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Public goods and common resources
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Analyze public goods and common resources using explicit assumptions, calculated results and a stated limit of the model.
Marginal social benefit and marginal social cost determine a supplied efficiency benchmark. Ordinary private-good market demand adds quantities at a common price. External effects can make private incentives differ from the social comparison.
| Term | What it means |
|---|---|
| Rivalry | One person's use reduces the amount or quality available to others at the relevant margin. |
| Excludability | The practical ability to prevent nonpayers or unauthorized users from accessing a good. |
| Public good | A good that is nonrival and nonexcludable over the modeled range. |
| Common resource | A rival resource from which exclusion is difficult or unavailable. |
| Club good | An excludable good that is nonrival over the relevant uncongested range. |
| Free riding | Benefiting from provision without contributing when exclusion is infeasible. |
| Vertical aggregation | Adding marginal willingness to pay at the same shared quantity. |
Two dimensions help explain why some goods are difficult to allocate through ordinary private transactions. Rivalry concerns whether one person's use leaves less available for others. Excludability concerns whether access can practically be withheld. These are distinct properties. A privately operated service can be nonrival over some range, and a government-provided item can be rival. Calling something a public good because a public agency supplies it confuses the provider with the good's economic characteristics.
A private good is both rival and excludable in the basic classification. If one person eats a particular apple, nobody else can eat that same apple, and the owner can ordinarily withhold it. A public good is nonrival and nonexcludable over the modeled range. One person's benefit from a warning signal need not reduce another's benefit, and excluding nonpayers from the signal may be infeasible. The example's physical and institutional conditions must be specified rather than assumed from a broad label.
A common resource is rival but difficult to exclude people from using. Harvesting a fish from an open-access fishery leaves fewer available to others. A club good is excludable but nonrival over a relevant range, such as access to an uncongested service that can be limited to members. Congestion can change rivalry: an additional user may be harmless when capacity is ample but reduce others' quality when a facility is crowded.
Technology and institutions can also change excludability. Access controls may make a previously open service excludable, though installing and operating them costs resources. Ownership or community rules can alter who is permitted to use a resource. The classification is therefore a model of a particular setting, not an immutable property of every object with the same name. State the use, scale and access conditions before assigning a category.
Another way: Public-good benefits add at a shared quantity
For a private good, different buyers consume separate units. At a common price, market demand adds their quantities horizontally. For a nonrival public good, the relevant users share the same provided quantity. Their marginal willingness to pay for an additional common unit must be added vertically. The distinction follows from what is being shared, not from an arbitrary graphing convention.
Suppose two residents receive the same service quantity Q. Their marginal benefits are MBa = 12 - Q and MBb = 8 - Q over a range where both are positive. Aggregate marginal benefit is 20 - 2Q. At Q = 2, the first values the extra unit at ten dollars and the second at six, so the common unit generates sixteen dollars of marginal benefit in total. Adding their quantities would double-count the shared service rather than add its benefits.
If marginal provision cost is eight dollars, efficient quantity solves 20 - 2Q = 8, giving Q = 6. At that quantity, individual marginal benefits are six and two, summing to eight. Neither person's marginal benefit alone needs to equal the entire marginal cost. The shared unit benefits both, so their combined valuation is the relevant comparison under the supplied efficiency criterion.
The benefit schedules' domains matter. If a linear expression becomes negative beyond some quantity but the model intends willingness to pay to stop at zero, aggregate benefit must be calculated piecewise. One cannot keep subtracting an unwanted negative valuation unless the model explicitly represents harm from excess provision. Our worked public-service cases choose an optimum where both supplied marginal benefits remain positive, avoiding an unstated extension beyond the intended range.
Another way: Free riding is an incentive problem, not zero value
When exclusion is infeasible, a person may receive the public good whether or not that person contributes to its cost. A voluntary contributor compares a private payment with a private benefit, while some benefit spills over to others. Each may hope others will pay. The resulting private contribution can be below the quantity justified by aggregate marginal benefit. This free-rider problem does not imply that people place no value on the good; it arises precisely because they can benefit without bearing the full provision cost.
The problem is not solved by simply asking each person for a valuation and assuming every report is truthful. If payments depend on reported willingness to pay, individuals may have incentives to understate or otherwise manipulate their reports. A model with known marginal benefits abstracts from that information problem. Actual collective provision requires institutions for eliciting information, making decisions and financing costs, with their own incentives and limitations.
