Long-Run Growth
Growth compounds — one extra percentage point a year makes a country twice as rich in 70 years. And what differs across countries is not knowledge but institutions, which the exam calls social infrastructure.
Compounding
Decompose the growth
| Source | Across countries | Over time |
|---|---|---|
| N*/POP | Not very important — varies little | Mattered in some periods (women's labor force participation) but cannot rise forever; diminishing returns blunt it |
| K*/N* | Very important — varies enormously | Somewhat important; diminishing returns mean doubling capital per worker less than doubles output per worker |
| Technology | Very important — with capital, roughly half of cross-country differences | Crucial — perhaps two-thirds of growth, by elimination |
Social infrastructure
The "technology" that varies across countries is institutions, not knowledge — knowledge is broadly available, the ability to deploy it is not. Hall and Jones: average labor productivity tracks social infrastructure closely.
- Markets
- A market-based system for allocating resources.
- Property rights
- Government protection of property from others — the rule of law.
- Protection from government
- Against corruption, theft, expropriation, arbitrary taxation. The third everyone forgets.
Drawing growth
Only permanent outward shifts in labor demand raise wages and employment in the long run, and labor demand is MRPL = P × MPL. Growth is whatever raises the price of what workers make (trade, better terms of trade) or their marginal product (capital, technology).
Where technology comes from
- New techniques
- Electric motor, tractor, assembly line, modern accounting.
- New products
- Nordhaus's list: aeronautics, air-conditioning, penicillin, the transistor, the digital computer.
- Better institutions
- Opening to trade.
Does the free market supply the optimal amount of invention? Almost certainly not. Inventions carry large positive externalities, especially basic science, so the inventor captures only part of the social benefit — Unit 11 applied to ideas. Hence: subsidize R&D, fund basic research, strengthen property rights in inventions, expand education. The 2025 Nobel to Mokyr, Aghion and Howitt sits here — Mokyr on connecting scientific innovation to practical and commercial knowledge and social acceptance of change; Aghion and Howitt modelling growth as creative destruction, driven by temporary patent monopolies.
Rules that earn points
- Decompose into N*/POP, K*/N*, T, then name the piece the question is about.
- Why poor countries stay poor: lead with institutions, not knowledge.
- Use the compounding numbers — 1 point faster doubles you in 70 years.
- Asked to draw growth: labor market, labor demand shifting out.
- Explaining cross-country income gaps with capital alone. Institutions do about half.
- Thinking poor countries lack knowledge. They lack the institutions to deploy it.
- Forgetting protection from government. It is a third of the social infrastructure answer.
Which is an important aspect of "social infrastructure"?
- ARule of law
- BProperty rights
- CProtection of property from the government
- DAll of the above
Answer
D — all of the above.
Social infrastructure is the set of building blocks that let markets function: rule of law, property rights, and protection of property from the government itself — corruption, expropriation, theft, arbitrary taxation. Hall and Jones showed average labor productivity tracks it closely.
C is the trap only in reverse: students who pick A or B alone are the ones who drop the third item, and it is the item the exam is fishing for.
Country A grows 1 percentage point per year faster than Country B from the same starting point. A is twice as rich as B after roughly:
- A10 years
- B25 years
- C70 years
- D200 years
Answer
C — about 70 years.
1.0170 ≈ 2. After 1 year A is 1% ahead; after 2 years 1.01² = 1.0201, so 2.01% ahead. The gap looks trivial year to year and dominates everything over a lifetime.
D is the trap: 200 years is right for the sevenfold gap, since 1.01200 ≈ 7.3. Doubling comes much sooner.
Which contributes most to the growth of potential output per person over time?
- AThe employment-to-population ratio N*/POP
- BCapital per worker K*/N*
- CTechnology, broadly defined
- DPopulation growth
Answer
C — technology, perhaps two-thirds of growth.
The argument is by elimination. N*/POP does not change much and cannot rise indefinitely; K*/N* matters somewhat, but diminishing returns mean doubling capital per worker less than doubles output per worker, and observed increases are too small to explain observed growth. What is left is technology.
B is the trap: capital per worker really does explain a lot across countries. The question asks about growth over time, where diminishing returns bite.
Relative to the social optimum, a free market on its own produces:
- AToo much invention, because patent monopolies over-reward inventors
- BToo little invention, because inventions have positive externalities
- CExactly the optimal amount, since inventors internalize the gains
- DToo little invention, because inventions have negative externalities
Answer
B — too little, because of positive externalities.
The inventor captures only part of the social benefit; everyone who later builds on the idea captures the rest. This is sharpest in basic science, where the payoff is distant and diffuse. Policy follows directly: subsidize R&D, fund basic research, secure property rights in inventions, expand education.
A is the trap: patents do create temporary monopolies (Aghion and Howitt's creative destruction runs on them), but they exist to close the externality gap, not to overshoot it.
Two countries have access to the same body of scientific and engineering knowledge, yet one has output per worker several times the other's. (a) Explain why knowledge cannot be the explanation. (b) Name the three components of social infrastructure and say what evidence supports the claim.
Model answer
(a) Knowledge is broadly available — techniques and product designs cross borders freely. What differs is whether a society can actually deploy them, so the binding constraint is institutions, which macro folds into the "technology" term. Capital per worker explains roughly half of cross-country differences; institutions explain about the other half.
(b) Social infrastructure is: a market-based system for allocating resources; government protection of property from others, the rule of law; and protection of property from the government itself — corruption, theft, expropriation and arbitrary taxation. Hall and Jones showed average labor productivity tracks social infrastructure closely across countries.
- Saying explicitly that knowledge is available but institutions are not.
- All three components named — especially protection from government.
- Citing Hall and Jones as the evidence rather than asserting the claim.
- Placing institutions inside the technology term of Y*/POP = (N*/POP) × (Y*/N*).
Use a labor market diagram to show the Malthusian trap before 1800 and the escape from it afterwards.
Model answer
Before 1800. Labor demand is essentially static. Clark's English data from 1250 to about 1640 scatter along a single downward-sloping labor demand curve: when population rose, labor supply shifted out along that fixed curve and real wages fell. More people meant lower living standards — the trap.
After 1800. Labor demand begins shifting out persistently, because capital accumulation and technology raise MPL and therefore MRPL = P × MPL. Now labor supply can shift out with population growth and wages still rise. Clark's scatter stops tracing a curve and becomes an arrow up and to the right.
- Labor supply moving along a fixed demand curve in the trap regime — not a demand shift.
- Labor demand shifting out in the escape regime, with the reason (capital, technology raising MPL).
- Stating the outcome in both regimes: wages fall, then wages and population rise together.
- Labelling axes and both equilibria.