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 demanded to determine the market demand. The optimal quantity occurs where marginal social benefit equals marginal social cost, represented by the intersection of the marginal social benefit curve and the supply curve. This approach ensures that the total value society places on the public good is maximized, highlighting the importance of understanding demand dynamics in public economics.

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 rivalrous and excludable. If we have two individuals in a society, we can illustrate their demand at various prices. At a price of $5, both individuals may demand 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 summing individual demands is referred to as horizontal addition, where we combine the quantities demanded by each individual at each price level to form the market demand curve. This method can be extended to larger populations, maintaining the same principle of aggregation.

Transitioning to public goods, the demand curve operates differently. Public goods are characterized by being non-rivalrous 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. To determine the optimal quantity of a public good, we must consider the collective willingness to pay rather than individual demands. This involves vertically summing the individual demand curves, as each person's valuation of the public good contributes to the overall demand. The intersection of the total willingness to pay and the cost of providing the public good helps identify the optimal quantity that maximizes social welfare.

In summary, while private goods require horizontal summation of individual demands to establish market demand, public goods necessitate vertical summation to reflect the collective value placed on the good by society. Understanding these distinctions is crucial for analyzing how public goods are allocated and funded in an economy.

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 leads to a unique approach in determining the total value society places on a public good.

To illustrate this, consider two individuals, Jane and Bob, who are contemplating hiring a security guard for their adjacent businesses. Since the security guard's presence protects both Jane's restaurant and Bob's auto shop 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.

Each individual has their own demand for security services. For instance, Jane is willing to pay $8 per hour for 10 hours of security, while Bob is willing to pay $10 per hour for the same amount. To find the total societal value for this quantity of security, we sum their willingness to pay, resulting in a total of $18 per hour for 10 hours of protection. Similarly, for 15 hours of service, Jane is willing to pay $4 per hour, and Bob $5 per hour, leading to a combined willingness to pay of $9 per hour.

This method of summing individual prices at each quantity allows us to construct the market demand curve for public goods. Unlike private goods, where we add quantities horizontally, for public goods, we add prices vertically. The optimal quantity of a public good is determined where the marginal social benefit (MSB) equals the marginal social cost (MSC). The MSB curve represents the total benefit derived from the good, while the MSC is represented by the supply curve of the good.

In this scenario, the optimal quantity of security services occurs at the point where the MSB equals the MSC, which can be visually represented on a graph. For example, if the equilibrium price is $9 for 15 hours of security, this indicates that the total societal benefit of the security service matches the cost of providing it. Thus, the marginal social benefit curve is derived from the sum of individual valuations, while the marginal social cost curve corresponds to the supply curve, assuming no externalities are present.

In summary, understanding the demand curve for public goods involves recognizing the unique characteristics of these goods and applying the principles of marginal benefit and cost to determine the optimal quantity that maximizes societal welfare.

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 movies
• 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 curve is the sum of the individual values consumers place on the public good, while the MSC curve is typically the supply curve, assuming no externalities. The intersection of these two curves indicates the quantity at which the total value to society is maximized, ensuring efficient allocation of resources.

Why do we add prices vertically for public goods?

We add prices vertically for public goods because they are non-rival and non-excludable. This means that the same quantity of the good can be consumed by multiple individuals simultaneously without reducing its availability to others. Therefore, to determine the total value society places on each quantity of the public good, we sum the individual prices each person is willing to pay for that quantity. This vertical summation reflects the collective willingness to pay for the public good at each quantity level.

What is the marginal social benefit (MSB) in the context of public goods?

The marginal social benefit (MSB) in the context of public goods is the total benefit that society receives from consuming an additional unit of the public good. It is calculated by summing the individual values that all consumers place on that additional unit. The MSB curve represents the collective willingness to pay for each quantity of the public good, reflecting the aggregated benefits to society.

How is the supply curve related to the marginal social cost (MSC) for public goods?

The supply curve for public goods is typically equated to the marginal social cost (MSC) curve, assuming no externalities. The MSC represents the cost to society of providing an additional unit of the public good. In the absence of externalities, the MSC is simply the supply curve, indicating the cost of producing and supplying the public good. The optimal quantity of the public good is found where the MSC intersects with the marginal social benefit (MSB) curve.