Governments are spending billions trying to attract or support strategic industries: semiconductors, electric vehicles, batteries, green technology and artificial intelligence.

The usual criticism is simple: why should taxpayers pay to help private firms?

But in some industries, only a handful of firms compete worldwide. Airbus and Boeing have spent decades fighting over which government subsidy was unfair. If one government helps its national firm, that firm may expand, push down the price, and force a foreign rival to produce less.

So a subsidy isn’t just helping a firm. It’s trying to change the game.

Can taxpayers actually win?

Two firms sell the same product. Firm 1 is based in Country A; Firm 2 is based in Country B. Both sell only to consumers in a third country.

Market demand is:

P = 100 − Q, where Q = q₁ + q₂

Both firms have the same marginal cost: MC = 20.

Each firm chooses its output at the same time, taking the other firm’s output as given, to maximise its own profit.

Q1: Without a subsidy, how much does each firm produce?

What is the market price, and how much profit does each firm make?

Q2: What happens if Country A subsidises Firm 1?

Country A gives Firm 1 a subsidy of 10 per unit, so Firm 1’s effective marginal cost falls to 10. Firm 2’s stays at 20.

What happens to each firm’s output, and to the market price?

Q3: Is Country A better off?

Calculate how much extra profit Firm 1 makes, including the subsidy it receives, and how much the subsidy costs Country A’s taxpayers.

Assume Firm 1 is entirely domestically owned. Country A’s welfare is the firm’s profit minus the subsidy cost.

Is Country A better off overall? Who else gains, and who loses?

Q4: What if Country B fights back?

Now suppose Country B can also give Firm 2 a subsidy of 10 per unit.

Assume the governments first choose whether to subsidise their firms. The firms then compete by choosing their outputs simultaneously.

What happens to each country? Set out the possible outcomes (neither subsidises, one does, both do) in a table showing each country’s welfare.

What would you expect both governments to do, and are they better off for it?

Q5: If this can work, why not subsidise every industry?

What does the argument for strategic subsidies depend on? How many reasons can you think of why it might fail in practice?

BONUS:

Suppose Country B doesn’t retaliate, and, as in Q4, Country A sets its subsidy before the firms choose their outputs.

What per-unit subsidy would make Country A as well off as possible? What is interesting about the firms’ outputs at that subsidy?

P.S. Roll up your sleeves and explore the questions. Once you’ve grappled with them for a while, if you’re still stuck, there are graduated hints below, but challenge yourself first! (The answer comes in the next issue. Subscribe to get it straight to your inbox.)

That is roughly how much UK energy customers were estimated to be overpaying each year because of weak competition in the domestic energy market.

The figure comes from the CMA’s major energy market investigation. In its final findings, the CMA estimated that customers had been paying about £1.4bn a year more than they would in a well-functioning market. Earlier provisional findings put the figure closer to £1.7bn.

Why does this matter?

Because competition is not just about how many firms exist.

It is about whether customers actually switch, compare prices, understand tariffs and force firms to fight for their business.

In the UK energy market, the concern was not simply that firms were too big. It was that many customers stayed on expensive default tariffs, while more active customers shopped around and got better deals. The CMA described large suppliers as taking many existing domestic customers for granted, especially those on standard variable tariffs.

That makes energy a useful microeconomics case study.

Weak competition can come from market concentration.

But it can also come from consumer behaviour: inertia, search costs, confusing pricing, low trust, hassle, and the belief that switching is not worth it.

The issue is newly relevant because E.ON has completed its acquisition of OVO, adding OVO’s roughly 4 million customers to E.ON Next’s existing 5.6 million. E.ON says the deal has completed after clearance by the relevant authorities, including the CMA. The Guardian reported that the deal would leave the UK household energy market with a smaller group of very large suppliers, with E.ON Next holding around a quarter of the market.

The economics lesson is simple:

Competition does not work automatically.

