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How does a country reach a point outside its frontier?
In 1961, Singapore had about 50 000 people looking for work and very little industry. Its land area was about 582 square kilometres, and it had no oil or coal of its own. Yet between 1960 and 1985, its real output per person grew by about 6% a year. Growth at that rate, kept up for 25 years, multiplies output per person by more than four.
The last lecture gives a puzzle here. A production possibility frontier (PPF) shows the most an economy can produce with its present resources and technology. Points outside it cannot be reached. So how did Singapore come to produce, by 1985, combinations that were far outside its 1960 frontier?
The last lecture already hinted at the answer, in its third trap: a point outside the frontier is impossible with today's resources and technology. It also promised that a change in resources or technology would move the frontier, and that this lecture would show how. Here it is. The frontier is not fixed. It can move outward, and when it does, points that were impossible become possible.
The first way: more resources
A frontier is drawn for a fixed amount of the four factors of production: land, labour, capital and enterprise. Add more of any of them, and the economy can produce more. So the frontier moves outward.
- More land. Singapore has made land, by filling in parts of the sea. Its land area has grown from about 582 square kilometres in the 1960s to about 745 square kilometres in the 2020s, an increase of about 28%. Other countries find new farmland, new mines or new oil fields.
- More labour. A population can grow. More people may move into the country to work. More of the people already there may take paid jobs. The last lecture ended its wartime United States case with exactly this point: during the war, many more people joined the workforce, and that moved the frontier itself.
- More capital. Factories, machines, roads, ports and computers are all capital. A new port can handle more ships. A new factory can make more goods.
- More enterprise. More people starting and running firms can bring land, labour and capital together in more places.
The second way: better resources and better ideas
The same resources can also produce more than before. This happens in two main ways.
The first is better technology. A farmer with a tractor ploughs far more land in a day than a farmer with a hand tool. The farmer is the same person, with the same land. The tool is better, so the same resources produce more.
The second is better-trained workers. Education and training raise what each worker can do. Economists call the skills and knowledge of the workforce human capital. Like a machine, it takes time and resources to build, and it then raises output for years.
Both ways, more resources and better resources, have the same effect on the picture. The frontier moves outward.
Economic growth is a rise in real output: the amount of goods and services produced, with the effect of rising prices removed.
Moving from inside the frontier towards it is short-run growth: idle resources are put to work. Moving the frontier itself outward is long-run growth: the economy's capacity to produce rises.
Return to the invented rice-and-computers country from the last lecture. Suppose it gains more workers, more land and more machines, all equally useful for rice and computers. Each combination on the frontier can now be produced with a quarter more of both goods. The figure shows the result.
Point X was out of reach before: with 40 thousand computers, the most rice was 45 thousand tonnes. On the new frontier, 40 thousand computers can come with up to about 81 thousand tonnes of rice. So X, with 80 thousand tonnes, can now be produced. This is how Singapore reached its "impossible" combinations. It did not break the frontier. It moved it.
That is it. That is the whole idea. Economic growth in the long run is an outward move of the frontier, and it comes from more resources or from better ones.
Not every shift is even
Now suppose something different happens. Engineers find a faster way to make computers. With the same resources, the country can now make half as many computers again as before. Rice farming does not change at all.
If every resource goes into rice, the country still grows 100 thousand tonnes, because nothing about rice has changed. So the frontier still starts at the same point on the rice axis. But every other point moves to the right. The frontier swings outward, like a door turning on a hinge. Economists say it pivots.
The new technology only helps computer making. So if the country chooses to make 30 thousand computers, can it now grow any more rice than before?
Show the answer
Yes. Before, 30 thousand computers left room for 70 thousand tonnes of rice. With the new technology, 30 thousand computers need fewer workers, machines and land. Those resources are free to grow rice. On the new frontier, 30 thousand computers come with 85 thousand tonnes of rice: 15 thousand tonnes more. Better technology for one good gives more of the other good too, everywhere except at the very end of the rice axis.
This is the hard part of the lecture, so read it twice if you need to. A pivot does not only give "more computers". It frees resources. Freed resources can make anything.
