Public Goods: Demand Curve and Optimal Quantity - Online Tutor, Practice Problems & Exam Prep

The demand curve for public goods differs from that of private goods. For public goods, which are non-rival and non-excludable, we add individual prices at each quantity to determine market demand. The optimal quantity occurs where marginal social benefit (MSB) equals marginal social cost (MSC). This relationship highlights the importance of understanding consumer surplus and the free-rider problem, as individuals benefit from public goods without directly paying for them. Thus, effective allocation of resources is crucial for achieving an efficient market outcome.

Demand Curve of a Private Good

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. First, before we get to public goods, I want to remind you how we create the demand curve for a private good. I'm going to 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, after this little discussion, I would suggest just going to the search bar and looking up a video. I'm almost certain it's just called "Individual versus Market Demand". So if you just type that in the search bar, you can get that video with a little more detail about these private goods 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 going to add all the individual quantities demanded at each price. At each price, we're going to take the quantity demanded of each person and add it together to get to our market demand. Cheeseburgers, for example, are typical private goods, something that's rival and excludable.

Let's keep it simple; we've got 2 people in this society, 2 individual demands, and then we'll find our market demand based on that. But you could imagine this could extend to thousands of people as well. At a price of $5, the first person is willing to buy 1 cheeseburger a week. The second person at that same price of $5 is also willing to purchase 1 cheeseburger. Now, at this price of $3, when the price goes down, the first person is going to buy 5 cheeseburgers that week, and the second person will buy 3 cheeseburgers.

So let me go ahead and get out of the way here and look at the market demand. To determine our market demand from these individual demands, we'll add all the quantities demanded at each price. At a price of $5, there is 1 quantity demanded from each, totaling 2 cheeseburgers demanded. What about at a price of $3? The first person will demand 5 cheeseburgers, and the second will demand 3, giving us a total of 8 cheeseburgers on our market demand curve.

In this case, what we're doing is adding the quantities demanded horizontally. The quantity plus the quantity gets us to the total demand. That's how we handle private goods, and remember if this was too quick for you, go back to that other video for more detail on how this happens.

Alright, let's go ahead and talk about public goods. I'm going to stop the video just so that we can restart fresh and let's pause here and continue in the next video with the demand curve for public goods. Cool, let's do that now.

Demand Curve of a Public Good

Alright, so here we are, the demand curve of public goods. So before we were adding quantities at each price, here we're going to do the opposite. We're going to add individual prices at each quantity, okay. So at each quantity demanded, we're going to add the price each person's 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 that sense, what we want to do is we want to find how much each person would pay for that quantity of good, and we can add all those prices together, right? If I would pay 5 and you would pay 3 and he would pay 2 and so on, 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 going to do this in a small setting, right. This isn't going to be a setting with a government. It keeps our example a little easier. We're going to have 2 individuals in this society, right? We're going to 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 2 businesses on this rural road, right. So they're the only 2 businesses that are 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 notice is that the security guard would cannot 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 Bob's Auto Shop, right? So it's non-excludable in this case, right? They're both going to get the benefit from the security guard being there, right? In the sense right next to each other or whatever. The guard 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. Let's look at their both of their demand curves for this Bodyguard or excuse me, Security Guard. So start with Jane. If we were to 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 more worried about his autos than Jane is worried about at a restaurant. Whatever it is, they each have their own individual demand for the security service. And just the same, if there was 15 hours of service right, now there's more service, they're not getting as much benefit from those later hours of service, it's those first few hours that are most beneficial to them, so you could imagine that they're going to have less, demand for a greater amount of hours, so Jane's 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 demand is going to look like. The market demand is going to 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 8 an hour and Bob is willing to pay 10 an hour, right? So what do we see? Whoops, wrong color. The 18, this 18 an hour is the sum of Jane's 10 and Bob or excuse me, Jane's 8 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 going to see with the 15 hours, right? At 15 hours, Jane is willing to pay 4 dollars Bob is willing to pay 5 dollars 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 we were adding horizontally, right. We were adding the quantities in that case. In this case, we're going to 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 going to build the demand curve 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 security guard service, 15 hours? What is going to be the optimal quantity of this public good? Well, just like we're used to, it's going to 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 going to go ahead I want to put in marginal social benefit and SB equals marginal social cost. That's just a little technicality because we're talking about society as a whole here, right? This Security Guard is for everyone in the society. This is going to be the marginal social benefit of the Security Guard, right? Now the cost, what about that marginal social cost? Well, the marginal social cost is just going to be our supply curve, right? If we don't have any externalities in this market, right, the supply of security guards is just going to be the supply curve for security, right, so what we're going to see is, alright, there'€™re 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 going to draw it in right there, right. That doesn't have to be the curve, but I drew it there and that is going to 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 going to be at a price of $9 for 15 hours of security guard services, right? So that's all that's how we find the optimal quantity, the curves kinda 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 add it 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 prices 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 going to be equal to our supply curve, right? As long as we don't have any externalities in this where, you know, we'd have to account for those if they did exist, right, we would want to account for all costs even to society, but without dealing with externalities, we're just going to have the marginal social cost be equal to the supply curve, right? We're going to find that point where marginal social benefit equals marginal social cost and that's going to 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.

