91Ó°ÊÓ

Public goods are unique types of goods that inherently belong to everyone in a community. They possess two main characteristics: non-excludability and non-rivalry. Non-excludability means that no individual can be effectively barred from using the good once it has been provided. Non-rivalry means one person's use of the good doesn't reduce availability for others. Think of things like clean air, national defense, or as in our exercise, streetlights.
The streetlights discussed in the exercise are public goods. Here’s why:

• **Non-excludability**: Once the streetlights are installed on a street, any resident or visitor can benefit from the improved safety and visibility, whether they contributed to its cost or not.
• **Non-rivalry**: Just because one person enjoys the security and advantage of the lights doesn't mean lessened availability for others.

These characteristics can make it challenging to provide public goods through private markets, as not everyone is willing, or able, to pay their share voluntarily. Regulating such goods often requires collective action or governance solutions, ensuring all who benefit contribute to its cost.

Willingness to pay (WTP) is the maximum amount an individual is willing to spend to procure a good or service. In the context of public goods, it represents the valuation different people place on communal benefits. Let's delve into how WTP functions in our exercise.
In the problem, we're assessing the interest of 10 people willing to pay for streetlighting. Every person on the street values each new streetlight at precisely \(\\(2\), demonstrating a consistent and straightforward WTP across all beneficiaries.

• **Aggregate Willingness**: With 10 individuals, the collective WTP for one streetlight becomes \(10 \times \\)2 = \$20\), scaling up to \(20x\) with \(x\) streetlights.
• **Understanding WTP as a Boundary**: By aligning the community's total WTP with the production cost, we ensure the resources for streetlighting are efficiently allocated, perfectly aligning societal value with expenditures.

Understanding WTP helps clarify how much society benefits from a public good, guiding decisions on how many streetlights should be funded collectively.

Cost-benefit analysis is a systematic approach to estimating the strengths and weaknesses of alternatives that satisfy transactions, activities, or functional requirements for a business. It assists in determining options that provide the best approach to achieving benefits while preserving savings. Let's see how cost-benefit analysis applies to our streetlight problem.
The main goal here is to determine when the costs of providing streetlights align well with the community's benefits.

• **Equating Costs and Benefits**: The Pareto efficient level of streetlighting occurs where total willingness to pay matches the cost curve. Our equation \(20x = x^2\) demonstrates this assessment, where the collective value from the streetlights should balance the monetary outlay for installing them.
• **Outcome Analysis**: Solving \(x^2 - 20x = 0\) gives us solutions; \(x = 0\) or \(x = 20\). In practice, \(x = 20\) emerges from the cost-benefit equation as the practical outcome, representing the balance of coverage and resource use.

By applying cost-benefit analysis, we ensure that the community’s resources provide maximum benefit, favoring informed decision-making in public policy.