Total consumer surplus as area

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Total consumer surplus as area발음듣기

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Let's say you run an orange stand.발음듣기

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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.발음듣기

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Or that very 100th pound, someone would be willing to pay $3 per pound.발음듣기

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But then the 101st pound would be a little bit less than that.발음듣기

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So that's the willingness to pay, or the marginal benefit of that incremental pound.발음듣기

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But let's say you decide to set the price at $2, and you are able to sell 300 oranges in that week.발음듣기

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What I want to think about is, what is the total consumer surplus that your consumers got?발음듣기

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And the way to think about consumer surplus is, how much benefit did they get above and beyond what they paid?발음듣기

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So for example, the person who bought - let's just think about the exact 100th pound.발음듣기

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The 100th pound, they paid $2.발음듣기

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They paid $2, but their benefit looks like it was, I don't know, $3.30.발음듣기

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But they only paid $2.발음듣기

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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.발음듣기

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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.발음듣기

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So if you wanted to figure out the entire consumer surplus, well, you just have to do it for all of the pounds.발음듣기

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So that was 100th pound.발음듣기

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So essentially, you could view this as the area of this little thing right over here.발음듣기

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And let me zoom in, just to make sure you understand what's going on.발음듣기

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That thing that I just drew, if we zoom in, will look something like this.발음듣기

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It was one pound wide.발음듣기

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And this right over here was $2.발음듣기

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And then we had our marginal benefit curve, or our demand curve, sloping down like that.발음듣기

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And this point right over here was $3.30.발음듣기

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And so to figure out the consumer surplus for that pound we said, OK, for that pound they were willing to pay $3.30.발음듣기

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The benefit to them was $3.30.발음듣기

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But they only had to pay $2.발음듣기

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So the height of this right over here was $1.30.발음듣기

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And so the consumer surplus is $1.30 per pound times one pound.발음듣기

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And so that's where we got the $1.30 consumer surplus.발음듣기

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Now, we could do that for every one of the pounds.발음듣기

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So we could do that for the 101st pound.발음듣기

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Let me get a different color.발음듣기

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The 101st pound, we would do it like that.발음듣기

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Then the 102nd pound, we would do it like that.발음듣기

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103rd pound like that.발음듣기

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We'd do it for the 99th pound like that.발음듣기

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And so you could imagine if we wanted to find the total consumer surplus, what are we doing?발음듣기

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Well, we're essentially just finding the area between our demand curve and this line where the price is equal to 2.발음듣기

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So we're just going to sum up this area.발음듣기

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And if you're familiar with calculus, you might know that you can actually make these things arbitrarily small.발음듣기

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You don't have to take a one pound wide rectangle.발음듣기

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You get a half a pound wide rectangle, or a quarter pound wide rectangle.발음듣기

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Then you'll just have more rectangles.발음듣기

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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.발음듣기

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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.발음듣기

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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.발음듣기

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And so if you want to know this consumer surplus - and I really want you to understand why this was.발음듣기

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I mean, just think about it for each pound.발음듣기

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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.발음듣기

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And we're just summing that up across all of the pounds.발음듣기

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So to really figure out the total consumer surplus, we just have to find this area of this blue area.발음듣기

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And that's just finding the area of a triangle.발음듣기

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So this right over here, you have a base of 300.발음듣기

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This length right over here is 300 pounds.발음듣기

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And then our height over here.발음듣기

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And we can just use this as the area of a triangle, because this is a simple linear demand curve.발음듣기

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We would actually have to use a little bit of calculus if this was a non-linear curve.발음듣기

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But the height here is 2.발음듣기

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So our area, the area between the demand curve and our price equals 2, is equal to 1/2 times base times height.발음듣기

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1/2 times the base, which is 300 pounds, times the height, which is $2 per pound.발음듣기

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The pounds cancel out.발음듣기

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1/2 times 2 is 1, times 300 is 300.발음듣기

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So we get 300.발음듣기

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And all we're left with is dollars.발음듣기

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So the total consumer surplus in this case is $300.발음듣기

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And it really is just the area between the demand curve and this price equals 2 line right over there.발음듣기

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