Consumer Surplus and Willingness to Pay - Online Tutor, Practice Problems & Exam Prep

Consumer surplus occurs when a consumer's willingness to pay exceeds the market price, representing the benefit gained from purchasing a good at a lower price. It can be calculated as the area below the demand curve and above the market price, often visualized as a triangle. A decrease in price typically increases consumer surplus, as existing buyers enjoy better deals and new consumers enter the market. Understanding this concept is crucial for analyzing market dynamics, demand curves, and the effects of price changes on consumer behavior.

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 going to 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 red 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'd pay for something, and we've actually already been dealing with this without even knowing it. This is the demand curve is going to represent the willingness to pay of the consumers, right? That kind of makes sense, right? The demand curve shows what prices the consumers are willing to purchase at. So this idea of surplus, right? Of consumer surplus, when we talk about surplus, we're going to be talking about getting good deals, right? Whenever you think of a time you got a good deal, that's the time when these surpluses exist. So when we talk about a consumer surplus, right, just like we said is 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 a 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? And you know maybe you would expect to pay or be willing to pay somewhere around 20 or 25 dollars 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 dollars right? It's insane, they've lowered the price of these rides insanely to the point that people are actually using taxis again, right? Think about I never used taxis until Uber came out, and if you don't have Uber, just use my code for your first free ride, get I'm just kidding. Alright. So let's go on here. Let's talk about 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 going to be the maximum willingness to pay, just to reiterate and the market price, right, and over here I'm going to write Uber so you don't forget this example. Cool.