Government provision financed through taxes is one possible arrangement, but public provision is not automatically efficient. The provider must still decide quantity, control cost and account for distribution. Voluntary associations, charitable provision, bundled private services or community agreements can also contribute under particular conditions. The good's characteristics explain a coordination challenge; they do not uniquely identify one flawless institution.
Efficiency in quantity also leaves the division of payments open. In the two-resident example at Q = 6, the marginal benefits sum to cost, but that condition does not require each resident to pay half. Equal payments, benefit-related payments and ability-to-pay rules distribute burdens differently. A policy debate can concern those distributions even when participants agree on the efficient quantity within the supplied model. The lesson grades the aggregation and allocation calculation rather than a preferred financing ethic.
Another way: Common resources face a different margin
A common resource combines difficult exclusion with rivalry. One user's extraction can reduce what others can obtain or increase their future costs. A user may consider the private benefit of an extra unit and the private effort needed to obtain it while neglecting the reduction imposed on others. The private incentive can then lead to excessive use relative to a social benchmark, unlike the underprovision problem commonly associated with a public good.
Consider a shared water source where an additional withdrawal lowers availability for other users. The efficient withdrawal comparison includes that marginal external cost. An open-access user who does not face it may withdraw too much. The logic resembles a negative externality, but the common-resource classification helps identify why the effect arises: users compete over a subtractable resource without effective exclusion or coordinated limits.
Open access and common ownership are not identical. A resource held by a community can be governed through membership rules, agreed extraction limits, monitoring and sanctions. Such institutions can change incentives. It is therefore inaccurate to say every communally managed resource must be overused. The outcome depends on the actual rules, enforcement and incentives, not merely the absence of an individual private owner.
Possible remedies include use charges, quotas, transferable rights, clearer property rights and collective governance. Each requires information and enforcement. A quota may control total use but allocate rights inefficiently; trading may improve allocation under suitable conditions. A fee can make users face scarcity costs but may have distributional consequences. Assigning rights can facilitate bargaining but also change who receives valuable claims. Compare the mechanisms rather than treating one policy name as a universal solution.
Congestion illustrates how categories can change at the margin. A park may be effectively nonrival when nearly empty but rival when additional visitors reduce space and enjoyment. Charging admission could make it excludable, but the charge also affects access. An analysis should identify whether the problem concerns financing a shared benefit, crowding, maintenance cost or several at once. A single label cannot replace those distinctions.
The common lesson across these cases is that the consumption and access structure determines the relevant private-social gap. For public goods, add marginal benefits at a shared quantity and consider contribution incentives. For common resources, account for the costs one person's use imposes on others and examine governance. In both, state what information and enforcement the proposed allocation assumes. That produces a more useful model audit than declaring every shared resource either automatically doomed or automatically well managed.
Another way: The relevant marginal cost is provision cost
For a nonrival service, adding another user to an already provided unit can have near-zero marginal use cost, while increasing the quantity or quality of the service can still be costly. The public-good efficiency equation compares the summed benefit of an additional common service unit with its provision cost. Confusing an extra user with an extra unit of provision can lead to the false conclusion that every public good should be supplied in unlimited quantity.
Two fictional residents share a warning service of quantity Q, with marginal benefits 12 - Q and 8 - Q dollars. Marginal provision cost is eight dollars. Aggregate marginal benefit is 20 - 2Q, so the efficient quantity is six. At that quantity the residents' marginal benefits are six and two. Adding their quantities would be wrong because both receive the same six units of service. The efficiency comparison adds the dollar benefits of the common increment.
If either resident can receive the service without paying, voluntary contributions may not finance that quantity. Each can hope the other will provide it. That does not establish that the service is unwanted, nor that an equal split of cost is the only legitimate financing rule. A collective decision needs both a quantity analysis and an explicit arrangement for paying and revealing preferences.
Now compare a nearby shared water source. A unit withdrawn by one resident is no longer available to the other. The source is rival, so it is not a pure public good under the same classification. If access is unrestricted and each user ignores the effect of withdrawals on others, excessive use can result. A community agreement limiting withdrawals changes the institution and may change the outcome; calling the source shared does not tell us whether such governance exists.
