Producer Surplus and Willingness to Sell - Online Tutor, Practice Problems & Exam Prep

Producer Surplus in a Small Setting

So we've talked about Consumer Surplus, now let's talk about the other side of the coin, Producer Surplus, right? Maybe you found something lying around the house that you're like, hey, if I could sell this on eBay for $5, that'd be awesome. Right? And you put it on eBay, it ends up being a collector's item and it sells for $50. You would have sold it for $5, right? Hey, so you've had some producer surplus. Let's dive in. Alright, so you're gonna see a lot of parallels here between what we do here and what we did with consumer surplus. It's just a lot of it's kind of the other way around. So when we talked about willingness to pay, right, that was the maximum that someone was willing to pay, a consumer was willing to pay. Well, willingness to sell is going to represent the minimum price for someone, for one of the suppliers to sell their thing, right? So the minimum price is the willingness to sell and we're just going to see just like the demand curve represented the willingness to pay, we've got the supply curve is going to represent our willingness to sell. Okay. So surplus. We're talking about producer surplus, but surplus is still good deals, right? We're talking about the good deals. We're now just talking about good deals for the producer, right? So this is when they're willing to sell for less than the market price, right? And when we talk about this willingness to sell, right, everyone's going to have a different willingness to sell. You could maybe think about maybe this company that produces teddy bears, right, and they produce them, you know, maybe they're willing to sell them for $10 and the market price is $20, right, and they have some surplus there, but you have your teddy bear at home, you know, your teddy bear, that teddy bear and you're not going to have that same willingness to sell, right? You probably wouldn't get rid of your teddy bear for $10, right? That teddy bear's got some serious emotional value there that's going to bring that willingness to sell way up. Alright, so that's kind of willingness to sell is going to be different for each supplier and that's where we're going to get this Producer Surplus is where we get the market price minus that willingness to sell, alright? And just like the willingness to pay, our demand curve represented marginal benefit, the willingness to sell and our supply curve is going to represent our marginal cost to society. Okay so the idea here is you know that company is willing to sell those teddy bears for $10, right, but the market price is $20 for a teddy bear, the marginal cost is still going to be that $10 that they're willing to sell it at, right? Because they would have got rid of it at $10, they're just getting that surplus, that extra money, so the idea here not to over complicate is that that supply curve is going to represent our marginal cost. Okay, so let's go ahead and do just like we did with consumer surplus, let's do a small setting example of producer surplus here. So I've got 4 names I picked at random, right? Bart, Lisa, Marge, and Homer, and they're going to be producers in this market and just like before, we're going to have only one thing per person, right? They're not going to be selling multiple units. Each person is just going to sell 1. They each have one of this. Maybe it's that golden cheesy poof, right? They each have one to sell, and let's go ahead and draw their supply curve in this small market. So let's start with Homer, right? When the price is low, Homer's going to be the only one that sells. So at a price of $2, Homer is the only one getting in the market, and there will be one supplied. How about when the price rises to $4? Now Homer will sell, but also Marge. So we'll have 2 supplied at a price of $4. The same thing here at a price of $6, you'll see Lisa get in the market. So 3 will be supplied, and finally, everybody sells when the price is at least $8, right? So let's go ahead and draw or draw our supply curve and remember we're not going to get that straight line because we're still in a small setting. We're going to get that jagged kind of supply curve until we have a lot more sellers. Right? So in this small market, we're going to have this shape. Right? And we draw it this way because it makes sense. If the price was $3 or something, you can always double-check, right? At this price of $3, the quantity is 1 which is still correct, right because Homer is the only one who sells at a price of $3 so the quantity should still be 1 there. Alright, so let's go ahead and calculate producer surplus at different price levels. I'm going to get out of the way here. We're going to start with the low price of $4 and then raise the price to see how as the price increases, the producer surplus is going to increase. Cool? Let's do it. Alright, so let's start with this price of $4 So when the price is 4, who is going to sell? At that price, Bart isn't going to sell, right? He will only sell if the price is at least $8. So since he doesn't sell, he doesn't get an opportunity to earn any consumer surplus. His is 0 producer surplus. His is 0. Lisa as well, she won't sell because the price is not high enough for her. Alright. How about Marge, though? Marge, she has a willingness to sell of 4 and the price is 4. So yeah, she will sell 4-four. However, she doesn't get any producer surplus. So she's just going to unload her item at what she's willing to sell it at. How about Homer? So Homer at a price of $4, he's willing to sell for $2. He's happy, right? So he's going to bring in $4 although he would have sold it for $2. He has producer surplus of $2 in this case. So what do we have? We sold 2 items, right? 