In A-level Economics, students are often taught that a National Minimum Wage imposed above the free-market wage can create unemployment.

The usual diagram is simple.

If the wage is pushed above equilibrium, labour supply rises, labour demand falls, and the gap between the two is unemployment.

That model is useful.

But today’s question asks us to take another look.

What if the labour market is not perfectly competitive?

What if one large employer has wage-setting power?

In that case, the effect of a minimum wage may not be what the standard diagram suggests.

The Margin is about things that are “worth another look”.

So today’s question is this:

Can a minimum wage increase employment?

A small town has one large employer.

Let:

L = number of workers hired

The firm’s total revenue from hiring workers is:

R(L) = 100L − L²

The wage it must pay to attract L workers is:

w(L) = 10 + L

So if the firm wants to hire more workers, it must pay a higher wage.

But there is a catch.

If it raises the wage to attract one extra worker, it must pay that higher wage to all the workers it already employs.

That is what gives the problem its twist.

Q1: Why does the labour supply curve w(L) = 10 + L give the firm wage-setting power?

Q2: To hire one more worker, the firm must raise the wage for everyone. Show that the extra cost of hiring one more worker (the marginal cost of labour) is 10 + 2L, and explain why it is higher than the wage.

Q3: Write down the firm's profit, and find the employment level L that maximises it. What wage does the firm pay?

Q4: What would employment and the wage be in a competitive labour market, where the wage equals the marginal revenue product of labour, w(L) = R′(L)?

Q5: The government introduces a minimum wage. What happens to employment if it is set at:
(a) 40?
(b) 60?

Q6: What does this reveal about the effect of minimum wages in competitive versus monopsonistic labour markets?

Bonus: For which minimum wages does employment rise above the level the firm would choose on its own?

P.S roll up your sleeves and explore the question… once you’ve grappled with it for a while, if you are still stuck…Graduated hints below — but challenge yourself first! (Answer comes in the next edition! Subscribe to receive it directly to your inbox!)

$450 bn

Marginal number: $450 billion

That is Morgan Stanley's estimate of global AI-related debt issuance so far in 2026, as of early September: more than double the total for the whole of 2025.

Source: Bank of England Financial Policy Committee, reported by Reuters, 30 September 2026. Reuters

Why does this matter?

The AI boom isn't just being written in code. It's being written in debt.

Data centres, chips, energy and cloud capacity all need enormous upfront investment, and more and more of it is being financed by borrowing. If the investment pays off, the debt will look sensible: firms will have borrowed to build the infrastructure for a new technological era. But if expectations run ahead of reality, the same debt becomes a source of fragility.

The worry for policymakers is where that debt ends up. AI-related borrowing is spreading through corporate bonds, private credit and data-centre financing, and so into the portfolios of banks, pension funds and insurers. If AI disappoints, the losses won't stay with a few tech firms.

That's why the Bank of England's Financial Policy Committee warned this week that the risk of problems in the financial system materialising has risen, pointing to AI-related borrowing as one of the reasons.

Big ideas still need balance sheets. And when a boom is financed by debt, the margin between transformation and vulnerability can become very thin.

Last time, we asked how bright a village of 10 fishermen and fisherwomen should make their lighthouse, and why they might end up with too little of it.

Each of them gets a benefit, in pounds, of:

B(x) = 500 ln(1 + x)

and the total cost of brightness is:

C(x) = 250x, where x ≥ 0.

The key feature is that the lighthouse is a public good. Everyone enjoys the same light, whoever pays for it.

First, with no brightness there is no benefit:

B(0) = 500 ln 1 = 0

As x rises, so does the benefit. To see how quickly, differentiate:

B′(x) = 500 ÷ (1 + x)

This is positive for every x ≥ 0, so more brightness always helps. But it shrinks as x grows:

The first units of brightness are enormously valuable, while extra brightness helps less and less. That makes economic sense: going from darkness to some light may dramatically reduce the risk of hitting the rocks, while making an already bright lighthouse slightly brighter helps only a little.

This is diminishing marginal benefit. Differentiating again confirms it:

B″(x) = −500 ÷ (1 + x)²

Since this is negative, the benefit curve is concave.

Each person receives 500 ln(1 + x), and all 10 enjoy the same brightness at the same time. So the total benefit to the village is:

TB(x) = 10 × 500 ln(1 + x) = 5000 ln(1 + x)

The lighthouse is only paid for once, so the total cost is still C(x) = 250x.

Social surplus is total benefit minus total cost:

S(x) = 5000 ln(1 + x) − 250x

This is what the village should maximise if it cares about everyone's welfare.

Differentiate:

S′(x) = 5000 ÷ (1 + x) − 250

Set this equal to zero:

5000 ÷ (1 + x) = 250

5000 = 250(1 + x)

20 = 1 + x

x* = 19

To check it's a maximum:

S″(x) = −5000 ÷ (1 + x)²

This is always negative, so x = 19 is indeed the maximum.

