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# Total revenue and elasticity

Thinking about how total revenue and elasticity are related. Created by Sal Khan.

Video transcript

So we're going back to
our little burger stand where we had our demand curve
in terms of burgers per hour. And now, I want to
think about something from the perspective
of our burger stand. And think about,
at any given point on this demand curve, how much
revenue would we get per hour. And when I talk about revenue,
for simplicity, let's just think that's really just
how much total sales will I get in a given hour. So let me just write
over here total revenue. Well, the total
revenue is going to be how much I get per burger times
the number of burgers I get. So the amount that I
get per burger is price. So it's going to
be equal to price. And then the total number
of burgers in that hour is going to be the quantity. Pretty straightforward. If I sell 10 things
at $5, I am going to get $50 of revenue,
$50 of sales in that hour. Now, let's think about
what the total revenue will look like at different
points along this curve right over here. And actually, let me just
make a table right over here. So I'll make one column
price, one column quantity. And then let's make one
column total revenue. So let's look at a
couple scenarios here. Well, we could actually
look at some of these points that we already have defined. At point A over
here, price is 9. So I'll do it in
point A's color. Prices is 9. Quantity is 2. $9 times
2 burgers, $9 per burger times 2 burgers per hour. Your total revenue
is going to be $18. And you can see it
visually right over here. This height right
over here is 9. And this width right
over here is 2. And your total
revenue is going to be the area of this rectangle. Because the height is the price. And the width is the quantity. So that total revenue is
the area right over there. Now, let's go to point--
let me do a couple of them just to really make
it clear for us. Let's try to point
B. So at point B when our price is 8 and our
quantity is 4, 4 per hour. Our total revenue is
going to be 8 times 4 which is $32 per hour. And once again, you
can see that visually. The height here is 8. And the width here-- so the
height of this rectangle is 8. And the width is 4. The total revenue is
going to be the area. It's going to be the height
times the width just like that. Now, let's go to a point that I
haven't actually graphed here. Actually, let me
just-- actually, I'll go through all the
points just for fun. So now at point C, we have 5.50. 5.50 is a price. The quantity is 9. 9 times 5.50. 9 times 5 is $45. And you have another 4.50. So that is 49.50. So once again, it's going to
be the area of this rectangle. Area of that rectangle
right over there. So you might already be
noticing something interesting. As we lower the price, at least
in this part of our demand curve, as we lower the
price, we are actually increasing not just
the quantity were increasing the total revenue. Let's see if this
keeps happening. So if we go to point D, I'll
do it in that same color. We have 4.50. And we are selling 11 units. So 11 times 4.50. Let's see, this is going
to be 44 plus 5.50. Once again, that is 49.50. So that this rectangle is
going to have the same area as that pink one that we
just did for scenario C. And I'll actually just
do one more down here, just to see what happens. Because this is interesting. Now we lower the price. And it looks like things
didn't change much. And now, let's go-- let's
just do one more point actually for the sake of time. Point E. And I encourage
you to try other ones. Try F on your own. Point E, my price
is $2 per burger. My quantity is 16
burgers per hour. I sell a total of 32 burgers. Now actually, let's
just do the last one, F, just to feel a
sense of completion. So $1 per burger. I sell 18 burgers per hour. My total revenue, when you
multiply them, is $18 per hour. And once again, that's the
area of this rectangle, this short and fat
rectangle right over here. And E was the area--
the total revenue in E was the area of that
right over there. And you could graph
these just to get a sense of how total
revenue actually changes with respect
to price or quantity. Lets plot the total revenue
with respect to quantity. So let's try it out. So if you-- let me plot it out. So this is going to
be total revenue. And this axis right over
here is going to be quantity. And we're going to, once
again, go from-- let's see. This is 0. This is 5. This is 10. This is 15. And this is 20 right over here. And then total revenue. Let's see, it gets as high--
it gets pretty close to 50. So let's go. This is 10 20, 30, 40, and 50. So that's 50, 40,
30, 20, and 10. So when our quantity is
2, and our price is 9. Well, we don't have price on
this axis right over here. But when our quantity is
2, our total revenues 18. So it's going to be
something like there. Then, when our quantity is
4, our total revenue is 32. Right about there. Then, when our quantity is 9,
our total revenue is almost 50. So right over there. And then, when
it's 11, it's also at that same point
right over there. And then, when we are quantity
is 16, our total revenues 32. 16. So 32. Right there. And then finally, when
our quantity is 18, our total revenue is 18. And what you see is
that it's plotting out a curve that looks like this. And if you remember
some of your algebra 2, this is a concave downwards
parabola right over here. And you can see
there was actually some point at which you could
maximize your total revenue. And if you really tried
all the points here, you would see that
maximum point is if you tried this point
right over here, right at price 5 and quantity 10. At price 5 and quantity 10, in
that hour, you would sell $50. So this is the maximum
point right over there $50. Now, the whole reason why
I'm talk think about this. I could have talked about this
independently of any discussion of elasticity just to see how
total revenue relates to price and quantity at different
points on the demand curve. But there is an
interesting relationship. In that very first
video, and we actually used this exact
demand curve for it. When we explored
elasticity, we saw that up here at this
part of the curve-- let me do this in
a different color. At this point of the curve in
orange for any change-- when you do a change in your price
since the prices are pretty high, that is a much
lower percent change in price than the impact
that you get on quantity. Because over here, although
they look like they're close. Or I should say the absolute. For every 1 that down
we move in price, we're moving 2 up quantity. But that 1 down in price is a
very small percentage of price because our prices
are high here. And it's a very large percentage
of quantity right over here. So you get huge changes
in percent quantity for very small changes in price
in this part of the curve. So this part of the
curve is elastic. Or you could say that its
price elasticity for demand is greater than 1. You get larger changes
in percent quantity for a given change
in percent price. Now, these parts of the
curve down here, we saw is the opposite's happening. You move 1 down, 1
unit down in price, you move 2 units to
the right in quantity. But over here, price
is a much lower. So this is a much larger
percentage change in price. And this is a much smaller
percentage change in quantity. So you get large
percentage changes in price for small percentage
change in quantity. That means that here, you
are relatively inelastic. And then right over here,
right at this point, right in this region,
right over here, we saw that we
had unit-- we were unit elastic right over there. So there's an interesting
relationship going on. While we were, so
while we were elastic, this part right over
here, when we lowered price in this region. While we were elastic,
when we lowered price, we got increases in revenue. So let me write this down. And this is generally,
too, there's a couple of boundary
cases on the math that make it a little bit, you
can't make it absolutely true. But while we are elastic, at
the elastic points of our demand curve, a decrease in price. Price goes down. Total revenue was going up. You do a price cut on this
part of the demand curve, you get more revenue. Then, when you are at unit
elasticity, what was happening? At unit elasticity, you were
right at this point right over here. Right at this point over here. And roughly, when
you do a price cut-- and I'm going to say
this is roughly true-- your total revenue
stays constant. But just right at
that point, right when you're going through
that unit elasticity point. And then finally, when you are
inelastic when a large percent changes in price result and
not so large percent change is in quantity demanded, then
a price change going down resulted in lower total revenue. Resulted in total
revenue going down. And this should, hopefully,
make a little bit of intuitive sense. Because over here, this
point, if given percent change in price, you were
getting a larger percent change in quantity. So the percent in
price went down. Your percent in
quantity grew even more. So you made up any
decrease in height with a increase in width. So your area increased. Down here, your decrease
in percent price wasn't made up for a
decrease in quantity. So when you made your
rectangles little bit shorter, you didn't, we weren't
able to compensate by growing the width as much. And so you actually had a lower
area, lower total revenue.