Consumer Surplus and Willingness to Pay - Video Tutorials & Practice Problems

Consumer Surplus in a Small Setting

have you ever been shopping and got a good deal? Well then you've had a firsthand experience with consumer surplus. Let's check it out. So we're gonna talk about this idea of willingness to pay, right? This is kind of self explanatory, right? It's the maximum amount that someone's willing to pay for something, right? The max let me get my rent maximum. Someone's willing to pay, right? That that's kind of what that means. Sometimes you'll hear the word reservation price, that just means the most I pay for something. Um and we've actually already been dealing with this without even knowing it. This is the demand curve is gonna represent the willingness to pay of the consumers, right? That kind of makes sense, right? The demand curve shows what what prices the consumers are willing to purchase that. So this idea of surplus, right? Of consumer surplus. When we talk about surplus, we're gonna be talking about getting good deals, right? Whenever you think of the time you got a good deal, that that's the time when these surpluses exist. So when we talk about a consumer surplus, right? Just like we said, it's when they're willing to pay more than the market price, right? When you get a good deal. So if you're willing to pay more than the price you actually had to pay, You got some consumer surplus there and great example I can think of is uber right? Uber now has these insanely cheap. Well, it's 2017 and their rides are still insanely cheap, right? Um and you know, maybe you would expect to pay or be willing to pay somewhere around $20 or $25 for a taxi ride across town or to the airport, and now you can get that same taxi ride to the airport for 5 $10 right? It's insane. They've they've lowered the price of these rides insanely to the point that people are actually using taxis again. Right? Think about I never use taxis until Uber came out. And if you if you don't have Uber, just use my code for your first free ride. You'll get I'm just kidding. All right. So, let's let's go on here. Um Let's talk about the the formula for consumer surplus, which is pretty simple. It's exactly what we've been saying. It's a difference between the willingness to pay of the consumer and the market price, right? So that's gonna be the maximum willingness to pay just to reiterate and the market price. Right? And over here, I'm gonna write Uber. So, you don't forget this example. Cool. All right. So, when we talk about willingness to pay and actually the demand curve, um we're gonna start talking about this idea of marginal benefit. Alright. So remember um we brought this up before and I remember beating it in that this is gonna be a really important topic, marginal benefit, marginal cost. Well, the idea here is that the demand curve basically represents the marginal benefit to society to the consumer and to society um of these trades being made right of these exchanges. So, the idea is maybe you went to uh I don't know to the store and bought a DVD, right? Maybe when you went to the store, you love this movie, you've been looking for this DVD, you would be willing to pay $20 for this DVD, right? And um you end up going to the register and it cost $12, right? So your benefit is still this. You know, we could say you had like $20 worth of joy. You were going to get out of this movie, right? That's what it represented to you. But you only have to pay $12, right? But that benefit to you was $20, right? It wasn't a $12 benefit. It was a $20 benefit, even though you paid 12. So, we'll think of the demand curve as that marginal benefit. All right? So let's go ahead and do this simple example in a small market and talk about consumer surplus. Alright, So, we've got a small market um with cartman Kyle stan and Kenny four names that kind of just pick that random. And just to keep things simple in this market will say that each person is only willing to buy one thing. They're only gonna buy one each, right? If they if they're gonna buy it, they'll buy one. They're not gonna buy three or four the same. Just to keep it simple. Um We'll say something like that. Like they're in the market for like a golden cheesy poof for something like that, right? Something that they only need one of and if you don't get it, this is like a South park thing going on, don't worry about it. So let's talk about the different willingness to pay that we have of each consumer. So you see cartman really wants this golden cheesy poof and is willing to pay up to $8 for it Kyle six stand for and Kenny too. So let's go ahead and put these onto our graph here, right? We've got our price and quantity axes there and we've got some prices there, some quantities, it's all set up for us. So we're gonna stay at a price of $8. How many people are willing to buy? Well we've got just cartman, right? So there's gonna be one quantity demanded at a price of $8. And what about at a price of $6? Well now cartman and Kyle both by. Right, so we'll be right here, stand down here, that's at a price of $4.3 people get in at a price of $2, all four of them are in the market and four will be exchanged there. So it almost looks like we got a demand curve here, right? You're ready to connect these points, but actually we've got kind of a funky demand curve in this case. Um Because it's such a small market that there's not people in between these points. So you can imagine like instead of connecting these diagonally like this, there's really nobody in the market at this price of $7 right? It would still only be cartman buying at that price. So we actually get this funky looking curve. Give me a second, that looks something like this, It's gonna have this stair step kind of look. So it's jagged because it's such a small market that we don't get that that smooth curve from having a lot of buyers and a lot of uh a lot of buyers in the market. So we get this kind of stair step thing going on here, right? And that makes sense because at a price of $7, if we look right here It's still only cartman that buys, right? So we have a quantity of one at a price of $7 or $8, right? So that's kind of how we're gonna draw in this small case, it's not so important. Um but it's gonna help us do this example easier. Um it helps us visualize the surplus. So let's go ahead and start with cartman, excuse me start with this price of $7, right? So let's say the price is $7 What is consumer surplus? How much is going to be exchanged here? Well we'll see that only cartman wants to get in the