Total consumer surplus as area

let's say you run an orange stand and this right here is you could do this either as the demand curve for your orange tan or your marginal benefit curve or really call it the willingness to pay that the first hundred pounds of oranges or that very hundredths pound that hundredths pounds someone would be willing to pay $3 per pound but then the hundreds in first pound it 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 site set the price at $2 and you are able to sell 300 300 oranges per in that week what I want to think about is what is the total consumer 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 the hundredth pound the hundredth pound they paid $2 sorry yeah they paid $2 but their benefit looks like it was like I don't know 3 dollars and 30 cents so 3 dollars and 30 cents but they only paid $2 so their benefit on that 1 pound there marked their benefit or their I should say their consumer surplus is going to be 330 minus the 230 so that person who bought that hundredth pound that not all the hundred pounds just that hundredth pound got a consumer surplus of 330 minus 2 dollars which is a $1 and 30 consumer surplus consumer surplus so if you wanted to figure out the entire consumer surplus well you would just have to do it for all of the pounds so that was the hundredth pound you would find you would find so that essentially that was the 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 1 pound wide it was 1 pound wide 1 pound 1 pound wide and it was this right over here this right over here was $2 and then we had D and then we had our marginal benefit curve our demand curve sloping down like that sloping down like that and this point right over here was three dollars and thirty and so to figure out the consumer surplus for that pound we said okay for that pound they were willing to pay three dollars thirty the benefit to them was three dollars and thirty but they only had to pay two dollars so the height of this the height of this right over here was one dollar thirty and so the consumer surplus is one dollar thirty per pound times one pound times one pound and so that's what that's where we got the one dollar thirty consumer surplus now we could do that for every one of the pounds so we could do that for the hundredth and first pound let me did a different colored one hundredth and first pound we would do it like that then the one hundred then second pound we would do it like that one hundredths and third pound like that we do it for the 99th pound like that and so you could imagine if we want 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 two so we're just going to sum up this area and if you're familiar with calculus you might know that it you can actually make these things arbitrarily small you could take smaller and smaller you could you don't have to take a one pile a one-pound wide rectangle you could take 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 nonlinear 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 find 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 and above the price equals two dollars 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 the area 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 300 300 pounds and then our height our height over here and we can we can just do use this as the area of a triangle because this is a this is a simple linear demand curve we would actually have to use a little bit of calculus if this was a nonlinear curve but the height here is 2 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 300 pounds times the height which is 2 dollars which is $2.00 per pound times $2 all right this way times $2 $2 per pound the pounds cancel out 1/2 times 2 is 1 times 300 is 300 so we get 300 300 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