Producer Surplus and Willingness to Sell - Video Tutorials & Practice Problems

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 laying around the house that you're like, hey, if I could sell this on Ebay for five bucks, that'd be awesome, right? And you put it on Ebay, it ends up being a collector's item and it sells for 50 bucks. You would have sold it for five bucks, right? Hey, so you've had some producer surplus, Let's dive in. All right. 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 gonna represent the minimum price for someone to, for one of the suppliers to sell their thing, right? So the minimum price is the willingness to sell and we're just gonna see just like the demand curve represented the willingness to pay. We've got the supply curve is gonna 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 not just talking about good deals for the producer, right? Um, so this is when they're willing to sell for less than the market price, right? And we talked about this willingness to sell, right? Everyone's kind of 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, you're a teddy bear, that teddy bear and you're not gonna have that same willingness to sell, right? You probably wouldn't get rid of your teddy bear for $10, right? That teddy bear has got some serious emotional value in there, that's gonna bring that willingness to sell way up. All right, So that's kind of willingness to sell is gonna be different for for each supplier, and that's where we're gonna 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, it's gonna 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 overcomplicate is that that supply curve is gonna represent our marginal cost. Okay, so let's go ahead. Um And do just like we did with consumer surplus. Let's do a small small setting example of of producer surplus here. So I've got four names I picked at random right? Bart lisa marge in homer. And they're gonna be producers in this market. And just like before we're gonna have only one thing per person, right? They're not gonna be selling multiple units. Each person is just gonna sell one. They each have one of this, maybe it's that golden cheesy poof. Right? They each have one to sell. Um And let's go ahead and draw their their supply curve uh in this small market. So let's start with Homer right, when the price is low, homer is gonna be the only one that sells 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 March. So we'll have to supplied at a price of $4. Same thing here at a price of six. You'll see Lisa get in the market. So three will be supplied. And finally everybody sells one of the prices at least $8. Right? So let's go ahead and drive draw our supply curve. And remember we're not gonna get that straight line because we're still in a small setting, we're gonna get that jagged kind of supply curve? Um until we have a lot more sellers. Right? So in this small market we're gonna have this shape right? 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 one which is still correct right? Because homer is the only one who sells at a price of $3. So the quantity should still be one there. Alright so let's go ahead and calculate producer surplus at different price levels. I'm gonna get out of the way here. We're gonna 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 prices for who is going to sell at that price, Bart isn't going to sell right? That he will only sell if the price is at least eight. So since he doesn't sell, he doesn't get an opportunity to earn any consumer surplus. His zero producer surplus. His zero lisa as well she won't sell because the price is not high enough for her. Right? How about Marj though marge she has a willingness to sell of four and the prices for. So yeah she will sell four minus four. However she doesn't get any producer surplus. So she's just gonna unload her item at what she's willing to sell it at how about homer? So homer at a price of four? He's willing to sell for two. He's happy. Right? So he's gonna bring in $4. Although he would have sold it for two. He has producer surplus of two in this case. So what we have, we sold two items, right? Two items were exchanged margin Homer. So our quantity supplied here at the bottom, we got our summary quantity supplied is gonna be too and our producer surplus is gonna be the total surplus there, which only Homer has some and that's gonna be too as well. Alright so let's go ahead and visualize this on the graph. I'm gonna use Green. Um I'm gonna use Green to represent this. Give me one second. So this is gonna be um the producer surplus right here. Right? Our price is $4. And Homer's surplus which is the total surplus is gonna be this area under that price. Right? The only area under the price is right there. Cool. So that represents the producer surplus at a price of $4. And notice there's no area under Mark charges point. So I guess let me let me go ahead and mark these off. So this is homer right here, right, Homer was the one selling a $2 Marj here lisa and barb 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 gonna 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 four. She's definitely gonna be willing to sell at five. She's even happier now. Right, so she's gonna have a market price of five minus her willingness to sell of four. Now March has some producer surplus right? The price increased and the producer surplus increased. How about homer? Homer is gonna be happier about this? Right? The price went up. He was already willing to sell for two. Now it's five. So here we go. His producer surplus is three there. Right five minus two. So what happened in this situation, the price went up and the quantity exchanged is still to write only margin homer sold. But what happened to producer surplus? It's gone up. It's went from to and now it's 41 plus three Is for our total producer surplus is four. Let's go ahead and mark that um in purple on the graph. So our extra producer surplus. Right? Our prices 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 are extra surplus is gonna be below that line, but above the supply curve, so this area right here is our extra surplus. But first I guess let me let me do this first. Um Let's talk