market, right? So he's willing to pay $8 but he only has to pay seven right minus seven. So he has a consumer surplus of one there. How about Kyle? Well at a price of seven Kyle's not gonna buy right, His willingness to pay Is $6. He doesn't buy at seven. So he doesn't get any surplus if he doesn't he can't have a chance at any surplus if he doesn't buy anything. So he has no surplus, he didn't buy stand also has a willingness to pay lower and so does Kenny. Right? None of them are gonna buy. Only cartman gets in this market. So at the bottom I've got this summary, I'm gonna get out of the way so we can fill these boxes. Um We've got a summary of what happened, right quantity demanded and consumer surplus, total consumer surplus in each situation. So the price of seven quantity demanded was just the one. Right, cartman is the only one that buys one. The price is $7. And total consumer surplus is one which is cartman's consumer surplus. I want to show you that on the graph real quick. So this this total consumer surplus of one. I'm gonna mark this green because I'm gonna mark the area in green over here. Um This consumer surplus of one is represented by this area right here that I'm marking in green, right? Just that area above the price of $7. Right? So there was our price of $7. Um And our consumer surplus is above that line and below the the maximum price there that he was willing to pay? So just so you can see, right, 8 -7. Right? That's gonna be this length right here is 8 -7 which is one. And this area right here, although it looks like to because but our notice how our graph is 1234 like that, so that's one as well, so one times one is one and that's our consumer surplus of one. Okay, so let's go on to a price of $5. What happens at a price of $5? Well, cartman is still gonna buy it, right, but now he's getting an even better deal. He's gonna be even happier about this. So 8 -5. He is gonna get three consumer surplus instead of one. Now right, notice how his consumer surplus has grown. Um How about Kyle? Well, at a price of $5 Kyle does get in the market, right? He's willing to pay six, but the price is five, so now Kyle is gonna buy um and he'll have a consumer surplus of one, right? Six minus the market price of five gives us one stan he still doesn't get in, right because the price is five and he's only willing to pay four. So he's still not gonna buy. He has no consumer surplus Kenny also will not buy because his willingness to pay is too low. All right, so what happened in this situation how much quantity was exchanged? Well, now cartman bought one and Kyle bought one, Right? So there was two exchanged. And how about the consumer surplus? Right? The consumer surplus is now cartman's three plus Kyle's 14, Right? So the price went down and consumer surplus increase, that kind of makes sense. Right? Everyone's getting good deals um as the price goes down, the good deals keep on coming. So, I'm gonna mark this area on the graph in blue. Right? But I wanna I'm gonna go piece by piece because I want to show you um where each surpluses. So remember, um this spot right here is cartman's demand, right? This this spot on the graph, the price of eight he's willing to demand. Right? And this right here represents Kyle, and we could say that this one just to put them all in here is stan and that's Kenny, right? Um So cartman's consumer surplus is right here, right? And his grew at a price of seven. He had one consumer surplus and now he has three. So let's see that area right there. So he's adding to his consumer surplus. This blue area that I just put in right here, right? Um that's cartman's additional consumer surplus at this price of $5, right? This is the price of $5 right here. But now, um, Kyle is also getting some consumer surplus, right? And that's represented by this area here, Kyle's demand and still above that price of $5. Right? So that's what we have right there. That additional area is three and it represents the additional consumer surplus that gets us to a total consumer surplus of four because cartman already had a little bit. Alright, so let's go on to this last case when the price is $4. Right? So now the price has dropped again to $4 cartman's consumer surplus. What do you think it's gonna keep increasing? Right? Because he's getting better and better deals? So he's getting more and more surplus eight minus four equals $4 Kyle six. His is gonna grow as well. Right? He was buying before he's gonna keep buying. So his consumer surplus grew to two. How about Stan now stan he is going to get into the market, right? The price is $4 he's willing to pay $4 for -4. However, he still has no surplus. Right? He's getting it at the maximum he's willing to pay. And actually, in this case he's actually indifferent whether he buys it or not because he he's at his maximum willingness to pay. But that doesn't matter. We're gonna say that he buys it here. Um and how about poor Kenny here, Portal Kenny still is not gonna pay his willingness to pay his $2 the prices for. He's not gonna buy it. All right, So, what's happened in this case? Well, now three people have bought. Right, cartman Kyle and stan are on the market, three or quantity demanded and what our consumer surplus? Well, we've got four from cartman Kyle's got to stan's got zero, so we've got four plus two plus zero is six. Right? Um So let's go ahead and represent this on the graph as well. I'll use this purple this time. Now let's first talk about cartman's additional surplus, just like you would expect it would be this area right here under his previous surplus. Right? So now cartman's total surplus, I'm gonna outline in black for just a second. Just so you see it, cartman's total surplus, is this whole area, right? All of that all for um Excuse me, all of those colors. Right there, all represented surplus and Kyle surplus. So he's gonna have this additional surplus here. Right? So now all that area is consumer surplus. And just to reiterate this would be Kyle's total surplus right here this area. Right, So his surplus is there. And what about stan? Well, stan did get in the market at $4 but he has no surplus and you'll see that right? As There's no space for me to highlight between that price of $4 and stands demand right there. Right, so our total consumer surplus is represented by all that highlighted area, the green, the blue and the purple. Alright, so whoops. So let's go ahead and um take this to the full market and see what this looks like once we have a full demand curve. Alright, let's do that in the next video.

