in this video, let's discuss what the demand curve for a public good would be and how we come up with the optimum quantity of a public good. So first, before we get to public goods, I kind of want to remind you how we create the demand curve for a private good. Right? I'm kinda gonna go a little quickly on this section, because we've had a video that really goes into detail about this. And if you guys are still tripped up up after this little discussion, I would suggest just go into the search bar and looking up a video, I'm almost certain it's just called individual uh verse market demand. Right? So if you just type that in the search to the search bar, um you can get that video with a little more detail about these private goods, right? And how we come up with the demand curve for a private good. So let's start here to create the demand curve of a private good. We're gonna add all the individual quantity demanded at each price. Alright, So at each price, we're gonna take the quantity demanded of each person and add it together to get to our market demand. So, let's start here. This could be the demand for cheeseburgers, right cheeseburgers, cheese cheeseburgers, cheeseburgers were one of our good examples of a private good. Write something that's rival and excludable. So let's go ahead and see what we've got on these two. So we'll keep it simple. We've got two people in this society to individual demands, and then we'll find our market demand based on that. But you can imagine this could extend to thousands of people as well. So we'll see is that this first person At a price of $5, right? We see this price of $5, they're willing to buy one cheeseburger, right? One cheeseburger will say one cheeseburger a week at $5. And the second person here on the second graph, right, This is to individual demands and market demand on the right, So the second person at that same price of $5 is also willing to purchase one cheeseburger. Right? So what about at this price of $3? If we see the price go down to $3? Well then person one here is gonna buy five cheeseburgers that week. Right? And person two at this lower price will buy three cheeseburgers. So let me go ahead and get out of the way here. And let's look at the market demand. So how do we get to our market demand um from these individual demands? Well, we're gonna add all the quantity demanded at each price. So in the blue circles, right, we have the price of $5. And at that price of $5 we've got one Quantity demanded, and one quantity demanded, right, there's gonna be two total quantity demanded. And that's what we see here, right, at that price of $5, right all the way across there, that price of $5, we see two are demanded. Right? One from each person. Now, what about at a price of $3? We're gonna see that the person, person one here is gonna demand five and person two will demand three. Right? So we're gonna have five and three gets us to this total eight demand on our market demand curve. Right? So what did we see happening there um in this case, Right, what we were doing is we were adding the quantities demanded. So what we call this is that we were adding, uh let me do it in. Red, add horizontally. Is what I'm gonna say, right? Because we're adding the quantities demanded. In this case we're adding horizontally, the quantity plus the quantity gets us this way. Right? So that's how we do private goods. And remember if this was too quick for you go back to that other video and get a little more detail on how this happens. All right, So let's go ahead and let's talk about public goods. Right. I'm gonna go ahead and stop the video just so that we can kind of re start fresh. And um let's let's pause here and continue in the next video with the demand curve for public goods. Cool, let's do that. Now

Alright, so here we are, the demand curve of public goods. So before we were adding quantities at each price, here we're gonna do the opposite, we're gonna add individual prices at each quantity. Okay? So at each quantity demanded, we're gonna add the price each person is willing to pay. Right? Because remember with public goods, what do we see with public goods? Public goods are non rival and non excludable. Right. So in this case that same quantity, right? If we were to provide one quantity of a public good, everyone can use that same quantity. So in the sense, in that sense, what we wanna do is we want to find, how much would each person pay for that quantity of good and we can add all those prices together, right? If I if I would pay five and you would pay three and he would pay two and we would add all of those together to find the total amount that the society values this public good. Right, at that quantity. So let's go ahead and we're gonna do this in a small setting, right? This isn't gonna be a setting with a government, it keeps our example a little easier. We're gonna have to individuals in this, in this society, right? We're gonna have this idea where we've got maybe jane who owns a restaurant, jane's restaurant and we've got down here bob, you know, bob's got his auto shop, right? And let's say that jane and bob have their restaurant and their auto shop right next to each other, right? And they're the only two businesses on this rural road, right? So they're the only two businesses there right next to each other and they're both scared at night. They think that if while they're not there that their businesses could get burglarized, right? So they're both considering hiring a security guard. And what they noticed is that the security guard um the security guard would cannot um guard one place without guarding the other. Right? So what we see is that it's non excludable, right? They can't prevent the guard from if jane hires bought a security guard, his presence there is going to also protect the bob bob's auto shop. Right? So it's non excludable in this case, right? They're both going to get the benefit um from the security guard being there right in the sense that