Question

The city of Falls Church, Virginia, subsidizes the planting of trees in homeowners' front yards when they are within 15 feet of the street. a. Using concepts in the chapter, explain why a municipality would subsidize planting trees on private property, but near the street. b. Draw a diagram similar to Figure \(16-4\) that shows the marginal social benefit, the marginal social cost, and the optimal Pigouvian subsidy on planting trees.

Short answer

Answer: The municipality provides subsidies for planting trees on private property near the street to internalize the positive externalities associated with tree planting, such as cleaner air, aesthetically pleasing neighborhoods, and potentially higher property values. These benefits are experienced by the entire community, not just the individual homeowner. The optimal Pigouvian subsidy should be equal to the difference between the marginal social benefit (MSB) and the marginal social cost (MSC) at the socially optimal quantity of trees (Qs), which can be determined by the intersection point of the new MSC curve and the MSB curve. This subsidy encourages homeowners to plant more trees, shifting the equilibrium from the private market quantity (Qp) to the socially optimal quantity (Qs), resulting in greater benefits to the entire community.

Step-by-step solution

In this situation, the municipality is providing subsidies for planting trees in the front yards, close to the street. We must understand that planting trees have positive externalities, which means that there are benefits experienced by third parties that are not directly involved in the transaction. The municipality wants to incentivize homeowners to plant more trees because this leads to positive externalities like cleaner air, aesthetically pleasing neighborhoods, and potentially higher property values. #Step_2# - Analyzing the externalities

In the case of planting trees, the positive externalities include the provision of cleaner air, a pleasant environment, and increased property values. These benefits are not limited to the individual homeowner but are experienced by the entire community living in the area. The municipality would like to promote these benefits and internalize the positive externalities by providing a subsidy. #Step_3# - Drawing the diagram

In this step, we will draw a diagram similar to Figure 16-4, showing the marginal social benefit (MSB), marginal social cost (MSC), and the optimal Pigouvian subsidy for planting trees. On the X-axis, we represent the quantity of trees planted, and on the Y-axis, we represent the cost and benefit associated with tree planting. There are two main curves – MSB and MSC. MSB is upward sloping, which indicates that the more trees planted, the higher the benefit to society. MSC curve represents the cost involved in planting more trees and is also upward sloping. When there is no subsidy, the intersection point of these two curves determines the private market equilibrium (Qp). To internalize the positive externalities, a subsidy should be introduced which lowers the MSC curve. The optimal Pigouvian subsidy should be equal to the difference between MSB and MSC at the socially optimal quantity of trees (Qs). This can be determined by the intersection point of the new MSC curve with the MSB curve. #Step_4# - Explaining the diagram

The diagram we just drew shows the optimal Pigouvian subsidy provided by the municipality for planting trees. This subsidy encourages homeowners to plant more trees, shifting the equilibrium from the private market quantity (Qp) to the socially optimal quantity (Qs). This leads to an increase in the overall quantity of trees planted near the street, providing greater benefits to the entire community, including cleaner air, improved aesthetics, and potentially higher property values.

Key concepts

Positive Externalities

When a homeowner decides to plant a tree near the street with the help of a subsidy, they might not realize the broader benefits this action has on their entire neighborhood. These benefits are known as positive externalities. They occur when a decision or action of an individual also benefits third parties. In the case of tree planting, these third parties are the community members who enjoy cleaner air, a more beautiful environment, and possibly even increased property values due to the enhanced aesthetic appeal.
Such externalities justify actions like subsidies from municipalities. They are efforts to encourage more of these beneficial activities, ensuring that the entire community can reap the rewards even if they didn't directly make the investment themselves.

• Cleaner air: Trees naturally filter pollutants and produce oxygen.
• Aesthetic value: Trees beautify neighborhoods, making them more appealing.
• Property value: Attractive, tree-lined streets can increase local property values.

The goal is to incentivize individuals so that these widespread community benefits are realized, thereby improving the quality of life for everyone in the area.

Marginal Social Benefit

Understanding marginal social benefit (MSB) is crucial when discussing subsidies. This concept refers to the additional benefit society gains from one more unit of a good or service being produced. In the context of tree planting subsidies, the MSB represents the added value that each additional tree brings to the community and is crucial in determining how many trees should ideally be planted.
As more trees are planted, the benefits to society – cleaner air, more beauty, and so forth – continue to increase, and thus, the MSB curve typically slopes upwards. However, towns need to find the balance point where the social benefits don't outweigh the costs too significantly.
The optimal number of trees is reached when the marginal social benefit equals the marginal social cost (MSC). At this point, the maximum societal benefit is achieved without unnecessary expenditure on planting even more trees. This understanding is what guides the setting of an optimal subsidy amount, ensuring that the societal benefits justify the costs involved.

Marginal Social Cost

The marginal social cost (MSC) is the total cost to society for producing an additional unit of a good. In the case of tree planting subsidies, it includes the financial cost of planting and maintaining trees beyond what individuals directly pay.
This cost typically grows with each additional tree planted, leading to an upward-sloping MSC curve. Municipalities have to consider these growing costs alongside the benefits to determine the most efficient number of trees that should be planted.

• Costs of planting: Includes labor, tools, and tree purchase costs.
• Maintenance: Regular care and any potential removal if necessary.
• Subsidization balance: Ensuring public spending isn't excessive while promoting the desired number of trees planted.

By calculating MSC effectively, along with MSB, the municipality can provide a subsidy that encourages the planting of the socially optimal number of trees, maximizing community benefits while keeping costs in check. This balance provides a better living environment for everyone, supported by wise economic decision-making.