Enter Values

$
Total cost to provide the public good
Person Valuation ($)
Person 1
Person 2
Person 3
Person 4
Person 5
5 of 100 people
Key Formulas
TSB = Σ Valuations
NSB = TSB − Cost
Aggregate-Value Test: TSB ≥ Cost
Equal Share: Cost / N
Free Rider: Valuationi < Share
Model Assumptions
  • Public good is non-excludable and non-rival in consumption
  • Valuations are truthfully reported (simplification — in practice, people may strategically misreport)
  • Binary provision decision: provide fully or not at all (single-project model)
  • Cost is fixed and does not depend on quantity or number of users
  • Equal cost sharing is one illustrative allocation rule (Lindahl pricing is the efficient alternative)

For educational purposes. Not financial advice. Market conventions simplified.

Ryan O'Connell, CFA
Calculator by Ryan O'Connell, CFA

Public Goods Analysis Results

Provision Analysis
Total Social Benefit $1,050.00
Net Social Benefit $50.00
TSB ≥ Cost? Threshold Met
Cost Sharing & Free Riders
Equal Cost Share $200.00
Free Rider Count 2 of 5
Free Rider % 40%
Voluntary Provision (Equal-Share Model)
Voluntary Total $600.00
Funding Gap $400.00
Voluntary Outcome Underfunded
Per-Person Breakdown
Person Valuation Equal Share Surplus vs. Share Free Rider? Contributes?

Formula Breakdown

TSB = Σ Valuations  |  NSB = TSB − Cost  |  Test: TSB ≥ Cost
Equal Share = Cost / N  |  Free Rider: Valuationi < Share

Understanding Public Goods & the Free Rider Problem

What Are Public Goods?

A public good has two defining characteristics: it is non-excludable (you cannot prevent people from using it) and non-rival (one person’s consumption does not reduce availability for others). Examples include national defense, street lighting, and tornado sirens. These properties distinguish public goods from three other categories:

  • Private goods (excludable + rival): food, clothing, housing
  • Club goods (excludable + non-rival): cable TV, fire protection
  • Common resources (non-excludable + rival): fish in the ocean, congested roads

The Free Rider Problem

Because public goods are non-excludable, individuals have an incentive to free ride — to benefit without contributing. Even when the total social benefit exceeds the cost, voluntary provision fails because each person hopes others will pay. This is the core problem described in Mankiw Chapter 11.

This calculator models free riding under an equal-share funding rule: each person is asked to pay Cost/N. A person is identified as a free rider (non-contributor) if their valuation of the good falls below this equal share — they would not voluntarily contribute because their personal benefit is less than their required payment.

Key Formulas (Mankiw Ch. 11)
TSB: Σ Valuations (sum of all willingness-to-pay)
NSB: TSB − Cost
Aggregate-Value Test: TSB ≥ Cost
Equal Share: Cost / N
Free Rider: Valuationi < Equal Share
Source: Mankiw, Principles of Microeconomics, Ch. 11

Cost-Benefit Analysis for Public Goods

A standard textbook cost-benefit test compares total social benefit (sum of everyone’s willingness to pay) to the cost of provision. If TSB ≥ Cost, the model indicates that aggregate stated valuation exceeds project cost. The challenge is that, unlike private goods with market prices, there is no direct way to observe how much each person values a public good — reported valuations may differ from true valuations.

Verification Example (Mankiw Ch. 11): Cost = $1,000; 5 people with valuations $400, $300, $200, $100, $50.
TSB = $1,050 > $1,000 → Threshold met. Equal share = $200.
Free riders: Person 4 ($100 < $200) and Person 5 ($50 < $200) = 40%.
Voluntary = 3 × $200 = $600 < $1,000 → Underfunded (gap = $400).
The aggregate-value test is satisfied, but the equal-share voluntary model does not fully fund the project.

Frequently Asked Questions

A public good is non-excludable (you cannot prevent people from using it) and non-rival (one person’s use does not reduce availability for others). Examples include national defense, street lighting, and public fireworks. Private goods are both excludable and rival — like food or clothing. Club goods (cable TV) are excludable but non-rival. Common resources (fish in the ocean) are rival but non-excludable. The key test: Can people be excluded from using it? Does one person’s use reduce another’s? If both answers are no, it is a public good.

The free rider problem occurs when people can enjoy a public good without paying for it. Because public goods are non-excludable, individuals have an incentive to let others pay while still receiving the benefit. This leads to underprovision — even when total social benefit exceeds cost, voluntary contributions may fall short. This calculator uses equal-share non-contribution as a measurable proxy: if a person’s valuation falls below their equal share of cost (Cost/N), they would rationally choose not to contribute voluntarily.

Compare the total social benefit (TSB — the sum of everyone’s willingness to pay) to the cost. If TSB ≥ Cost, the model’s aggregate-value test is satisfied. This is the standard cost-benefit framework in Mankiw Chapter 11. Voluntary provision can still fall short because of the free rider problem, so textbooks often compare different funding arrangements separately from the calculation itself.

Common examples include national defense, tornado sirens, public fireworks displays, street lighting, uncongested roads, basic scientific research, and public radio/TV. The key characteristics are non-excludability (everyone benefits whether they pay or not) and non-rivalry (one person’s enjoyment doesn’t reduce another’s). Some goods that appear public are actually club goods (excludable) or common resources (rival) — the classification depends on the specific context.

The tragedy of the commons applies to common resources (rival but non-excludable), not public goods. Common resources — like fish in the ocean or shared grazing land — tend to be overused because individuals do not account for the negative externality their consumption imposes on others. Public goods face the opposite problem: underprovision rather than overuse. Both market failures stem from non-excludability, but the rivalry dimension determines the direction of the failure.

Lindahl pricing assigns each person a personalized price based on their marginal benefit from the public good, so higher-valuation individuals pay more than lower-valuation ones. Under truthful reporting the shares sum to exactly the cost of provision, but in practice people have an incentive to understate their valuations. Equal cost sharing (Cost/N), used in this calculator as an illustrative benchmark, is simpler but creates free riders when some valuations fall below the equal share.

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Disclaimer

This calculator is for educational purposes only. Results are based on a simplified equal-share funding model for a single binary public good. Real-world public goods provision involves strategic behavior, measurement uncertainty, political processes, and general-equilibrium effects not captured here. This tool should not be used for policy or investment decisions.