they're, you know, they're right next to each other or whatever. The guard can has to protect both businesses at the same time and it's also non rival right by one business being protected. It doesn't stop the other business from being protected. The same quantity of protection is used by both businesses. Cool. So let's look at their both of their demand curves for this bodyguard. Excuse me, security guard. So start with jane. If we were gonna have 10 hours of security jane is willing to pay up to $8 an hour for these 10 hours of security, right? So let's go down to bob's graph, I know it doesn't all fit here, but bob's graph shows that at that 10 hours, right, Those same 10 hours bob is willing to pay up to $10 an hour. Right? And that might be bob's business, right? He's he's more worried about his autos than jane is worried about her restaurant, whatever it is, they each have their own individual demand for the, for these uh for the security service. And just the same If there was 15 hours of service right now there's more service. Um they're not getting as much benefit from those later hours of services, those first few hours um that are most beneficial to them. So you can imagine that they're going to have less demand for a greater amount of hours. So Jane is only willing to pay up to $4 an hour for 15 hours of protection. Where Bob would be paying, willing to pay up to $5 an hour for 15 hours of protection here. Right. So again, what we're going to see is we have these different prices at these different quantities, but in this case, since it's a public good right? We can find the total benefit that they would get from having this public good available and that's what the market demands. It's gonna look like. The market demand is gonna include their total benefits by adding the price at each quantity, right? So at a quantity of 10 hours jane is willing to hire to pay eight an hour. And bob is willing to pay 10 an hour. Right, so what do we see? Oops, wrong color. The 18 this 18 an hour is the sum of jane's 10 and bob Excuse me, James eight and bob's 10 an hour. Right? So together they would be willing to pay up to $18 an hour for 10 hours of protection. Right? And that makes sense because they're going to be sharing this good, right, so they can clump up the money together to see what it's worth in total. And the same thing we're gonna see with the 15 hours, right? At 15 hours Jane is willing to pay for, Bob is willing to pay five so we get a $9 an hour for 15 hours. Right, so what did we see happen here? Up above we were adding vertically. Right. We added the curves, we added the individual demands, excuse me horizontally. Right. We were adding the quantities in that case, in this case we're gonna be adding them vertically. Right? We add the prices add vertically. Right? So up above we added them horizontally. Where we added the quantities and that was for a private good. Right, and here a public good. We add the prices, we add vertically. Cool. So that is kind of how we're gonna build the demand curve for a for a public good. But how do we go about and say so what is the right amount? Right, what is going to be the right amount? Should we have 10 hours of service, of security guard service? 15 hours? What is gonna be the optimal quantity of this public good? Well, just like we're used to it's gonna be where that marginal benefit equals the marginal cost, right? Marginal benefit equals the marginal cost. We've been talking about this all throughout the course. Right. And here it comes up again. So here we have that marginal benefit curve. And I guess I'm gonna go ahead. I want to put in marginal social benefit. M. S. B. Equals marginal social cost. That's just a little technical because we're talking about society as a whole here, right? This security guard is for everyone in the society, this is gonna be the marginal social benefit of the security guard right now, the cost. What about that marginal social cost? Um Well, the marginal social cost is just gonna be our supply curve, right? If we don't have any externalities in this market, right? The supply of security guards is just gonna be the supply curve for security, Right? So, what we're gonna see is, alright, there's no externalities here, when we think about a security service. So we'll just say that there's some sort of supply curve of security service and I'm gonna draw it in right there, right? That doesn't have to be the curve. But I drew it there and that is gonna be our marginal social cost. That's just our supply curve. Right? So what do we see? We found a point where marginal social benefit equals marginal social cost and that's gonna be at a price of $9.15 hours of of security guard services. Right? So that's all, that's how we find the optimal quantity. Um The curves kind of have to be given to you there, at least the cost curve. Right? The social benefit curve, you could be given a bunch of individuals and added up to make the demand, the market demand there. So just to reiterate the marginal social benefit curve is the sum, let me do it in red. The sum of the individual values, right? The individual values, consumers place on the public good these values. That's the price is right. This is the prices that they would be willing to pay for those goods. Right? And the marginal social cost curve. Well, that is just gonna be equal to our supply curve, right? As long as we don't have any externalities in this, where, you know, we have to account for those if they did exist right, we would want to account for all all costs, even to society, but without dealing with externalities, we're just gonna have the marge social costs be equal to the supply curve, right? We're gonna find that point where marginal social benefit equals marginal social cost and that's gonna be the quantity, the optimal quantity of this good. Cool. So that's how we build the demand curve and find the optimal quantity of public goods. Let's go ahead and move on to the next video.