The economic interpretation: at the optimum, the benefit to the whole village of one more unit equals its cost. Each person's marginal benefit is 500 ÷ (1 + x), and ten people benefit, so the social marginal benefit is 5000 ÷ (1 + x). At x = 19, that's 5000 ÷ 20 = £250, exactly equal to the marginal cost of £250.

Now suppose one fisherman or fisherwoman chooses the brightness alone. They get only their own benefit, but pay the whole cost. Their private surplus is:

P(x) = 500 ln(1 + x) − 250x

Differentiate and set equal to zero:

500 ÷ (1 + x) = 250

500 = 250(1 + x)

2 = 1 + x

x = 1

So the privately chosen brightness is x = 1, against a social optimum of x = 19.

How much does the village lose? Compare social surplus at the two levels:

S(19) = 5000 ln 20 − 250 × 19 ≈ £10,229

S(1) = 5000 ln 2 − 250 × 1 ≈ £3,216

Stopping at x = 1 throws away about £7,013, roughly 69% of the value the lighthouse could create.

When one person decides whether to pay for an extra unit of brightness, they count only their own benefit:

Private MB = 500 ÷ (1 + x)

But all 10 people benefit, so the true marginal benefit to society is:

Social MB = 5000 ÷ (1 + x)

The individual ignores the benefits to the other nine people. These are external benefits.

At x = 1, the individual sees a private marginal benefit of 500 ÷ 2 = £250. That equals the marginal cost, so they stop. But the social marginal benefit at the same point is 5000 ÷ 2 = £2,500. Society would gain £2,500 from another unit of brightness that costs only £250.

The individual hasn't made a mistake: they are behaving perfectly sensibly given their own costs and benefits. The problem is that private incentives and social incentives point in different directions. That is the public-good problem.

This condition has a name: the Samuelson condition, after the economist Paul Samuelson. For a public good, efficiency requires the sum of everyone's marginal benefits to equal the marginal cost:

ΣMB = MC

For a private good, each person's own marginal benefit equals the marginal cost. For a public good, we add them up, because everyone consumes the same unit at the same time.

Now suppose each person chooses how much brightness to fund. Let xᵢ be the amount paid for by person i, so total brightness is:

x = x₁ + x₂ + … + x₁₀

Person i pays 250xᵢ, but enjoys the benefit of the total brightness, 500 ln(1 + x). So they want to maximise:

500 ln(1 + x) − 250xᵢ

Adding a unit of brightness gives them a marginal benefit of 500 ÷ (1 + x), at a personal cost of £250. So nobody wants to push brightness beyond the point where:

500 ÷ (1 + x) = 250, which gives x = 1.

More precisely, if the others have already funded brightness x₋ᵢ, person i will only top it up to 1: they contribute max(0, 1 − x₋ᵢ). So total brightness ends up at exactly 1, but who pays is undetermined. One person might fund it all while nine free ride, or the cost might be shared. Either way, the village gets the same dim lighthouse: x = 1, not x = 19.

With N people, the social marginal benefit is 500N ÷ (1 + x). Setting it equal to £250 gives the social optimum:

x* = 2N − 1

So with 10 people, x* = 19. With 20 people, x* = 39. With 100 people, x* = 199.

But each individual still compares their own marginal benefit with the cost they personally pay, so voluntary provision stays at x = 1, however large the village. The bigger the group, the bigger the shortfall, because more people can hope that someone else will pay. This is the free-rider problem.

The lighthouse is dramatically underprovided. That isn't because people are irrational, or because they undervalue the lighthouse. It's because each person bears the full cost of their contribution but receives only a fraction of the benefit it creates.

That is one of the central results in public economics: individually rational behaviour can produce a collectively inefficient outcome. It's why public goods create a case for collective funding, taxation or government provision.

The lighthouse is the textbook example of a public good, but in 1974, the economist Ronald Coase went back to the historical records. He found that many English lighthouses had actually been built by private individuals, under letters patent from the Crown, which granted rights to collect light dues from vessels passing specific stretches of coastline. Those dues were levied at port.

Because the fee was collected when ships called at port, it was hard to avoid paying, which partly solves the free-rider problem.

Lighthouses in England and Wales are still funded this way today: light dues are levied on commercial vessels and larger pleasure boats calling at ports in the UK, and the UK Department for Transport sets the level of light dues, which is reviewed annually.

So is a lighthouse a public good or not? The light itself is non-rival and non-excludable. But the payment can be tied to something that is excludable: using a port. Sometimes a public-good problem can be solved not by the government, but by finding a clever way to charge.

Coase's reading of history has been challenged, though. Although many lighthouses were depicted by Coase as privately operated, the right to collect non-negotiable light dues was supported by a patent from the crown. So even the "private" lighthouses depended on the state to make everyone pay. HandWiki

Marginal gains… Answer for today’s question is out in two days… Come back then or subscribe to get it direct to your inbox!

P.P.S.

Feel free to share this resource with a friend!