A frontier can also move inward. An earthquake or a war can destroy factories, roads and farms. A disease can kill or weaken many workers. Large numbers of skilled workers may leave the country. Machines wear out, and if they are not replaced, capital shrinks. In each case, the economy's capacity falls, and points that were possible become impossible.
Sort the events below. Some move the frontier, and some only move the economy's point.
Each card describes an event in a country that makes food and machines. Choose a card, then choose what happens to the frontier.
This table sorts eight events by what they do to a country's frontier for food and machines.
| Event | What happens |
|---|---|
| Many young people finish technical training and start work. | The frontier shifts outward |
| Land is reclaimed from the sea, and new factories are built on it. | The frontier shifts outward |
| A new seed variety doubles crop yields. Machine making is unchanged. | The frontier pivots outward |
| A faster way to assemble machines is invented. | The frontier pivots outward |
| A cyclone destroys many factories and farms. | The frontier shifts inward |
| Many skilled workers leave to work in other countries. | The frontier shifts inward |
| A recession leaves one worker in ten without a job. | No shift: the point moves inside |
| With everyone still employed, workers move from farms to factories. | No shift: the point moves along |
The last two cards are the ones to read twice. Unemployment does not destroy any resources. The workers are still there, so the frontier stays where it is. Only the economy's point has moved inside it.
A bigger frontier does not mean people are better off
An outward shift says what the economy can produce. It does not say what it will produce. A country can build new factories and then fall into a recession. Its frontier has moved out, but its point sits inside the new frontier, and some of the new capacity stands idle. Potential growth and actual growth are different things.
There is a second reason for care. Suppose the frontier moves out because the population grows by 10%. If output also grows by 10%, there is more in total, but no more for each person. So economists often divide output by the number of people. Output per person rises only if output grows faster than the population.
The hardest choice: goods for now or goods for later
Every economy produces two kinds of goods. Consumer goods are used up by people now: food, clothes, phones, holidays. Capital goods are used to produce other goods later: machines, factories, roads, ports. Training a worker is like making a capital good. It uses resources now and pays back for years.
Draw a PPF with capital goods along the bottom and consumer goods up the side. The economy must choose a point on it. A point with more capital goods means fewer consumer goods this year. That is the opportunity cost, and people feel it: less to buy, smaller homes, fewer treats. But more capital goods also move next year's frontier further out. So a country that gives up more today can have much more later.
Test this trade-off in the model below. It is invented, and it is deliberately simple.
Choose the share of the economy's resources that goes into capital goods each year. Watch consumer goods this year, and the frontier in 10 years' time.
Try:
This table shows an invented economy that can produce 100 units of goods this year. Each 100 units of capital goods add 20 units to next year's capacity, and 2% of capacity wears out each year. Consumer goods are what is left after capital goods. In the table, "Share" is the share of resources put into capital goods, "Growth" is the change in capacity each year, and the other three columns are consumer goods: this year, in 10 years and in 20 years.
| Share | Now | Growth | Year 10 | Year 20 |
|---|---|---|---|---|
| 0% | 100 | −2% | 81.7 | 66.8 |
| 10% | 90 | 0% | 90.0 | 90.0 |
| 20% | 80 | +2% | 97.5 | 118.9 |
| 30% | 70 | +4% | 103.6 | 153.4 |
| 40% | 60 | +6% | 107.5 | 192.4 |
A bigger share gives fewer consumer goods now but more later. The 40% plan has fewer consumer goods than the 10% plan this year and in each of the next six years. From year 7 on, it has more.
You should have seen the trade-off clearly. A bigger share for capital goods means less to consume today, but more in later years. Below 10%, worn-out machines are not even replaced, and the frontier moves inward. The model also leaves out three important things. First, every new machine here adds the same amount of capacity, but in real economies each extra machine tends to add a little less than the one before. Second, it ignores new ideas, which raise output without more machines. Third, it says nothing about how long people can wait. A family that has too little to eat today cannot easily give up more now for a reward in twenty years. Keep these limits in mind as you read the real case.