2 items were exchanged, margin Homer. So our quantity supplied here at the bottom, we got our summary. Quantity supplied is going to be 2 and our Producer Surplus is going to be the total surplus there which only Homer has some and that's going to be 2 as well. Alright, so let's go ahead and visualize this on the graph. I'm going to use green. I'm going to use green to represent this. Give me one second. So this is going to be the producer surplus right here right? Our price is $4 and Homer's surplus, which is the total surplus, is going to be this area under that price. Right. The only area under the price is right there. Cool. So that represents the Producer's Surplus at a price of $4 and notice there's no area under Marge's point, so I guess let me go ahead and mark these off. So this is Homer right here, right? Homer was the one selling at $2. Marge here. Lisa and Bart at the top. Right? So notice Marge's sale, she had no producer surplus, right? And that's because there's no area there under that price of $4 It's right on her willingness to sell. Let's go ahead and raise the price to $5 So at a price of $5 we're going to see that Bart still doesn't sell, right? Because he's only willing to sell if it's at least $8 Lisa the same, The price isn't high enough for Lisa to sell hers, but how about Marge? Marge, she was willing to sell at $4. She's definitely going to be willing to sell at $5. She's even happier now, right? So she's going to have a market price of $5 minus her willingness to sell at $4. Now Marge has some producer surplus, right? The price increased and the producer surplus increased. How about Homer? Homer is going to be happier about this, right? The price went up. He was already willing to sell for $2. Now, it's $5. So, here we go. His producer surplus is $3 there, right? $5 minus $2. So what happened in this situation? The price went up and the quantity exchanged is still 2. Right? Only Marge and Homer sold, but what happened to producer surplus? It's gone up. It went from 2 and now it's 4. $1 + $3 is $4. Our total producer surplus is $4. Let's go ahead and mark that, in purple on the graph. So our extra producer surplus, right, our price is now $5 right here that I'm marking on the graph. So let me go ahead and mark that all the way over to the line, and you can assume and you can guess, right that our extra surplus is going to be below that line but above the supply curve. So this area right here is our extra surplus, but first, I guess let me do this first. Let's talk about Homer. First, Homer's going to get a little extra surplus, right? Because Homer was willing to sell for $2 and at $4 he was already getting some surplus. At $5, he's going to get a little more, which is this area right here. Whoops. Right. That that little area is Homer's extra surplus because of the price increase and Marge is now going to earn some surplus right. That area. Those right there represents Marge's surplus now that the price went up, right? So that purple area is the extra surplus because the price rose from $4 to $5. Now let's see if the price rises to $7, what happens? So at a price of $7, Bart is still too attached to his golden cheesy poof and will not sell. Lisa, however, is finally ready to sell. She might get some saxophone reeds or something and she has enough for it now, right? So a price of $7 minus $6. She's going to have producer surplus of $1. How about Marge? Marge's surplus is going to keep increasing, right? She had a willingness to sell at $4, but now she can sell it for $7. Her surplus is $3 and Homer, he's ecstatic. He's willing to sell for $2 and now the price is $7, so his surplus has increased to $5. So notice as that price keeps increasing, the surplus keeps increasing, right? So now the quantity exchanged, the supply is going to be 3, right? At this price, Lisa, Marge, and Homer all sell, and our surplus, what's it going to be? We've got the $1 plus the $3 plus the $5 gives us $9 total surplus. Alright? So let's go ahead and represent that on the graph. So we've got this price of $7 here and hopefully, you guys can start visualizing what's happening. So you can kinda see what area I'm going to fill in, but let's fill it in piece by piece. So let's first talk about Homer's additional surplus. That's going to be this area right here that he gained, right, from that increased price. Marge is going to get some extra surplus. Oops. And then Lisa gets her surplus as well, right? Now that she got in the market and the price is above her willingness to sell. Alright So that's kind of how we're going to see this, right? As the price goes up, you're going to see more producer surplus. So let's go ahead to the next video and extend this idea to the full supply curve of the market.