Consumer Surplus and Market Demand

Alright. So now let's extend the discussion to the full demand curve here. Right? So now you see on the graph, that demand curve that we're used to, right? It's not that jagged one anymore, this is that downward demand, the double Ds. We've got a price axis and our quantity axis. So how did we get to this kind of full demand curve? Right? So in this situation there's more people in the market right before we only had four for buyers. But now you can imagine right cartman was gonna buy for eight uh Kyle for six whatever. Now there's gonna be other people, someone who might be able to be willing to pay $6.25. Someone willing to pay $6.50. Someone willing to pay $7.03 right? All these different willingness to pay kind of smooth out the line just because there's way more customers now and now there's the opportunity we're gonna make it. You know, you could buy more than one now too right? Maybe you would buy the first unit for $6 and another unit for $4 right? You but you could be in multiple places along this line. But um regardless the idea here is that we've got our smooth demand curve now, right? So our consumer surplus to calculate it, let's say we're at this price here of p um our consumer surplus is going to be that area just like it says the area below the demand curve and above market price. Right? So here's below the demand curve and above market price, right? We're gonna get this triangle, right? And that's why we have our triangle formula right there in the box as well, right? Half base times height. That's how we would calculate this. Consumer surplus is by taking uh that area. So we could say that this could be like the base right here, right? The base between this point and the market price. Um And we would have to be given this point, right? If we're going to calculate it, we we don't know what it is, it would have to be given to us or something. Uh And then we've got our height right here, right? This is gonna be the height of the triangle. Um And what does that represent? Well, the height is just the quantity demanded right there at that price, right? That's what we see kind of happening here. Is that that length there is just the quantity demanded. So there you go. If you have those numbers, you'd be able to calculate uh a consumer surplus there. So now let's talk about the idea of what's gonna happen to this consumer surplus after a price decrease. So first, let's think logically, like what do you think, do you think consumer surplus is going to increase or decrease after the price goes down? So if the price goes down, think about it, we're gonna have more surplus, right? Because people are getting better deals right? There's the people who are already buying before are going to be getting better deals because the price went down, and now that there's a lower price new people are gonna be getting in the market, We're also gonna be getting some consumer surplus, right? So this price decrease, just like we saw above as the price went down and down and down, cartman surplus kept rising, The new people's surplus started coming in, right? So let's go ahead and see what happens to surplus here. Um Let me pop out of the way here. Alright, so we're still gonna have that same original surplus, right? Well first let me mark here um We got a price axis or quantity axis. And now we're at this I'm gonna call it P. L. Like low price, right? A lower price. Um And let's go ahead and talk about the consumer surplus. So this purple um that's our original surplus, right? The surplus that already existed at the higher price, there was already some surplus at that higher price. We still get that surplus. Um Well those consumers that were buying before still get the surplus and then those consumers also get more surplus, just like we saw cartman surplus increasing as the price dropped, that's going to be represented by this box. So the people who are are in the market are now getting more surplus because the price went down there, getting an even better deal, they get more surplus, right? So that's represented by that green box is the additional surplus to the people who are already buying. And then this blue box is gonna represent new surplus to new customers, right? People who are not in the market before, but now that the price decreased, they are in the market, right? So that's gonna be our additional surpluses, gonna be that green. And the blue is the extra surplus we just got because of the price decrease. Um But you can see that the total surplus still makes this triangle, right? We've got, you know, the triangle that includes all of the areas is still our total consumer surplus, All of this area. That is our total consumer surplus. So we can still calculate with the half bh right? If we had the numbers we needed, we could calculate the area there, but they could also ask us for, you know, these other areas, if they wanted to, they could say, hey, what was the original surplus in this situation? And we would know to calculate the area of the purple, they could say, what is the additional surplus to consumers that were already in the market, right? People who are already buying, what additional surplus did they get? And we would know it's this this green box here, right? The green area, That whole green area. And I'm drawing the boxes smaller just so you can see, but it does include the whole area there. Um And then they could also ask us what is the new surplus to new consumers at the new price. Right? So we would have to calculate this little area down here, right? And they would have to give us the numbers, right? We would have to have numbers for prices at the different points and different quantities, Right? So we would have to have a bunch of information, but we could calculate those areas, right? So that's about how it is with consumer surplus on the full scale here, we're gonna be calculating areas of triangles like that. So just know it's gonna be that area below the demand curve and above the market price. Alright, let's go ahead and move on to some examples and practice problems.