For markets to discipline firms, customers need genuine alternatives, clear prices and enough confidence to move.

Otherwise, the cost of weak competition can show up not as an abstract diagram, but as billions of pounds on household bills.

Last time, we looked at a graph of how fast countries grew after 1960, plotted against how rich they were in 1960, and asked: do poor countries catch up?

Start with the axes.

As in #010, always read the axes before the picture.

What’s surprising?

1. The line is too generous. It runs from Botswana down to the US, so it suggests poor countries grew much faster than rich ones. But it isn’t a line of best fit. At around $1,000 in 1960, the line sits at roughly 5.5% growth, while most countries there (Uganda, Malawi, Burundi, Nepal, Pakistan) grew at 0–2.5%. The line runs through the best performers, not through the middle of the data. A proper line of best fit across all countries would be much flatter.

2. Poor countries ended up everywhere. Rich countries in 1960 sit in a tight cluster, growing at about 2–3% a year. Poor countries range from Botswana and South Korea (about 6% a year) to the Democratic Republic of Congo (about −2%). Where a poor country started tells you very little about where it ended up.

3. The big bubbles tell a different story. China and India, both very poor in 1960, grew fast. Count countries, and catch-up looks weak. Count people, and it looks much stronger: a large share of the world’s poor lived in countries that caught up.

If poorer countries automatically caught up, the dots would sit tightly around a clear downward-sloping line: the poorest countries would all grow fastest, the richest slowest, with little scatter. That isn’t what we see.

Rewrite y = √k as y = k^½ and differentiate:

dy/dk = ½ k^−½ = 1 / (2√k)

This is the marginal product of capital: the extra output from one more unit of capital per worker. Try a few values:

It’s always positive, but it falls as k rises: diminishing marginal returns to capital. (Differentiating again gives a negative second derivative, confirming it.)

That’s the case for catch-up. A poor country has little capital, so each new machine, road or factory adds a lot of output. A rich country already has plenty, so the next one adds much less. For the same amount of investment, a poor country should grow faster.

It also suggests capital should flow from rich countries to poor ones, because it earns more there. Keep that in mind for Q5.

Using y = √k:

Δk = s√k − δk

Compare the two parts as k rises:

Sketch them on the same axes: investment is a curve that flattens out; depreciation is a straight line through the origin.

And if k were above the steady state, depreciation would exceed investment, and capital would shrink back. So the economy is pulled towards the steady state from either side.

Growth slows not because the country stops investing, but because more and more of its investment goes on simply replacing capital that wears out. You can see this in the growth rate of capital: Δk / k = s/√k − δ, which falls as k rises.

In the steady state, Δk = 0:

s√k = δk

Divide both sides by √k: s = δ√k, so √k = s/δ.

Steady-state capital: k* = (s/δ)²
Steady-state output: y* = √k* = s/δ

Country A (s = 20%, δ = 10%): s/δ = 2, so k* = 4 and y* = 2.
Country B (s = 40%, δ = 10%): s/δ = 4, so k* = 16 and y* = 4.

Check Country B: investment = 0.4 × 4 = 1.6; depreciation = 0.1 × 16 = 1.6. ✓

So saving more does make a country richer: doubling the saving rate doubles steady-state income (and quadruples the capital stock).

But it doesn’t make it grow faster forever. Once Country B reaches its steady state, income per worker stops growing, just like Country A’s. Higher saving raises the level of income, not its long-run growth rate. Country B grows faster only during the transition, while it builds up its extra capital.

So where does long-run growth come from? Not from capital alone. That’s where A comes in.

(A stretch point: saving more isn’t always better. People care about consumption, not output. Consumption per worker is (1 − s) × y. For Country A, that’s 0.8 × 2 = 1.6; for Country B, 0.6 × 4 = 2.4, so B is better off. But save 90%, and consumption is 0.1 × 9 = 0.9. In this model, consumption is highest when s = 50%, known as the “golden rule” saving rate.)