Producer Surplus and Market Supply

Alright. So now let's extend that idea of producer surplus to the entire market. So, like we see here in the green box, we've got the area below market price, right, and above the supply curve. That's going to be our producer surplus just like we kind of saw in the examples in the small market. We're going to see it going on here. So let's start with this original producer surplus before we change the price. We've got our price axis here, our quantity axis, and say that there's this price on the market, right, whatever the market price is, and we're going to supply this quantity at that price. Right? And notice that now we've got our smooth supply curve. It's no longer that jagged curve that we saw before, and this is because there's a lot of suppliers now. Right? Before we had, you know, Homer supplying at $2, Mark at $4. Well, now there are suppliers that will supply at $3, at $3.5, right? All the willingness to sell, of all these multitude of suppliers now, and that's going to smooth out our curve and give us this straight line, and we got that upward supply, right? We had that downward demand; supply is the other one that goes upwards. Cool. So at this price p, what is our producer surplus? Well, it's going to be that area below market price and above the supply curve. So I'm going to highlight it here in this purple. Right? And you see that we get a triangle again. Right? We've got this triangle, and we could, right, theoretically get the area of this triangle if we had the right information, right, we'd need some information about what that quantity is, we'd have our base and our height, right, And we could figure out what that producer surplus is. We might need this number right here too. What's that minimum supply?

Well anyhow, let's go ahead and see what happens when we decrease the price, right? So when you decrease the price, what would you expect to happen to producer surplus? Would you expect producer surplus to increase or decrease? Well, the idea is that it's going to decrease, right? It's going to decrease because fewer people are willing to sell at a lower price. It goes back to that law of supply, lower price, fewer people supplying, less quantity supplied. So let's go ahead and see what happens here to our producer surplus. So, right, we had that original price, P, but let's say we were at this low price. We'll say PL again. PLow, L for low. Right? So our original surplus for the producers was this whole purple area just like we had on the other side, right? That whole triangle, I'm going to get rid of it and let's go ahead and highlight our new producer surplus in purple, right. So we expected it to decrease, we've got this low price of PL and it's going to be everything below the market price and above the supply curve. So we're going to get this little baby area right there is going to be our remaining producer surplus after the price decrease. So what happened to our Producer Surplus? Where did it go? Well first we're going to see that producers that are still selling, right, they're still selling at this lower price because the lower price is still above their willingness to sell or equal to their willingness to sell, they're still going to sell but they're going to lose surplus because the price dropped and that's represented by this green area right here. That green rectangle represents the surplus lost to the suppliers that are still in the market. Right? And just like with consumer surplus, the price change is going to drop these producers out of the market. Right? So this blue triangle represents suppliers that were selling at the higher price, but now that the price has decreased, their willingness to sell is above that price and they're no longer going to sell, right? So we lose that producer surplus from those people that exited the market, right?

So when they ask us questions, right, we could calculate the area. They could ask us to calculate the original producer surplus, right, and that's the entire area. That was the original surplus before the price change, but now we've got our new surplus, right? What is the remaining producer surplus? They could ask you to calculate that triangle right there. They could ask you, hey, what is the surplus lost by the people still selling? And that's going to be this rectangle, right? Or they could say what is the surplus lost because people left the market? And the producer surplus that we lost is the blue area because people left the market. Right? So if we had the right data, numbers for prices, numbers for quantities, we'd be able to calculate these areas and find out what these different parts of producer surplus are. So remember, it's going to be the area below the market price and above the supply curve. Alright, we've still got just like before, right the discussions and explanations. So let's go ahead and do some examples, some practice, and let's get this producer surplus stuff down pat. Alright. Let's do that in the next video.

