Public and Private Goods: Study Guide (Microeconomics 6.3)

Two questions about any good

Markets work well for most goods. You pay for a sandwich, you eat it, and nobody else can eat it. But some goods do not behave like a sandwich. To see why, ask two questions about any good.

1. Is it rival? A good is rival if one person’s use leaves less of it for everyone else. Your sandwich is rival: once you eat it, it is gone. A good is non-rival if one more person can enjoy it without reducing anyone else’s enjoyment. A flood-warning siren is non-rival: when one more family hears the warning, every other family still hears it just as well.

2. Is it excludable? A good is excludable if the seller can stop people who do not pay from using it. A cinema seat is excludable: no ticket, no entry. A good is non-excludable if it is impossible, or far too costly, to keep non-payers out. Street lighting is non-excludable: you cannot switch off the light for one pedestrian who has not paid.

“Excludable” is about what is practical, not what is legal. Fish in the open sea could in theory be guarded, but in practice nobody can stop a boat from fishing there.

The four types of good

Putting the two questions together gives a grid.

• Private goods are rival and excludable. Sellers can charge, and each buyer pays for what they use. Markets usually provide these well.
• Public goods are non-rival and non-excludable. Markets usually fail to provide them.
• Open-access resources (often called common resources) are rival but non-excludable. Some natural resources are like this by nature. Markets let them be overused.

How the type of good changes behaviour

Public goods and the free rider problem

A free rider is someone who enjoys the benefit of a good without paying for it. Free riding is possible whenever a good is non-excludable.

Think about how a rational household reasons about a flood-warning siren. “If my neighbours pay for the siren, I hear the warning anyway, so why pay? If they do not pay, my small contribution will not be enough to buy it.” Either way, paying nothing looks best for each household. When everyone reasons like this, too little money is raised, and the siren is not built, even if its total benefit is far greater than its cost.

So private firms usually lack the incentive to produce public goods: they cannot charge enough people to cover the cost. That leaves government as the main, and often only, producer. It can make everyone contribute through taxes and then provide the good free to all. This is the “insufficient production of public goods” market failure you met in Topic 6.1.

Non-rivalry adds a second point. Once a public good exists, letting one more person use it costs nothing extra. Even if a seller could exclude people, keeping out someone whose benefit is above zero would waste surplus.

Private goods provided free by government

Governments sometimes produce private goods and allow free access. Schooling is the main example. A place in a classroom is rival (a class has room for only so many pupils), and it is excludable (a school can refuse entry). So schooling is a private good, whoever provides it.

Governments provide it free because they judge the benefits to society to be larger than the benefits each family would weigh alone (for example, a better-educated workforce), and because they want every child to have access. Free access does not make the good public. Because it is still rival, it must be rationed in some other way: by catchment areas, waiting lists or crowded classrooms.

Open-access resources and overuse

Some natural resources are rival and non-excludable by nature: fish in a lake that anyone may fish, or groundwater under many farms. A free city road at rush hour behaves the same way, although it is not a natural resource. Each fish caught is one fewer for everyone else (rival), yet nobody can be kept out (non-excludable).

Each user compares their own benefit with their own cost. They ignore the cost they impose on other users, such as a smaller catch, a lower water table or a slower journey. This ignored cost acts like a negative externality (Topic 6.2). Private individuals therefore overconsume the resource: the quantity used is greater than the socially optimal quantity.

Governments limit overuse with the tools from Topic 6.2: quotas or licences that cap use, fees or charges per unit used, and property rights that give someone an owner’s incentive to protect the resource. Each policy works by making users face the cost they impose on others, or by making the resource excludable.

Worked example 1: a flood-warning siren in Quarrow

Question. Quarrow, a fictional coastal town, has 400 households. A flood-warning siren system would cost $9,000 per year and would protect every household. Annual valuations are: 100 households value it at $60 each, 200 at $25 each and 100 at $10 each. (a) Classify the siren and say whether it is efficient to provide it. (b) Would any household buy it alone? Explain what happens if the town asks for voluntary payments. (c) The council pays for the siren with an equal tax on every household. Find the tax and each group’s net gain.

(a) The siren is non-rival (one more household hearing it does not reduce the warning for others) and non-excludable (nobody can be stopped from hearing it). It is a public good.

1. Total benefit = 100 × $60 + 200 × $25 + 100 × $10 = $6,000 + $5,000 + $1,000 = $12,000 per year.
2. Total benefit ($12,000) > cost ($9,000), so providing it is efficient: net gain $3,000 per year.