With y = A√k:

A raises output at every level of capital. Double A, and the same machines and workers produce twice as much.

A also raises the return on extra capital:

dy/dk = A / (2√k)

Now the steady state. Set sA√k = δk:

√k = sA/δ, so k* = (sA/δ)²

y* = A√k* = A²s/δ

A appears squared. That’s because it works twice: it raises output directly, and higher output means more saving, so the country can sustain more capital. Double productivity, and steady-state income quadruples.

This changes the catch-up story. Each country converges towards its own steady state, set by its own s, δ and A. A poor country with low productivity may already be close to its (low) steady state, so the model predicts little growth. Poor countries only catch up if they can also raise A.

It also explains why capital doesn’t flood to poor countries. Compare:

Four times the capital, yet exactly the same return on the next unit. If rich countries have higher productivity, capital can earn as much, or more, there as in poor countries. The economist Robert Lucas pointed out this puzzle in 1990: by the simple model, capital should pour into poor countries, but it doesn’t.

A is everything that makes workers and capital more productive, apart from the amount of capital itself. It includes:

Two countries with the same capital per worker can produce very different amounts, because capital is only as productive as the people, organisations and rules around it. A tractor is worth far more with fuel, spare parts, a road to market, a trained driver, and secure ownership of the farm.

A is sometimes called “a measure of our ignorance”: it’s whatever the model can’t explain by counting capital. That makes it the most important letter in the model, and the hardest to change.

No: it’s predicting something more subtle than automatic catch-up.

The simple model predicts conditional convergence: each country moves towards its own steady state. Countries with similar saving, depreciation and productivity should converge. Countries with different ones shouldn’t.

That’s exactly what the graph shows.

South Korea and the DRC make the point brilliantly. In 1960, the DRC was actually richer than South Korea. Over the next half-century, South Korea grew at about 6% a year; the DRC shrank. The difference wasn’t where they started: it was A, and the conditions for investment.

Botswana, one of the poorest countries in 1960, grew fastest of all. Diamonds helped, but plenty of resource-rich countries grew slowly. Botswana’s stable, well-run institutions made the difference.

And the line? It flatters the model by running through the best performers. A fair summary would show weak convergence on average, with enormous variation among poor countries.

There’s a hopeful postscript. Recent research suggests that since the mid-1990s, poorer countries have, on average, grown faster than richer ones, mainly because growth in the developing world has accelerated. One reading: as more poor countries improved their institutions and policies, their steady states moved closer to rich countries’, and conditional convergence started to look unconditional.

They can, but not automatically. Diminishing returns give poor countries a head start: each new machine adds more where machines are scarce. But capital alone runs out of steam, and where a country ends up depends on its productivity: its skills, institutions, stability and ability to use technology well.

Catch-up isn’t a law of economics. It’s an opportunity, and some countries took it.

“The New Era of Unconditional Convergence” (Patel, Sandefur and Subramanian, Center for Global Development, 2021): the research showing that, since the mid-1990s, poorer countries have started catching up. The opening pages are readable without the technical detail.

And if you want a book to read… try…

Why Nations Fail (Daron Acemoglu and James A. Robinson, 2012): why some countries grow rich and others stay poor. Their answer is institutions: countries prosper when their rules spread opportunity and protect property, and stagnate when a narrow elite captures the gains. It’s the best book-length answer to “what sits inside A?” Acemoglu and Robinson shared the 2024 Nobel Prize in Economics, with Simon Johnson, for this research.

Poor Economics (Abhijit Banerjee and Esther Duflo, 2011): growth seen from the ground up. Rather than grand theories, Banerjee and Duflo look at the everyday decisions of people living on very little (about health, schooling, saving and borrowing) and test what actually helps. A brilliant reminder that A is made of millions of small things, not one big one. They shared the 2019 Nobel Prize in Economics, with Michael Kremer.

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.

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