The two cases have difficult exclusion in common but different rivalry conditions. One raises a provision problem for a shared benefit, the other an extraction problem for a subtractable resource. An audit that identifies those differences can ask the right next questions about marginal benefits, external costs, monitoring and distribution. The exercise's numerical service calculation is exact under the stated schedules, while the choice of real governance would require further evidence and objectives.
Public good describes nonrivalry and nonexcludability, not government ownership. Add benefits vertically for a shared public quantity; add private-good quantities at a common price. Common resources are rival, and community governance is not the same as unrestricted open access.
Hold the shared quantity fixed.
Both residents receive the same Q
Nonrival consumption means one resident's use does not subtract the other's service.
Add marginal willingness to pay vertically.
SMB = 22-2Q
For a public good, willingness to pay sums at each common quantity.
Evaluate aggregate benefit at two.
22-2(2) = 18
This is a sum of benefits in dollars per extra service unit.
Equate aggregate benefit with marginal cost.
22-2Q = 10; Q = 6
Efficient provision counts both residents' marginal benefits.
Find the initial marginal net benefit.
22-10 = 12
Subtracting cost at Q=0 identifies the first marginal increment's gain, not the entire project's net benefit.
Hold the shared quantity fixed.
Both residents receive the same Q
Nonrival consumption means one resident's use does not subtract the other's service.
Add marginal willingness to pay vertically.
SMB = 24-2Q
For a public good, willingness to pay sums at each common quantity.
Evaluate aggregate benefit at two.
24-2(2) = 20
This is a sum of benefits in dollars per extra service unit.
Equate aggregate benefit with marginal cost.
24-2Q = 12; Q = 6
Efficient provision counts both residents' marginal benefits.
Find the initial marginal net benefit.
24-12 = 12
Subtracting cost at Q=0 identifies the first marginal increment's gain, not the entire project's net benefit.
Hold the shared quantity fixed.
Both residents receive the same Q
Nonrival consumption means one resident's use does not subtract the other's service.
Add marginal willingness to pay vertically.
SMB = 26-2Q
For a public good, willingness to pay sums at each common quantity.
Evaluate aggregate benefit at two.
26-2(2) = 22
This is a sum of benefits in dollars per extra service unit.
Equate aggregate benefit with marginal cost.
26-2Q = 14; Q = 6
Efficient provision counts both residents' marginal benefits.
Find the initial marginal net benefit.
26-14 = 12
Subtracting cost at Q=0 identifies the first marginal increment's gain, not the entire project's net benefit.
Check the domain of both benefit schedules.
At Q=6, MBa=9 and MBb=5
Both remain positive, so the stated aggregation formula applies at the calculated optimum.
Hold the shared quantity fixed.
Both residents receive the same Q
Nonrival consumption means one resident's use does not subtract the other's service.
Add marginal willingness to pay vertically.
SMB = 28-2Q
For a public good, willingness to pay sums at each common quantity.
Evaluate aggregate benefit at two.
28-2(2) = 24
This is a sum of benefits in dollars per extra service unit.
Equate aggregate benefit with marginal cost.
Find the initial marginal net benefit.
In the fictional Elm model, two residents share the same nonrival public service quantity Q. Their marginal benefits are MBa=17-Q and MBb=13-Q over the relevant positive range; marginal provision cost is 18 dollars. Exclusion is infeasible. Calculate aggregate marginal benefit at Q=2, efficient public-service quantity, and the total benefit-minus-cost contribution of the first infinitesimal unit (the marginal net benefit at Q=0). Do not add residents' quantities.
| Calculated value | |
|---|---|
| Aggregate MB at two | |
| Efficient quantity | |
| Initial marginal net benefit |
In the fictional Dune model, two residents share the same nonrival public service quantity Q. Their marginal benefits are MBa=16-Q and MBb=12-Q over the relevant positive range; marginal provision cost is 16 dollars. Exclusion is infeasible. Calculate aggregate marginal benefit at Q=2, efficient public-service quantity, and the total benefit-minus-cost contribution of the first infinitesimal unit (the marginal net benefit at Q=0). Do not add residents' quantities.
Calculate aggregate mb at two.
g0
This is a sum of benefits in dollars per extra service unit.
Calculate efficient quantity.
g1
Efficient provision counts both residents' marginal benefits.
