Why does nobody sell streetlights door to door? Not because they’re worthless — because once one is lit, you cannot stop anyone using it, and nobody pays for what they get anyway. That is the free-rider problem, and it is why markets that price coffee perfectly fail completely at lighthouses. It is also a topic an online economics tutor in London gets asked about every term — the summation trick at its heart catches almost everyone first time.
1 · Two questions sort every good
Ask two questions of any good. Is it rival — does your use leave less for me? And is it excludable — can a seller keep non-payers out?
A flat white is both: you drink it, it’s gone, and the café won’t hand it over without payment. That’s a private good, and markets handle it well. A public good is neither. Street lighting, flood defences, national defence, clean air: your consumption subtracts nothing from mine (non-rival), and there is no practical way to switch it off for people who didn’t pay (non-excludable).
In between sit club goods (non-rival but excludable — a quiet toll road) and common resources (rival but non-excludable — a fish stock). Examiners love the borderline cases, so classify with the two questions, not memorised lists.
2 · Non-excludability breaks the market
If you cannot exclude non-payers, you cannot charge a price. And if you cannot charge, no firm will supply — however much the good is worth in total. Each individual reasons the same way: if others provide it, I get it free; if they don’t, my contribution barely matters. Everyone waits for everyone else. That is free-riding, and the result is a market that under-provides or simply never exists — a missing market.
Notice what the problem is not. It is not that people don’t value the good. Total willingness to pay can be enormous. The failure is that no mechanism collects it.
3 · Adding demands: sideways for private, upwards for public
Here is the technical heart of the topic, and the exam trap.
For a private good, market demand adds individual demands horizontally: at each price, sum the quantities. You buy your coffees, I buy mine, and the market total is yours plus mine.
For a public good, everyone consumes the same units. The question flips: for a given quantity, what is it worth to everyone together? So you add marginal benefit curves vertically: at each quantity, sum what each person would pay for one more unit. The vertical sum is the marginal social benefit, ΣMB.
Efficiency then sits where that vertical sum meets marginal cost: provide another unit as long as the group’s combined valuation covers it. With two people, the condition is MB₁ + MB₂ = MC.
Worked example — lamps in a shared courtyard
Two households share a courtyard and are deciding how many outdoor lamps to install. Each lamp costs £6 a month to lease and run. Lamps are non-rival here: both households enjoy every lamp at once.
Step 1 — The valuations. Household 1’s marginal benefit is MB₁ = 10 − Q and household 2’s is MB₂ = 8 − Q, in £ per lamp per month, where Q is the number of lamps.
Step 2 — Sum vertically. Both consume every lamp, so add valuations at each Q: ΣMB = (10 − Q) + (8 − Q) = 18 − 2Q, valid up to Q = 8, where household 2’s valuation hits zero.
Step 3 — The efficiency condition. Keep adding lamps while the combined valuation beats the cost: ΣMB = MC.
Step 4 — Solve. 18 − 2Q = 6 gives Q* = 6 lamps.
Step 5 — Check the stack. At Q = 6, household 1 values a lamp at 10 − 6 = £4 and household 2 at 8 − 6 = £2. Together: £6, exactly the cost. If each paid their own valuation — £4 and £2 — every lamp would be financed precisely. Economists call those personalised prices Lindahl prices.
Step 6 — Now leave it to the market. Suppose lamps are simply bought privately. Household 1, acting alone, buys until 10 − Q = 6: four lamps. Household 2 wanted only two — and four are already shining. So household 2 contributes nothing and free-rides on all four.
Step 7 — Count the loss. Voluntary provision stops at 4 lamps against the efficient 6. On each missing lamp the two households jointly valued the light above £6; adding that gap up across the two missing lamps comes to £4 a month of surplus nobody collects.
Step 8 — Interpretation. With two neighbours, a conversation and a split bill fix this. With two million residents and a flood barrier, no conversation can — which is why public goods are financed by taxation, where contribution is not optional.
Sure which way to add the demand curves — sideways for a private good, upward for a public one? That flip is the whole topic: get it the wrong way round and ΣMB = MC stops meaning anything. Drilling it until the direction is automatic is exactly what a one-on-one online economics tutor does with your own problem sets. Book a trial session.
Practice
Q1. Two neighbours value minutes of a shared fireworks display at MB₁ = 12 − Q and MB₂ = 6 − Q; a minute costs £9. Find the efficient length of the display, what each neighbour buys acting alone, and the shortfall.
Q2. A private good: two buyers have demands q₁ = 10 − p and q₂ = 14 − 2p. Find the market quantity at p = 4 and at p = 8.
Q3. Three residents of a shared mews each value winter gritting visits at MB = 20 − 2Q; a visit costs £24. Find the efficient number of visits and the cost share that finances it exactly.
Answers. Q1: ΣMB = 18 − 2Q = 9 gives Q* = 4.5 minutes, where the stack is 7.5 + 1.5 = 9. Alone, neighbour 1 buys 3 minutes (12 − Q = 9); neighbour 2 buys none, since £6 is the most they’d ever pay for a minute. Voluntary provision is 3 — a shortfall of 1.5 minutes. Q2: at p = 4, Q = 6 + 6 = 12; at p = 8, buyer 2 has left the market (their choke price is 7), so Q = 2. Q3: ΣMB = 60 − 6Q = 24 gives Q* = 6 visits; each resident’s valuation there is 20 − 12 = £8, and the three £8 shares cover the £24 cost exactly.
Key takeaways
- Two questions classify any good: rival or not, excludable or not. Public goods are neither.
- Non-excludability is the killer. No exclusion means no price, no price means no supply — however large total valuation is.
- Sum demands vertically for a public good, horizontally for a private one. Efficiency: ΣMB = MC.
- Free-riding under-provides. The larger valuer provides some; the smaller valuer rides free; the efficient quantity is never reached voluntarily.
Why London students choose our online economics tutoring
- Exam-shaped sessions: the vertical-versus-horizontal summation question appears on first-year papers across LSE, UCL and King’s, and tutors drill the diagram until the flip is automatic.
- One-on-one pace: an online economics tutor works through your own problem sets live on a shared screen, catching the exact step where the summation direction goes wrong.
- PhD-level tutors: graduate-trained economists explain the “why” behind ΣMB = MC, not just the recipe.
FAQ
Q: What is a public good in economics?
A: A good that is non-rival — one person’s use doesn’t reduce anyone else’s — and non-excludable, meaning non-payers can’t be kept out. Street lighting and flood defences are the standard examples.
Q: What is the free-rider problem?
A: When a good is non-excludable, each person can enjoy it without paying, so each waits for others to provide it. Voluntary contributions then fall short of what the good is worth to everyone combined.
Q: Why are demand curves for public goods added vertically?
A: Because everyone consumes the same units. Instead of asking how many units each person buys at a price, you ask what one more unit is worth to all of them together — so you stack willingness to pay at each quantity.
Q: Are public goods always provided by the government?
A: No. Government usually finances them through taxation because markets under-provide, but production can be private — and small-scale public goods are sometimes provided by clubs, charities or neighbours splitting costs.
Q: Is the BBC a public good? Is a park?
A: Broadcast signals are non-rival and, without encryption, non-excludable — close to a public good. A park is non-excludable but congestible, so only non-rival up to a point: a quasi-public good.
Book an online economics tutor in London or anywhere
Public goods questions reward students who can switch between the private-good and public-good logic without hesitating. One-on-one online sessions build exactly that reflex — the two classification questions, the vertical sum, the free-rider argument — on past-paper questions from your own course. Tell us your university and module, and we’ll match you with the right tutor this week, online in London or anywhere in the world.