(b) The highest single valuation is $60, far below $9,000, so no household would buy it alone. With voluntary payments, each household knows it will hear the siren whether or not it pays, so each has an incentive to free ride. Even if the 100 keenest households each paid their full $60, that raises only $6,000. Contributions fall short and the siren is not built, although society would gain $3,000.

(c)

1. Tax per household = $9,000 ÷ 400 = $22.50.
2. Net gains: $60 − $22.50 = +$37.50; $25 − $22.50 = +$2.50; $10 − $22.50 = −$12.50.
3. Total: 100 × $37.50 + 200 × $2.50 − 100 × $12.50 = $3,750 + $500 − $1,250 = $3,000.

Interpretation. Compulsory taxes beat free riding, and the town as a whole gains $3,000. Not every household gains: the 100 low-value households lose $12.50 each. Public provision raises total surplus, but it does not make everyone better off.

Worked example 2: overfishing Lake Vessa

Question. Anyone may fish Lake Vessa (fictional). More boats deplete the stock, so each boat catches less. Each boat costs $8,000 per season to run, and fish sell for $1,000 per tonne at a price set in a much wider market. A boat enters if its own catch at least covers its cost.

Boats	5	6	7	8	9	10	11	12
Total catch (tonnes per season)	75	84	91	96	99	100	99	96
Catch per boat (tonnes)	15	14	13	12	11	10	9	8
Extra catch from the last boat (tonnes)	11	9	7	5	3	1	−1	−3

(a) How many boats fish under open access? (b) What number is efficient? (c) Compare the net value of the fishery and explain the difference. (d) Find a licence fee per boat that would lead to the efficient number.

(a) A boat sees only its own catch. Each boat’s catch is still worth at least $8,000 while the catch per boat is 8 tonnes or more. At 12 boats it is exactly 8 tonnes ($8,000), so boats keep entering up to 12 boats.

(b) Society should add a boat only while the extra catch it brings is worth at least $8,000. The 6th boat adds 9 tonnes ($9,000 > $8,000); the 7th adds only 7 tonnes ($7,000 < $8,000). The efficient number is 6 boats.

(c)

1. At 6 boats: catch value 84 × $1,000 = $84,000; cost 6 × $8,000 = $48,000; net value $36,000.
2. At 12 boats: $96,000 − $96,000 = $0.

The 7th boat catches 13 tonnes for itself, but total catch rises by only 7 tonnes. The other 6 tonnes are fish the existing boats no longer catch. The owner ignores that cost, just as a polluter ignores an external cost. Open access wipes out the whole $36,000 of value, and with 12 boats the catch is even below its peak of 100 tonnes.

(d) With a fee of $6,000 per boat: the 6th boat earns $14,000 − $8,000 − $6,000 = $0 and still enters; the 7th would earn $13,000 − $14,000 = −$1,000 and stays out. Any fee above $5,000 and up to $6,000 works. The fee makes users face the cost they impose on others; the government collects 6 × $6,000 = $36,000.

Check. The difference between catch per boat and extra catch (for example 13 − 7 = 6 tonnes for the 7th boat) is the cost each new boat imposes on the others. It grows as boats enter, which is why open access goes so far past the optimum.

Common misconceptions

• “A public good is anything the government provides.” The type depends only on rivalry and excludability. Free state schooling is a private good provided publicly.
• “Non-rival means there is an unlimited amount.” It means one more user does not reduce what others get. A siren is non-rival but still costs $9,000 to build.
• “Open-access resources are public goods.” They are non-excludable, but they are rival. That difference turns the problem from underprovision into overuse.
• “A free rider is someone who breaks the law.” A free rider simply benefits without paying. Free riding is a rational response to a non-excludable good.
• “If total benefit is greater than cost, the market will provide it.” Not when the good is non-excludable: the provider cannot collect the benefit as revenue.
• “Open access is efficient because each user chooses freely.” Each user weighs only private cost. The cost imposed on other users is ignored, so use goes past the optimum.
• “Public provision makes everyone better off.” It can raise total surplus while some taxpayers lose, as Worked example 1 shows.

Where this leads

Next, Topic 6.4, The Effects of Government Intervention in Different Market Structures, looks at how taxes, subsidies, price controls and regulation change outcomes in competitive and imperfectly competitive markets. To review external costs first, see the Topic 6.2 study guide. Test yourself with the practice questions, then use the revision notes and the checklist to consolidate.