about homer first, homer is gonna get a little extra surplus, right? Because Homer was willing to sell for two. And at four he was already getting some surplus at five. He's gonna 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 those squares 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 seven, what happens? So the price of seven 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. Um and she has enough for it now. Right, so a price of seven minus six. She's gonna have producer surplus of one. How about marge, marge? Is surplus is gonna keep increasing, right? She had a willingness to sell a four, but now she can sell it for seven. Her surpluses three and homer. He's ecstatic. He's willing to sell for two. And now the price is seven. So his surplus has increased to five. So notices that price keeps increasing the surplus keeps increasing. Right? So now the quantity exchanged, the supply is gonna be three. Right at this price lisa margin homer all cell and our surplus. What's it gonna be? We've got the one plus the three plus the five gives us nine total surplus. Alright, So let's go ahead and represent that on the graph. So, we've got this price of seven here and hopefully you guys can start visualizing what's happening. So you can kind of see what area I'm gonna fill in. But let's fill it in piece by piece. So let's first talk about homer's additional surplus. That's gonna be this area right here, that he gained right from that increased price marge is going to get some extra surplus 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. All right, So that's kind of how we're going to see this right as the price goes up. You're gonna 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 gonna be our producer surplus. Just like we kind of saw in the examples in the small market, um we're gonna see it going on here. So let's start with this original producer surplus before we change the price. So we've got our price axis here, our quantity access and say that there's this price on the market, right? Whatever the market prices, and we're gonna 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 March at four. Well now there's suppliers that will supply at $3 at $3.05 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 the straight line and we got that upward supply, right? We have that downward demand supplies, 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 gonna highlight it here in this purple, right, and you'll see that we get a triangle again, right? We've got this triangle. Um And we could right theoretically get the area of this triangle? If we had the right information, right? We need some information about what that quantity is. We have our base and our height, right? And we could figure out um what that producer surplus is. We might need this number right here to what's that minimum supply. Well anyways 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 less people are willing to sell at a lower price. It goes back to that law of supply, lower price, less people supplying less quantity supply. 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're at this low price, we'll say P. L. Again, P. Lo L. Low. Right? So our original surplus for the producers was this whole purple area just like we had on the other side, right? Um that whole triangle. I'm gonna 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 P. L. And it's gonna be everything below the market price and above the supply curve. So we're gonna 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 gonna see that producers that are still selling right, they're still selling at this lower price because the lower prices still um above their willingness to sell or equal to their willingness to sell, um they're still gonna sell but they're gonna 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 changes gonna 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 prices decreased, their willingness to sell is above that price and they're no longer gonna 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, um 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 gonna be this uh rectangle, right? Or they could say what is um the surplus lost because people left the market and that's 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 surpluses. 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 half Bh so let's go ahead and do some examples. Um Some practice. And let's 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? Three 1000 right here. Right. So what's the area below the 3000? It's gonna be everything here but above the supply curve. Right. So we're gonna stop when we reach the supply curve and that's gonna be our producer surplus in this case. Is that triangle? Right? So we need to find the area of this triangle. If you remember area of a triangle is gonna be half times base times height. Right? Half be h. 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 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 in our height there. Right? So let's go ahead and see how do we calculate the base? Well, the base is gonna 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 3000. So we need the distance between that and we're gonna get half times. So the base is gonna be the difference of those two, right? 3000 minus 500. That's gonna give us the length of this 3000 minus 500 is the length um of the base there. And let's do the same thing with height. What do we see with height? Height? Well it's just it starts at zero. So we're not gonna have a subtraction here, starts all the way at zero and it goes to this 00.7 50. So the height is just gonna be 7 50 in this case times 7 50. Alright, so we've got all our numbers, we just gotta do some quick arithmetic and we'll have our area which is our producer surplus, so half times 2500 times 7 50. So our area is gonna be let me do some quick math in my head. It's gonna be 9 37 500. Right? I did that all in my head real quick. Um I'm just kidding. But the idea here is right, we'll do that math half times 2500 times 7 50. And that is our producer surplus, right, 9 37 500. And that is here at a price of 3000 producer surplus. A 9 37. 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