The benefit of an additional unit of a public good is:

• A. The highest price someone would pay for it
• B. The lowest price someone would pay for it
• C. The sum of the reservation price of all the people who use it
• D. None of the above

If the benefit of a public good does not exceed its cost:

• A. The government should not provide the public good
• B. The government should provide the public good
• C. The government is indifferent about producing the public good
• D. None of the above

To find the benefit of an additional unit of a public good, we sum the individual demand curves:

• A. Horizontally
• B. Vertically
• C. Diagonally
• D. None of the above

Two roommates plan to spend their evening with a marathon of Saw horror movies. Because it is a marathon, they must start with the first movie in the series and continue in order. Their willingness to pay for the rental of each movie is as follows:The marginal benefit from renting the third movie is: 

• A. $36
• B. $8
• C. $5
• D. $3

Two roommates plan to spend their evening with a marathon of Saw horror movies. Because it is a marathon, they must start with the first movie in the series and continue in order. Their willingness to pay for the rental of each movie is as follows:If each movie rental costs $6, how many movies should they rent? 

• A. One movie
• B. Two movie
• C. Three movies
• D. Four movies

Which of the following is not a possible solution to the tragedy of the commons?

• A. Users sharing the work needed to manage the use of the resource
• B. Private ownership
• C. Government regulation
• D. All of the following are possible solutions to the tragedy of the commons.

Here’s what students ask on this topic:

What is the difference between the demand curve for public goods and private goods?

The demand curve for public goods differs from that of private goods primarily in how it is constructed. For private goods, which are rival and excludable, the market demand curve is derived by horizontally summing the individual quantities demanded at each price. In contrast, for public goods, which are non-rival and non-excludable, the market demand curve is derived by vertically summing the individual prices each person is willing to pay for each quantity. This means adding the prices at each quantity to determine the total value society places on the public good.

How do you determine the optimal quantity of a public good?

The optimal quantity of a public good is determined where the marginal social benefit (MSB) equals the marginal social cost (MSC). The MSB is the sum of the individual values consumers place on the public good, while the MSC is typically represented by the supply curve, assuming no externalities. The intersection of the MSB and MSC curves indicates the optimal quantity, ensuring that the resources are allocated efficiently and the total benefit to society is maximized.

What is the free-rider problem in the context of public goods?

The free-rider problem occurs when individuals benefit from a public good without directly paying for it. Since public goods are non-excludable, people cannot be prevented from using them, even if they do not contribute to their provision. This leads to underfunding and potential under-provision of the good, as individuals rely on others to bear the cost. Addressing the free-rider problem often requires government intervention to ensure adequate provision and funding of public goods.

Why is it important to understand consumer surplus in the context of public goods?

Understanding consumer surplus is crucial in the context of public goods because it represents the difference between what consumers are willing to pay and what they actually pay. For public goods, consumer surplus helps measure the total benefit to society, as individuals often receive more value from the good than the cost they incur. This concept is essential for evaluating the efficiency and effectiveness of resource allocation, ensuring that public goods are provided at levels that maximize societal welfare.

How do you construct the market demand curve for a public good?

To construct the market demand curve for a public good, you add the individual prices each person is willing to pay for each quantity of the good. This process is known as vertical summation. For example, if one person is willing to pay $5 for a certain quantity and another is willing to pay $3 for the same quantity, the total willingness to pay for that quantity is $8. By summing these prices at each quantity level, you create the market demand curve, reflecting the total value society places on the public good.