Worked example and a real case
A school canteen makes noodle bowls and sandwiches. This example and its numbers are invented. With one chef and one kitchen, in one hour it can make 100 noodle bowls, or 80 sandwiches, or any mixture on a straight line between them.
(a) The canteen hires a second chef and doubles its kitchen space. Each dish can now be made twice as fast. Describe the new frontier. (b) Then it buys a noodle machine. With all its resources on noodles, it can now make 250 bowls an hour. Sandwiches are unchanged. Describe the change. (c) With the noodle machine, how many sandwiches can it make alongside 100 noodle bowls? Compare with before the machine.
Think first. Ask what changed at each end of the frontier.
(a) Both ends double: 200 noodle bowls or 160 sandwiches. The whole frontier shifts outward, because the extra chef and space help both dishes.
(b) The sandwich end stays at 160, and the noodle end moves from 200 to 250. The frontier pivots outward from the sandwich axis.
(c) On a straight frontier, the sandwiches fall evenly as noodle bowls rise. Before the machine, 100 bowls is half of 200, so half of the sandwiches are left: 80. With the machine, 100 bowls is of the most, so of the sandwiches are left: .
Check. The noodle machine makes 16 more sandwiches possible, although it cannot make a single sandwich. It makes the 100 bowls with fewer chef-hours, and those hours go into sandwiches. ✓ This is the pivot lesson from the Stop and think, with numbers.
The situation. In the early 1960s, Singapore had high unemployment, little industry and very little land. The last lecture described how its government set up the Economic Development Board in 1961 to attract factories and create jobs.
The policy. Over the next two decades, Singapore put a very large share of its output into capital goods: factories, ports, housing and roads, much of it built with money from abroad. It also invested in training. Its Vocational and Industrial Training Board, set up in 1979, trained and certified about 112 000 skilled workers by 1991, about 9% of the workforce.
The prediction. On a PPF of capital goods and consumer goods, Singapore chose a point far towards capital goods. The PPF predicts two things. Consumer goods would be smaller at first than they could have been. And the frontier would move outward fast.
What happened. Investment rose from about 9% of output in 1960 to about 43% in 1984, one of the highest shares in the world. Real output per person grew by about 6% a year from 1960 to 1985.
| Singapore | 1960 | 1984–85 |
|---|---|---|
| Investment as a share of output | about 9% | about 43% (1984) |
| Real output per person (1960 = 1) | 1 | about 4.3 (1985) |
(Sources: A. Young, "A Tale of Two Cities: Factor Accumulation and Technical Change in Hong Kong and Singapore", NBER Macroeconomics Annual, 1992, using Summers and Heston data; National Library Board Singapore, Infopedia, "Vocational and Industrial Training Board"; C.-T. Hsieh, American Economic Review, 2002.)
Verdict. The prediction fits: the frontier moved out very fast, and a large share of each year's output went into goods for later, not goods for now. But economists disagree about which of the two ways did the work. The economist Alwyn Young measured how much of Singapore's growth came from more inputs and how much from producing more with the same inputs. He found that almost all of it came from more capital and more, better-educated workers, and that better technology added next to nothing. In 1994, Paul Krugman used this to argue that such growth must slow down, because adding more and more machines brings smaller and smaller gains. Later, Chang-Tai Hsieh used a different method, based on wages and the returns earned on capital. He found much faster technical progress in Singapore. The debate is still open. What nobody disputes is the trade-off itself: Singapore gave up consumer goods early, and its frontier moved out far.
Three traps
A bigger frontier is a bigger possibility. The economy may still be inside it because of a recession, and output per person rises only if output grows faster than the population. Say what has happened to the point, and to the number of people, before you say anyone is better off.
A pivot frees resources. With better computer technology, the same computers need fewer resources, and the rest can grow rice. Only at the very end of the axis, where nothing is spent on computers, is there no gain.
When idle workers get jobs, the economy moves from inside towards its frontier. The frontier does not move, because the workers were already counted in it. That is short-run growth. Only more or better resources move the frontier itself.
Work each one on paper first. Open a hint only when you are stuck.
