one point.

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And also the slope of
my indifference curve,

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which we've learned
was the marginal rate

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of substitution, is the exact
same as the slope of our budget

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line right over there,
which we learned

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earlier was the relative price.

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So this right about here
is the optimal allocation

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on our budget line.

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That right here is optimal.

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And how do we know
it is optimal?

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Well, there is no other
point on the budget line

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that is to the top right.

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In fact, every other
point on our budget line

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is to the bottom left of
this indifference curve.

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So every other point on our
budget line is not preferable.

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So remember, everything
below an indifference curve--

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so all of this shaded area.

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Let me actually do
it in another color.

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Because indifference
curve, we are different.

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But everything below an
indifference curve, so all

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of this area in green,
is not preferable.

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And every other point
on the budget line

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is not preferable to that
point right over there.

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Because that's the only point--
or I guess you could say,

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every other point
on our budget line

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is not preferable to the points
on the indifference curve.

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So they're also not preferable
to that point right over there

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which actually is on
the indifference curve.

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Now, let's think
about what happens.

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Let's think about what
happens if the price of fruit

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were to go down.

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So the price of fruit were to
go from $2 to $1 per pound.

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So if the price of fruit
went from $2 to $1, then

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our actual budget line
will look different.

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Our new budget line.

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I'll do it in blue,
would look like this.

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If we spent all our
money on chocolate,

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we could buy 20 bars.

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If we spent all of our money
on fruit at the new price,

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we could buy 20 pounds of fruit.

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So our new budget line would
look something like that.

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So that is our new budget line.

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So now what would be
the optimal allocation

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of our dollars or the best
combination that we would buy?

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Well, we would do the
exact same exercise.

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We would, assuming
that we had data

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on all of these
indifference curves,

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we would find the
indifference curve that

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is exactly tangent to
our new budget line.

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So let's say that this
point right over here

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is exactly tangent to
another indifference curve.

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So just like that.

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So there's another indifference
curve that looks like that.

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Let me draw it a
little bit neater.

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So it looks something like that.

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And so based on how the price--
if we assume we have access

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to these many, many, many,
many, many indifference curves,

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we can now see based
on, all else equal,

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how a change in
the price of fruit

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changed the quantity
of fruit we demanded.

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Because now our optimal spent
is this point on our new budget

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line which looks like it's
about, well, give or take,

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about 10 pounds of fruit.

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So all of a sudden,
when we were-- so let's

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think about just the fruit.

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Everything else
we're holding equal.

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So just the fruit, let's
do, when the price was $2,

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the quantity demanded
was 8 pounds.

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And now when the price
is $1, the quantity

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demanded is 10 pounds.

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And so what we're
actually doing,

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and once again, we're kind of
looking at the exact same ideas

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from different directions.

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Before we looked at it in terms
of marginal utility per dollar

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and we thought about
how you maximize it.

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And we were able to
change the prices

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and then figure out and derive
a demand curve from that.

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Here we're just looking at it
from a slightly different lens,

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but they really are
all of the same ideas.

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But by-- assuming
if we had access

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to a bunch of
indifference curves,

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we can see how a change in
price changes our budget line.

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And how that would change
the optimal quantity

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we would want of
a given product.

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So for example, we
could keep doing this

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and we could plot
our new demand curve.

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So I could do a demand
curve now for fruit.

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At least I have two points
on that demand curve.

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So if this is the
price of fruit and this

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is the quantity demanded of
fruit, when the price is $2,

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the quantity demanded is 8.

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And when the price
is-- actually,

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let me do it a
little bit different.

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When the price is $2--
these aren't to scale--

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the quantity demanded is 8.

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Actually let me
do it here-- is 8.

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And these aren't to scale.

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But when the price is $1,
the quantity demanded is 10.

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So $2, 8, the quantity
demanded is 10.

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And so our demand curve,
these are two points on it.

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But we could keep changing
it up assuming we had access

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to a bunch of
indifference curves.

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We could keep changing
it up and eventually plot

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our demand curve, that might
look something like that.