Alright so when we talk about willingness to pay and actually the demand curve, we're going to start talking about this idea of marginal benefit. Alright, so remember, we brought this up before and I remember beating it in that this is going to 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, of these trades being made, right, of these exchanges. So the idea is maybe you went to, I don't know, to the store and bought a DVD, right? Maybe when you went to the store you loved this movie, you've been looking for this DVD, you would be willing to pay 20 dollars for this DVD, right? And you end up going to the register and it costs 12 dollars right, so your benefit is still this you we could say you had like 20 dollars worth of joy you were going to get out of this movie, right, that's what it represented to you, but you only had to pay 12 dollars, right, But that benefit to you was 20 dollars though, right? It wasn't a 12 dollar benefit, it was a 20 dollar benefit even though you paid 12. So we'll think of the demand curve as that marginal benefit. Alright. 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 with Cartman, Kyle, Stan, and Kenny, four names I kind of just picked at random, and just to keep things simple in this market, we'll say that each person's only willing to buy one thing. They're only going to buy 1 each. Right? If they could if they're going to buy it, they'll buy 1. They're not going to buy 3 or 4 of the same just to keep it simple, we'll say it's something like that, like they're in the market for like a golden cheesy poof or 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'll see Cartman really wants this Golden Cheesy poof and is willing to pay up to 8 dollars for it. Kyle, 6, Stan, 4, and Kenny, 2. So let's go ahead and put these onto our graph here. Right? We've got our price and our quantity axes there, and we've got some prices there, some quantities. It's all set up for us. So we're going to say at a price of 8 dollars how many people are willing to buy? Well we've got just Cartman, right, so there's going to be one quantity demanded at a price of 8 dollars, and what about at a price of 6 will now Cartman and Kyle both buy, right? So we'll be right here. Stan down here. That's at a price of 4 3 people get in and a price of 2. All 4 of them are in the market and 4 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 because it's such a small market that there's not people in between these points. So you could imagine like instead of connecting these diagonally like this, there's really nobody in the market at this price of 7 dollars 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 going to have this stair-step kind of look. So it's jagged because it's such a small market that we don't get that smooth curve from having a lot of buyers and a lot of, yeah, 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 dollars if we look right here, it's still only Cartman that buys, right, so we have a quantity of 1 at a price of 7 or 8 dollars right? So that's kind of how we're going to draw it in this small case. It's not so important, but it's going to help us do this example easier. It helps us visualize the surplus. So let's go ahead and start with Cartman or excuse me, start with this price of 7 dollars right? So let's say the price is 7 dollars 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 dollars but he only has to pay 7, right? Minus 7, so he has a consumer surplus of 1 there. How about Kyle? Well, at a price of 7, Kyle's not going to buy, right? His willingness to pay is 6 dollars He doesn't buy at 7, so he doesn't get any surplus if he doesn't, buy anything. So he has no surplus, he didn't buy. Stan also has a willingness to pay lower and so does Kenny, right? None of them are going to buy. Only Cartman gets in this market. So at the bottom, I've got this summary. I'm going to get out of the way so we can fill these boxes. We've got a summary of what happened, right? Quantity demanded and consumer surplus. Total consumer surplus in each situation. So at a price of 7 dollars, quantity demanded was just the one, right? Cartman's the only one that buys when the price is 7 dollars and total consumer surplus is 1 which is Cartman's consumer surplus. I want to show you that on the graph real quick. So this total consumer surplus of 1, I'm going to mark this green because I'm going to mark the area in green over here. This consumer surplus of 1 is represented by this area right here that I'm marking in green, Right? Just that area above the price of 7 dollars right? So there was our price of 7 dollars and our consumer surplus is above that line and and below the the maximum price there that he was willing to pay. So just so you can see right, 8 minus 7, right, that's going to be this length right here is 8 minus 7 which is 1, and this area right here, although it looks like 2 because it but our notice how our graph is 1, 2, 3, 4 like that. So that's 1 as well. So 1 times 1 is 1 and that's our consumer surplus of 1. Okay. So let's go on to a price of 5 dollars What happens at a price of 5 dollars? Well, Cartman's still going to buy it. Right? But now he's getting an even better deal. He's going to be even happier about this. So 8 minus 5, he is going to get 3 consumer surplus instead of 1 now. Right? Notice how his consumer surplus has grown. How about Kyle? Well, at a price of 5 dollars Kyle does get in the market. Right? He's willing to pay 6, but the price is 5. So now Kyle is going to buy, and he'll have a consumer surplus of 1. Right? 6 minus the market price of 5 gives us 1. Stan, he still doesn't get in, right, because the price is 5 and he's only willing to pay 4, so he's still not going to buy. He has no consumer surplus. Kenny also will not buy because his willingness to pay is too low. Alright, so what happened in this situation? How much quantity was exchanged? Well now Carmen bought 1 and Kyle bought 1, right? So there was 2 exchanged, And how about the consumer surplus, right? The consumer surplus is now Cartman's 3 plus Kyle's 1 is 4, right? So the price went down and consumer surplus increased. That kind of makes sense, right? Everyone's getting good deals, as the price goes down. The good deals, keep on coming. So I'm going to mark this area on the graph in blue, right, but I want to go piece by piece because I want to show you, where each surplus is. So remember, this spot right here is Cartman's demand. Right? This this spot, on the graph, the price of 8, 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? So Cartman's consumer surplus is right here, right, and his grew. At a price of 7, he had 1 consumer surplus and now he has 3. 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? That's Cartman's additional consumer surplus at this price of 5 dollars right? This is the price of 5 dollars right here, but now Kyle is also getting some consumer surplus surplus right and that's represented by this area here. Kyle's demand and it's still above that price of 5 dollars right. So that's what we have right there. That additional area is 3 and it represents the additional consumer surplus that gets us to a total consumer surplus of 4 because Cartman already had a little bit. Alright, so let's go on to this last case when the price is 4 dollars right? Right? So now the price has dropped again to 4 dollars Cartman's consumer surplus, what do you think? It's going to keep increasing, right, because he's getting better and better deals So he's getting more and more surplus. 8 minus 4 equals 4 dollars. Kyle, 6. His is going to grow as well, right? He was buying before, he's going to keep buying so his consumer surplus grew to 2. How about Stan? Now Stan, he is going to get into the market, right? The price is 4 dollars, he's willing to pay 4, 4-four, 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 going to say that he buys it here. And how about poor Kenny here? Poor old Kenny still is not going to pay. His willingness to pay his 2 dollars. The price is 4. He's not going to buy it. Alright. So what's happened in this case? Well now 3 people have bought, right? Cartman, Kyle, and Stan are all in the market. 3 are quantity demanded, and what's our consumer surplus? Well, we've got 4 from Cartman. Kyle's got 2. Stan's got 0. So we got 4 plus 2 plus 0 is 6, right? 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 going to 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, excuse me. All of those colors right there all represent a surplus and Kyle's surplus. So he's going to 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 dollars, 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 dollars and Stan's demand right there. Right, so our total consumer surplus is represented by all highlighted area, the green, the blue, and the purple. Alright, so let's go ahead and 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. Now you see on the graph, the demand curve that we're used to; it's not that jagged one anymore. This is that downward demand, the double d's. We've got our price axis and our quantity axis. So, how did we get to this kind of full demand curve, right? In this situation, there are more people in the market, right? Before, we only had 4 buyers, but now you could imagine Cartman was going to buy for 8, Kyle for 6, and now there are going to 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 $7.30. All these different willingness to pay kind of smooth out the line just because there are way more customers now, and now there's the opportunity, we're going to 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 could be at multiple places along this line, but, 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. 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 the market price. Right. We're going to 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 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, and we would have to be given this point, right, if we were going to calculate it. We don't know what it is. It would have to be given to us or something, and then we've got our height right here right. This is going to be the height of the triangle and what does that represent? Well, the height is just the quantity demanded right there at that price. 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 a Consumer Surplus there. So now let's talk about the idea of what's going to 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 going to have more surplus, right, because people are getting better deals, right? There are the people who were 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 going to be getting in the market who are also going to be getting some consumer surplus. Right. So this price decreased just like we saw above. As the price went down and down and down, Cartman's surplus kept rising, the new people's surplus started coming in right, so let's go ahead and see what happens to the surplus here. Let me pop out of the way here. Alright so we're still going to have that same original surplus right? Well first let me mark here we got our price axis, our quantity axis, and now we're at this I'm going to call it PL like low price right? A lower price and let's go ahead and talk about the consumer surplus. So this purple, 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. Well, those consumers that were buying before still get the surplus and then those consumers also get more surplus just like we saw Cartman and surplus increasing as the price dropped. That's going to be represented by this box. So the people who are already in the market are now getting more surplus, because the price went down. They're getting an even better deal. They get more surplus. Alright. So that's represented by that green box is the additional surplus to the people who were already buying, and then this blue box is going to represent new surplus to new customers, right, people who were not in the market before but now that the price decreased, they are in the market. Right, so that's going to be our additional surplus is going to be that green and the blue is the extra surplus we just got because of the price decrease, 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 could 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? We would know it's 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. And then they can 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 going to be calculating areas of triangles like that, so just know it's going to 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