Consumer Surplus

Alright, let's try this one. The graph below represents the market for funky fresh rhymes at a price of $3,000 per funky fresh rhymes. What is the consumer surplus? All right, cool. So what do we got here? They're asking us for consumer surplus. Right. We've got a bunch of quantities on the graph, a bunch of prices. We've got our curves there, right? So they're asking us about consumer surplus. And remember that's the area below the demand curve and above the market price. Right? We're gonna get a triangle out of that and it's gonna be this area right here. I'm gonna highlight it in green. So our market price, what was it? $3,000? And that's right here. So we want to get the area above the market price, but below the demand curve, right, this is our downward demand, right? The double d downward demand right here, let's go ahead and highlight that area. So it's all of this green area right here, right below the demand curve above market price. So how do we calculate that? Well, it is a triangle as you can see, right? So we've got the area of a triangle is gonna be half times the base times the height. Right? So let's go ahead and find out what our base and our height are. So base and height are gonna be these two sides here and this side right here, right? That's gonna we'll call that our base. Either one can be based. Either one can be height, as long as you pick them. All right, so what's gonna be our base, right? Our base is gonna be this length between the 3000 and the 7000. So it's gonna be half times our base is the difference between the 7000 and the 3000. Right? It's gonna be that 4000 difference, but I'm gonna write it out here. 7000 minus 3000, Right? That's that length of of the base. And what's the length of the height here? What do you see here? We've got a bunch of numbers. Well, it's actually gonna be that quantity demanded at that price of 3000. The quantity demanded is 7 50. And that represents this length right? From 0 to 7 50 times 7 50 in that case. Right? There's no subtraction needed there because we're going all the way from zero. So, that's that's pretty much the bulk of it. Let's do this math and figure out what the answer is. So half times 7000 minus 3000 is 4000 times 7 50 right? Uh 4000 times 7 50 three million and half of that is 1.5 million. Right? And that's going to be the area of that triangle, which is our consumer surplus. So, our answer here at a price of $3000 per funky fresh rhyme. What is consumer surplus? It is going to be be $1.5 million. Alright, let's go ahead and move on to the next video

Use the graph for funky-fresh rhymes above. If price increases from $3,000 to $5,000 per funky-fresh rhyme, what is the change to consumer surplus? 

• A. $500,000 increase
• B. $500,000 decrease
• C. $1,000,000 increase
• D. $1,000,000 decrease

Kanye West is ready to create his next hit single. He knows that he is willing to pay up to $3,000 for a funky fresh rhyme, and that he will need a total of ten funky fresh rhymes to create his hit single. After rounding up his best ghostwriters, he summarized the following schedule. If Kanye values all funky-fresh rhymes equally, what is his maximum consumer surplus? 

• A. $6,000
• B. $12,000
• C. $24,000
• D. $30,000

The demand curve for Nickelback's new album is downward sloping. At a price of $2, nationwide demand is 100 albums. If the price rises to $3, what happens to consumer surplus?

• A. It falls by less than $100
• B. It rises by more than $100
• C. It falls by more than $100
• D. It rises by less than $100