Producer Surplus

Alright, let's do this example. The graph below represents the market for funky fresh rhymes. So at a price of $3,000 per funky fresh rhyme, what is the producer surplus? Right. So we dealt with this graph with consumer surplus. Now we're talking about producer surplus. Okay? So how do we see what the producer surplus is in this case? Remember, producer surplus is going to be the area below the market price and above the supply curve, okay? So what is our market price here? $3,000 right here, right? So what's the area below the $3,000? It's going to be everything here, but above the supply curve right so we're going to stop when we reach the supply curve and that's going to be our producer surplus in this case is that triangle right. So we need to find the area of this triangle. If you remember, the area of a triangle is going to be half times base times height. Right? 12bh. So we need to find what the base is and what the height is and then we can calculate this. So I tend to always put my base on the up-down axis. It doesn't really matter which one you call base, which one you call height, you'll get the same answer. So that's our base and our height there. Right? So let's go ahead and see how do we calculate the base. Well, the base is going to be this length right and it doesn't go all the way down to the bottom. It only goes up it stops at that 500 point, right, so it goes from 500 up to 3,000. So we need the distance between that and we're going to get half times so the base is going to be the difference of those 2, right? 3,000 minus 500. That's going to give us the length of this. 3,000 minus 500 is the length of the base there, and let's do the same thing with height. What do we see with height? Well, it's just it starts at 0 so we're not going to have a subtraction here. It starts all the way at 0 and it goes to this point 750. So the height is just going to be 750 in this case times 750. Alright. So we've got all our numbers. We just got to do some quick arithmetic and we'll have our area which is our Producer surplus. So half times 2,500 times 750. So our area is going to be let me do some quick math in my head. It's going to be 937,500 right. I did that all in my head real quick. I'm just kidding, but the idea here is right we'll do that math half times 2,500 times 750 and that is our producer surplus right. 937,500 and that is here at a price of 3,000 producer surplus. A 937,500. Cool. Let's move on to the next problem.

Use the graph for funky-fresh rhymes above. If a shift in demand causes equilibrium price to increase from $3,000 to $5,000 per funky-fresh rhyme, what is the change to producer surplus? 

• A. $2,250,000 increase
• B. $2,250,000 decrease
• C. $1,312,500 increase
• D. $1,312,500 decrease

Here’s what students ask on this topic:

What is producer surplus and how is it calculated?

Producer surplus is the difference between the market price at which producers sell a good and the minimum price they are willing to accept. It represents the economic benefit producers receive from selling at a market price higher than their minimum acceptable price. To calculate producer surplus, you find the area below the market price and above the supply curve on a graph. Mathematically, it can be represented as:

$P_S=\frac{(P_m-P_w)*Q_m}{2}$

where Pm is the market price, Pw is the minimum price producers are willing to accept, and Qm is the quantity sold.

How does a change in market price affect producer surplus?

A change in market price directly impacts producer surplus. When the market price increases, producer surplus rises because producers are receiving more than their minimum acceptable price, leading to greater economic profits. Conversely, when the market price decreases, producer surplus falls. This reduction can cause some producers to exit the market if the new price is below their minimum acceptable price. The change in producer surplus can be visualized as the area between the new and old market prices and the supply curve on a graph.

What is the relationship between willingness to sell and producer surplus?

Willingness to sell is the minimum price at which a producer is willing to sell a good. Producer surplus is the difference between the market price and this minimum acceptable price. If the market price is higher than the willingness to sell, the producer gains a surplus. For example, if a producer is willing to sell a product for $10 but the market price is $20, the producer surplus is $10. This relationship highlights the economic benefit producers receive when market conditions allow them to sell at higher prices than their minimum acceptable price.

How is producer surplus represented on a supply and demand graph?

On a supply and demand graph, producer surplus is represented by the area below the market price and above the supply curve. This area forms a triangle when the supply curve is linear. The base of the triangle is the quantity sold, and the height is the difference between the market price and the minimum price producers are willing to accept. As the market price changes, the area representing producer surplus will expand or contract accordingly, reflecting changes in economic benefits to producers.

What happens to producer surplus when the price decreases?

When the price decreases, producer surplus generally decreases. This is because the lower price reduces the difference between the market price and the minimum price producers are willing to accept. Some producers may find the new price below their minimum acceptable price and exit the market, further reducing the total producer surplus. The decrease in producer surplus can be visualized on a graph as a reduction in the area between the new lower price and the supply curve.