The graph below represents the market for funky fresh rhymes. At a price of $3,000 per funky fresh rhyme, what is the consumer surplus? Alright. Cool. So, what do we have 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 going to get a triangle out of that, and it's going to be this area right here. I'm going to 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 the 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 going to 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 going to be these two sides here and this side right here, right? That's going to, we'll call that our base. Either one can be the base, either one can be the height, as long as you pick them. Alright. So what's going to be our base, right? Our base is going to be this length between the 3,000 and the 7,000. So it's going to be half times our base is the difference between the 7,000 and the 3,000, right? It's going to be that 4,000 difference, but I'm going to write it out here. 7,000 minus 3,000, right? That's that length 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 going to be that quantity demanded at that price of 3,000. The quantity demanded is 7.50 and that represents this length, right, from 0 to 7.50 times 750 in that case, right. There's no subtraction needed there because we're going all the way from 0. So that's the bulk of it. Let's do this math and figure out what the answer is. So the area calculation is: 12× (7000-3000) ×750, which simplifies to:0.5×4000×750 = 1,500,000. So, the consumer surplus at a price of $3,000 per funky fresh rhyme is $1,500,000. 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

Here’s what students ask on this topic:

What is consumer surplus and how is it calculated?

Consumer surplus is the difference between what consumers are willing to pay for a good or service and what they actually pay. It represents the benefit consumers receive from purchasing at a lower price than their maximum willingness to pay. To calculate consumer surplus, you can use the area below the demand curve and above the market price. In a graphical representation, this area is often a triangle. The formula for the area of a triangle is:

$\frac{1}{2}\times \mathrm{base}\times \mathrm{height}$

Here, the base is the quantity demanded, and the height is the difference between the maximum willingness to pay and the market price.

How does a decrease in price affect consumer surplus?

A decrease in price generally increases consumer surplus. When the price drops, existing consumers who were already purchasing the good enjoy a better deal, increasing their individual consumer surplus. Additionally, new consumers who were previously unwilling to buy at the higher price enter the market, contributing to the overall consumer surplus. Graphically, this is represented by a larger area between the demand curve and the new, lower market price. The total consumer surplus is the sum of the additional surplus gained by existing consumers and the surplus from new consumers entering the market.

What is the relationship between willingness to pay and the demand curve?

The demand curve represents the willingness to pay of consumers at different price levels. Each point on the demand curve indicates the maximum price that consumers are willing to pay for a specific quantity of a good or service. As the price decreases, the quantity demanded increases, reflecting higher willingness to pay among more consumers. Therefore, the demand curve can be seen as a graphical representation of the marginal benefit to consumers, showing how much value they place on additional units of the good or service.

Can you provide an example of consumer surplus in a small market?

Consider a small market with four consumers: Cartman, Kyle, Stan, and Kenny. Their willingness to pay for a product is $8, $6, $4, and $2, respectively. If the market price is $5, Cartman and Kyle will buy the product. Cartman's consumer surplus is $8 - $5 = $3, and Kyle's is $6 - $5 = $1. Stan and Kenny will not buy because their willingness to pay is below the market price. The total consumer surplus in this market is $3 (Cartman) + $1 (Kyle) = $4. This example illustrates how consumer surplus is calculated based on individual willingness to pay and market price.

What is the formula for calculating consumer surplus using the demand curve?

The formula for calculating consumer surplus using the demand curve is the area of the triangle formed by the demand curve and the market price. The formula is:

$\frac{1}{2}\times \mathrm{base}\times \mathrm{height}$

In this context, the base is the quantity demanded at the market price, and the height is the difference between the maximum willingness to pay (as indicated by the demand curve) and the market price. This calculation provides the total consumer surplus in the market.