Public Goods: Demand Curve and Optimal Quantity: Videos & Practice Problems

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

To understand the demand curve for public goods, it's essential to first grasp how we derive the demand curve for private goods. The demand curve for a private good is created by aggregating the individual quantities demanded at each price point. For instance, consider cheeseburgers as a private good, which is both rival and excludable. If we have two individuals in a society, we can illustrate their demand at different prices. At a price of $5, both individuals may be willing to purchase one cheeseburger each, resulting in a total market demand of two cheeseburgers. If the price drops to $3, the first individual might demand five cheeseburgers while the second demands three, leading to a total market demand of eight cheeseburgers at that price.

This process of determining market demand involves adding the quantities demanded by each individual at each price, which is referred to as horizontal summation. This means that for each price level, we sum the individual demands to find the total market demand.

When transitioning to public goods, the approach to determining demand changes significantly. Public goods are characterized by being non-rival and non-excludable, meaning that one person's consumption does not diminish another's ability to consume the good, and individuals cannot be effectively excluded from using it. This fundamental difference necessitates a different method for calculating the demand curve for public goods, which will be explored further in subsequent discussions.

Demand Curve of a Public Good

The demand curve for public goods operates differently than that of private goods. Instead of adding quantities at each price, we add individual prices at each quantity demanded. Public goods are characterized as non-rival and non-excludable, meaning that one person's use of the good does not diminish another's ability to use it, and individuals cannot be effectively excluded from its benefits. This unique nature allows us to assess how much each person is willing to pay for a given quantity of the public good, ultimately leading to a total societal valuation of that good.

To illustrate this concept, consider a scenario involving two individuals, Jane and Bob, who own neighboring businesses—a restaurant and an auto shop, respectively. Both are concerned about potential burglaries and are contemplating hiring a security guard. Since the security guard's presence would protect both businesses simultaneously, the good is non-excludable. Additionally, the protection provided does not reduce the level of security available to either business, making it non-rival as well.

When determining their willingness to pay for security, Jane might be willing to pay $8 per hour for 10 hours of service, while Bob might be willing to pay $10 per hour for the same amount. To find the total societal benefit for 10 hours of security, we sum their individual valuations, resulting in a total willingness to pay of $18 per hour. For 15 hours of service, Jane's willingness drops to $4 per hour, and Bob's to $5 per hour, leading to a combined total of $9 per hour.

This process of summing individual prices at each quantity allows us to construct the market demand curve for public goods. Unlike private goods, where quantities are added horizontally, public goods require vertical addition of prices to reflect the total benefit to society.

To determine the optimal quantity of a public good, we look for the point where marginal social benefit equals marginal social cost. The marginal social benefit curve represents the total value that consumers place on the public good, derived from their individual willingness to pay. Conversely, the marginal social cost is represented by the supply curve of the good, assuming no externalities are present. By identifying the intersection of these two curves, we can ascertain the optimal quantity of the public good that maximizes societal welfare.

In summary, the demand curve for public goods is constructed by aggregating individual willingness to pay at each quantity, and the optimal provision of such goods is determined where the marginal social benefit equals the marginal social cost. This framework is essential for understanding how public goods are valued and allocated within society.

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

Answer: (C)

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

Answer: (A)

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

Answer: (B)

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

Answer: (B)

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

Answer: (C)

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.

Answer: (D)

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.