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# More on total revenue andÂ elasticity

## Video transcript

I want to do one more video
on total revenue and price elasticity of demand. Just to make sure that you, the
relationship between the two is an intuitive one. So let's draw an
arbitrary demand curve. So this is my price axis. That is my quantity
demanded axis. Quantity axis. And let me just draw an
arbitrary demand curve right over here. So let's say that
is my demand curve. And let's pick some
price and quantities on this demand curve. So let's say that
the price is up here. Let's call that P1. And then, the quantity demanded. Let's call that Q1. And we already know
that the total revenue is the area of this
rectangle right over here. This is the total revenue. It's just the price
times the quantity. If I'm selling 2 burgers an
hour and for $9 a burger, I'm going to make $18 per hour. That's going to be this
area right over here. Now, let's assume in
this part of the curve that the price elasticity
of demand is greater than 1. So we are elastic. So let me write this. So the price, the elasticity
of demand-- actually, I should say the absolute value
of the elasticity of demand. It will be actually
be a negative number. But the absolute value of
the elasticity of demand is greater than 1 which means
for a 1% drop in price you have more, you have a greater
than 1% increase in quantity. And that comes straight
out of the expression or our formula for
what elasticity is. Remember, elasticity
is our percent change in quantity over
percent change in price. So if this, if the
absolute value of this is greater than 1-- these
move in opposite directions. That's why it would be negative. But if we say the absolute
value of this is greater than 1, that means that this
quantity is going to be larger than this quantity. So if we have a
1% drop in price, the change in our quantity is
going to be greater than 1%. And so for point right over
here, if we lower this by 1%, we're going to increase
this by more than 1%. So any drop in our any
reduction in our height will be more than made up for. And this is generally the case. Will be more than made up for
by an increase in our width. So total revenue will increase. So when price drops, so 1% drop
in price and a larger than 1% increase in quantity means
that total revenue will go up. Now, if we go down here. If we go down to this
part of the curve. And let's say that this-- let's
call this-- let's call that P2. And let's call that quantity 2. And then, this area right over
here would be total revenue 2. Let's call that total
revenue 1 over there. Price times the quantity. Now, what's happening over here? We're going to assume that our
price elasticity of demand, the absolute value of it
over here, is less than 1. So the absolute value of our
price elasticity of demand is less than 1 at this
point in the curve. And all that is a
fancy way of saying that for a 1% drop in price,
we get less than a 1% drop. Sorry, less than a 1% increase. They move in
opposite directions. 1% increase in quantity. So we're lowering the height. If we have a 1% drop,
we're lowering that by 1%. But we're not getting a
1% increase in our width. So the width isn't going
to be increasing that much. So in general, this
is going to result in a lowering of this area. This area will get smaller. We're reducing our
height more than we are expanding our width. So in this situation, total
revenue would go down. And remember, this is
an elastic situation. So when it is elastic, total
revenue tends to go up. And when it is
inelastic-- I want to say, when it's elastic
a drop in price tends to make total
revenue go up. And when it is inelastic,
a drop in price tends to make total
revenue go down. And then, you can imagine,
right when you're it unit elasticity,
someplace around there, a 1% a drop in price
will result in exactly 1% increase in quantity demanded. And so they will trade off. You won't get a noticeable
change in your revenue. And the reason why I say that
is that actually some, many econ textbooks will tell you that you
don't get a change in revenue. But if you actually will do a
detailed look at that math-- let me write it over here. So the absolute value
of the price elasticity of demand at that point is 1. Which tells us that
a 1% drop in price will, or goes along with
a 1% increase in quantity. But if you look at the math. So if the old area. So let's call this price 3. And let's call this
quantity 3 right over here. And so total revenue
3-- let me do this in a new color-- which
is this area right over there, is going to be equal to
price 3 times the quantity 3. Now, if we increase price by,
or if we decrease price by 1%, then this will become
0.99 times our price. And if we increase
our quantity by 1%, then this will become
1.01 times our quantity. Now, let's think about what
this number right over here is. And this is why I'm
saying it's not exactly, the total revenues aren't
going to be exactly unchanged. If you multiply 0.99 times 1.01,
you don't you get exactly 1. You don't get exactly 1. Another way to think
about it, 0.99 times 0.01 is going to be 1%
less than 1.01. And 1% of 1.01 is
slightly larger than 1. Or another way to
think about it, this value is going to
be 1% larger than 0.99. And 1% larger than, 1%
of a 0.99 is less than 1. So it's not going to get a 1. And you can see it
with your calculator. 0.99 times 1.01 gets
you to very close to 1. So this is going to be equal
to 0.9999 times P3 Q3, which is equal to 0.9999
times total revenue 3. But it is-- total revenue 3. But it is roughly unchanged. So we can-- that's the
general rule of thumb. So when you are at
unit elasticity, then, a decrease in
price roughly says, no change, approximately
no change in total revenue. So I just wanted to make
sure that it makes sense. It really just comes
from these areas. If you're reducing
the height by a less than you're
increasing the width, obviously, the area
is going to increase. Or most of the
cases, I should say. It depends on where you are. If you are, if
you're compensating, whatever you reduce the height,
you are compensating perfectly with the increase in
width, then you're not going to have a
change in revenue. And if you decrease
the height by more, if you're taking more
area from the top than you're adding on
the width, then you're going to have a total
decrease in total revenue.