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# Total consumer surplus as area

## Video transcript

Let's say you run
an orange stand. And this right here,
you could view this as either the demand curve
for your orange stand or your marginal benefit
curve, or really you could call it the
willingness to pay, the first 100 pounds of oranges. Or that very 100th
pound, someone would be willing to
pay $3 per pound. But then the 101st pound would
be a little bit less than that. So that's the
willingness to pay, or the marginal benefit
of that incremental pound. But let's say you decide
to set the price at $2, and you are able to sell
300 oranges in that week. What I want to
think about is, what is the total consumer surplus
that your consumers got? And the way to think
about consumer surplus is, how much benefit did they
get above and beyond what they paid? So for example, the
person who bought-- let's just think about
the exact 100th pound. The 100th pound, they paid $2. They paid $2, but their
benefit looks like it was, I don't know, $3.30. But they only paid $2. So their benefit on that
one pound, their benefit, or I should say their
consumer surplus, is going to be
$3.30 minus a $2.30. So that person who bought that
100th-- not all the 100 pounds, just that 100th pound-- got a
consumer surplus of $3.30 minus $2, which is a $1.30
consumer surplus. So if you wanted to figure out
the entire consumer surplus, well, you just have to do
it for all of the pounds. So that was 100th pound. So essentially,
you could view this as the area of this little
thing right over here. And let me zoom in,
just to make sure you understand what's going on. That thing that I just
drew, if we zoom in, will look something like this. It was one pound wide. And this right over here was $2. And then we had our marginal
benefit curve, or our demand curve, sloping down like that. And this point right
over here was $3.30. And so to figure out the
consumer surplus for that pound we said, OK, for that pound
they were willing to pay $3.30. The benefit to them was $3.30. But they only had to pay $2. So the height of this
right over here was $1.30. And so the consumer surplus
is $1.30 per pound times one pound. And so that's where we got
the $1.30 consumer surplus. Now, we could do that for
every one of the pounds. So we could do that
for the 101st pound. Let me get a different color. The 101st pound, we
would do it like that. Then the 102nd pound, we
would do it like that. 103rd pound like that. We'd do it for the
99th pound like that. And so you could
imagine if we wanted to find the total consumer
surplus, what are we doing? Well, we're essentially
just finding the area between
our demand curve and this line where the
price is equal to 2. So we're just going
to sum up this area. And if you're familiar
with calculus, you might know that
you can actually make these things
arbitrarily small. You don't have to take a
one pound wide rectangle. You get a half a
pound wide rectangle, or a quarter pound
wide rectangle. Then you'll just
have more rectangles. It doesn't matter so much if
you have a linear demand curve, but if you had a
non-linear demand curve then it would matter. You'd want to get smaller and
smaller and smaller, or thinner and thinner and
thinner rectangles, so you could get better
and better approximations for the consumer surplus. But needless to say, what
you're really doing-- especially if you get unbelievably
thin rectangles, and you have an unbelievably
high number of them-- you're really just estimating the
area under the demand curve and above the price equals $2. And so if you want to know
this consumer surplus-- and I really want you to
understand why this was. I mean, just think
about it for each pound. It was just how much
more value that pound, whoever bought that pound,
how much more value do they get relative to what they paid. And we're just summing that
up across all of the pounds. So to really figure out
the total consumer surplus, we just have to find this
area of this blue area. And that's just finding
the area of a triangle. So this right over here,
you have a base of 300. This length right over
here is 300 pounds. And then our height over here. And we can just use this
as the area of a triangle, because this is a simple
linear demand curve. We would actually have to
use a little bit of calculus if this was a non-linear curve. But the height here is 2. So our area, the area between
the demand curve and our price equals 2, is equal to 1/2
times base times height. 1/2 times the base, which is 300
pounds, times the height, which is $2 per pound. The pounds cancel out. 1/2 times 2 is 1,
times 300 is 300. So we get 300. And all we're left
with is dollars. So the total consumer
surplus in this case is $300. And it really is just the
area between the demand curve and this price equals 2
line right over there.