Calculate initial marginal net benefit.
g2
Subtracting cost at Q=0 identifies the first marginal increment's gain, not the entire project's net benefit.
In the fictional Fern model, two residents share the same nonrival public service quantity Q. Their marginal benefits are MBa=18-Q and MBb=14-Q over the relevant positive range; marginal provision cost is 20 dollars. Exclusion is infeasible. Calculate aggregate marginal benefit at Q=2, efficient public-service quantity, and the total benefit-minus-cost contribution of the first infinitesimal unit (the marginal net benefit at Q=0). Do not add residents' quantities.
Aggregate MB at two: b0
Efficient quantity: b1
Initial marginal net benefit: b2
In the fictional Grove model, two residents share the same nonrival public service quantity Q. Their marginal benefits are MBa=19-Q and MBb=15-Q over the relevant positive range; marginal provision cost is 22 dollars. Exclusion is infeasible. Calculate aggregate marginal benefit at Q=2, efficient public-service quantity, and the total benefit-minus-cost contribution of the first infinitesimal unit (the marginal net benefit at Q=0). Do not add residents' quantities.
Aggregate MB at two: b0
Efficient quantity: b1
Initial marginal net benefit: b2
In the fictional Harbor model, two residents share the same nonrival public service quantity Q. Their marginal benefits are MBa=20-Q and MBb=16-Q over the relevant positive range; marginal provision cost is 24 dollars. Exclusion is infeasible. Calculate aggregate marginal benefit at Q=2, efficient public-service quantity, and the total benefit-minus-cost contribution of the first infinitesimal unit (the marginal net benefit at Q=0). Do not add residents' quantities.
| Calculated value | |
|---|---|
| Aggregate MB at two | |
| Efficient quantity | |
| Initial marginal net benefit |
Two residents receive the same warning-service coverage. A budget proposal incorrectly adds the quantities each would buy privately. Reconstruct the combined willingness to pay for a common increment, then compare it with the cost of providing that increment. In the fictional Island model, two residents share the same nonrival public service quantity Q. Their marginal benefits are MBa=21-Q and MBb=17-Q over the relevant positive range; marginal provision cost is 26 dollars. Exclusion is infeasible. Calculate aggregate marginal benefit at Q=2, efficient public-service quantity, and the total benefit-minus-cost contribution of the first infinitesimal unit (the marginal net benefit at Q=0). Do not add residents' quantities.
| Calculated value | |
|---|---|
| Aggregate MB at two | |
| Efficient quantity | |
| Initial marginal net benefit |
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
In the fictional Juniper model, two residents share the same nonrival public service quantity Q. Their marginal benefits are MBa=22-Q and MBb=18-Q over the relevant positive range; marginal provision cost is 28 dollars. Exclusion is infeasible. Calculate aggregate marginal benefit at Q=2, efficient public-service quantity, and the total benefit-minus-cost contribution of the first infinitesimal unit (the marginal net benefit at Q=0). Do not add residents' quantities.
| Calculated value | |
|---|---|
| Aggregate MB at two | |
| Efficient quantity | |
| Initial marginal net benefit |
Reconstruct the model without the worked example. Explain each requested measure's units and identify an assumption that the conclusion depends on.
10. In the fictional Dune model, two residents share the same nonrival public service quantity Q. Their marginal benefits are MBa=16-Q and MBb=12-Q over the relevant positive range; marginal provision cost is 16 dollars. Exclusion is infeasible. Calculate aggregate marginal benefit at Q=2, efficient public-service quantity, and the total benefit-minus-cost contribution of the first infinitesimal unit (the marginal net benefit at Q=0). Do not add residents' quantities., step 4
28-2Q = 16; Q = 6
Efficient provision counts both residents' marginal benefits.
10. In the fictional Dune model, two residents share the same nonrival public service quantity Q. Their marginal benefits are MBa=16-Q and MBb=12-Q over the relevant positive range; marginal provision cost is 16 dollars. Exclusion is infeasible. Calculate aggregate marginal benefit at Q=2, efficient public-service quantity, and the total benefit-minus-cost contribution of the first infinitesimal unit (the marginal net benefit at Q=0). Do not add residents' quantities., step 5
28-16 = 12
Subtracting cost at Q=0 identifies the first marginal increment's gain, not the entire project's net benefit.