WEBVTT

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I want to do one more video
on total revenue and price

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elasticity of demand.

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Just to make sure that you, the
relationship between the two

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is an intuitive one.

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So let's draw an
arbitrary demand curve.

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So this is my price axis.

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That is my quantity
demanded axis.

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Quantity axis.

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And let me just draw an
arbitrary demand curve

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right over here.

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So let's say that
is my demand curve.

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And let's pick some
price and quantities

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on this demand curve.

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So let's say that
the price is up here.

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Let's call that P1.

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And then, the quantity demanded.

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Let's call that Q1.

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And we already know
that the total revenue

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is the area of this
rectangle right over here.

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This is the total revenue.

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It's just the price
times the quantity.

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If I'm selling 2 burgers an
hour and for $9 a burger,

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I'm going to make $18 per hour.

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That's going to be this
area right over here.

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Now, let's assume in
this part of the curve

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that the price elasticity
of demand is greater than 1.

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So we are elastic.

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So let me write this.

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So the price, the elasticity
of demand-- actually,

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I should say the absolute value
of the elasticity of demand.

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It will be actually
be a negative number.

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But the absolute value of
the elasticity of demand

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is greater than 1 which means
for a 1% drop in price you have

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more, you have a greater
than 1% increase in quantity.

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And that comes straight
out of the expression

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or our formula for
what elasticity is.

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Remember, elasticity
is our percent change

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in quantity over
percent change in price.

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So if this, if the
absolute value of this

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is greater than 1-- these
move in opposite directions.

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That's why it would be negative.

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But if we say the absolute
value of this is greater than 1,

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that means that this
quantity is going

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to be larger than this quantity.

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So if we have a
1% drop in price,

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the change in our quantity is
going to be greater than 1%.

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And so for point right over
here, if we lower this by 1%,

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we're going to increase
this by more than 1%.

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So any drop in our any
reduction in our height

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will be more than made up for.

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And this is generally the case.

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Will be more than made up for
by an increase in our width.

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So total revenue will increase.

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So when price drops, so 1% drop
in price and a larger than 1%

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increase in quantity means
that total revenue will go up.

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Now, if we go down here.

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If we go down to this
part of the curve.

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And let's say that this-- let's
call this-- let's call that P2.

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And let's call that quantity 2.

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And then, this area right over
here would be total revenue 2.

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Let's call that total
revenue 1 over there.

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Price times the quantity.

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Now, what's happening over here?

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We're going to assume that our
price elasticity of demand,

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the absolute value of it
over here, is less than 1.

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So the absolute value of our
price elasticity of demand

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is less than 1 at this
point in the curve.

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And all that is a
fancy way of saying

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that for a 1% drop in price,
we get less than a 1% drop.

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Sorry, less than a 1% increase.

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They move in
opposite directions.

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1% increase in quantity.

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So we're lowering the height.

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If we have a 1% drop,
we're lowering that by 1%.

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But we're not getting a
1% increase in our width.

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So the width isn't going
to be increasing that much.

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So in general, this
is going to result

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in a lowering of this area.

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This area will get smaller.

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We're reducing our
height more than we

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are expanding our width.

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So in this situation, total
revenue would go down.

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And remember, this is
an elastic situation.

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So when it is elastic, total
revenue tends to go up.

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And when it is
inelastic-- I want to say,

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when it's elastic
a drop in price

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tends to make total
revenue go up.

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And when it is inelastic,
a drop in price

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tends to make total
revenue go down.

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And then, you can imagine,
right when you're it

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unit elasticity,
someplace around there,

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a 1% a drop in price
will result in exactly 1%

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increase in quantity demanded.

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And so they will trade off.

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You won't get a noticeable
change in your revenue.

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And the reason why I say that
is that actually some, many econ

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textbooks will tell you that you
don't get a change in revenue.

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But if you actually will do a
detailed look at that math--

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let me write it over here.

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So the absolute value
of the price elasticity

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of demand at that point is 1.

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Which tells us that
a 1% drop in price

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will, or goes along with
a 1% increase in quantity.

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But if you look at the math.

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So if the old area.

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So let's call this price 3.

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And let's call this
quantity 3 right over here.

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And so total revenue
3-- let me do

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this in a new color-- which
is this area right over there,

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is going to be equal to
price 3 times the quantity 3.

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Now, if we increase price by,
or if we decrease price by 1%,

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then this will become
0.99 times our price.

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And if we increase
our quantity by 1%,

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then this will become
1.01 times our quantity.

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Now, let's think about what
this number right over here is.

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And this is why I'm
saying it's not exactly,

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the total revenues aren't
going to be exactly unchanged.

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If you multiply 0.99 times 1.01,
you don't you get exactly 1.

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You don't get exactly 1.

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Another way to think
about it, 0.99 times 0.01

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is going to be 1%
less than 1.01.

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And 1% of 1.01 is
slightly larger than 1.

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Or another way to
think about it,

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this value is going to
be 1% larger than 0.99.

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And 1% larger than, 1%
of a 0.99 is less than 1.

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So it's not going to get a 1.

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And you can see it
with your calculator.

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0.99 times 1.01 gets
you to very close to 1.

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So this is going to be equal
to 0.9999 times P3 Q3, which

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is equal to 0.9999
times total revenue 3.

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But it is-- total revenue 3.

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But it is roughly unchanged.

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So we can-- that's the
general rule of thumb.

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So when you are at
unit elasticity,

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then, a decrease in
price roughly says,

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no change, approximately
no change in total revenue.

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So I just wanted to make
sure that it makes sense.

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It really just comes
from these areas.

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If you're reducing
the height by a less

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than you're
increasing the width,

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obviously, the area
is going to increase.

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Or most of the
cases, I should say.

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It depends on where you are.

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If you are, if
you're compensating,

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whatever you reduce the height,
you are compensating perfectly

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with the increase in
width, then you're not

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going to have a
change in revenue.

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And if you decrease
the height by more,

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if you're taking more
area from the top

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than you're adding on
the width, then you're

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going to have a total
decrease in total revenue.