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An invented country's frontier passes through these combinations of tables and bicycles (thousands per year): (0 tables, 60 bicycles), (10, 50), (20, 30), (25, 0). (a) Is (20 tables, 36 bicycles) possible? (b) More workers arrive, and every combination grows by 20%. Is (20, 36) possible now?
Hint 1
Compare 36 with the most bicycles possible alongside 20 thousand tables, before and after.
Hint 2
After the change, the combination (20, 30) becomes . What about the point with exactly 20 thousand tables?
Full answer
(a) No. With 20 thousand tables, the most is 30 thousand bicycles, so (20, 36) is outside the frontier. (b) The new frontier passes through (0, 72), (12, 60), (24, 36) and (30, 0). At 24 thousand tables, 36 thousand bicycles are possible. So at only 20 thousand tables, even more bicycles than 36 are possible, because fewer tables leave more resources for bicycles. (20, 36) is now inside the new frontier. Check: the old (20, 30) has grown to (24, 36), and (20, 36) has fewer tables and the same bicycles, so it must be within reach. ✓
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For each event, say whether the frontier shifts outward, pivots, shifts inward, or does not move. (a) A country builds a new port and new roads. (b) A drought ruins the harvest for one year. (c) Unemployed workers find jobs after a recession.
Hint 1
Ask whether the economy's capacity has changed, and whether the change helps one good or all goods.
Hint 2
A drought does not destroy factories or workers, but it does reduce what the land can grow that year.
Full answer
(a) Shifts outward: more capital that helps many goods. (b) For that year, the frontier pivots inward on the food axis, because the land can grow less food while factories can make as much as before. When the rain returns, the frontier moves back. (c) No shift: the economy moves from inside towards its frontier. Check: only (a) and (b) change what the resources can produce. In (c) the resources were there all along. ✓
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On the invented island from the last lecture, 10 workers can each catch 4 fish or pick 12 coconuts a day. So the island's frontier is a straight line from 40 fish to 120 coconuts. Then better nets double each worker's catch to 8 fish. (a) Draw or describe the new frontier. (b) What is the new opportunity cost of one fish? (c) How many coconuts can the island pick alongside 20 fish, before and after the nets?
Hint 1
If all 10 workers fish, how many fish now? If all pick coconuts, has anything changed?
Hint 2
One worker now gives up 12 coconuts to catch 8 fish. For 20 fish, how many workers must fish, before and after?
Full answer
(a) A straight line from 80 fish to 120 coconuts: the frontier pivots out on the fish axis. (b) coconuts per fish, down from 3. (c) Before: 20 fish need 5 workers, leaving 5 workers to pick coconuts. After: 20 fish need only workers' days, leaving 7.5 to pick coconuts. Check: . ✓ Better nets for fish gave 30 more coconuts.
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A stretch. Two invented countries each produce 100 units of goods this year, and follow the rule in the model above. Country A puts 10% of its resources into capital goods every year. Country B puts 30%. (a) How many consumer goods does each have this year? (b) By how much does each one's capacity change each year? (c) After 10 years, how many consumer goods does each have? (d) In which year does B first have more consumer goods than A? (e) Give one reason why B's real gains might be smaller than this model says.
Hint 1
In the model, capacity changes each year by .
Hint 2
For B, capacity grows by 4% a year, so after years it is . Consumer goods are 70% of that. Find the first that gives at least 90.
Full answer
(a) A: 90. B: 70. (b) A: , no change. B: , 4% growth a year. (c) A: still 90. B: . (d) , still below 90. , above 90. So B first has more in year 7. (e) The model assumes every extra machine adds the same capacity. In real economies, each extra machine tends to add a little less, so B's growth would slow. This is the point Alwyn Young and Paul Krugman made about Singapore. Check: B gives up 20 units of consumer goods a year at first. It takes 7 years for its faster growth to pay that back in yearly consumption, and longer still to make up the total given up. ✓
The last lecture showed two ways for a country to become better off. It can move out to its frontier by using idle resources, or it can move the frontier itself. The first way stops when every resource is in use. The second has no such limit, and small rates of growth add up over time. A frontier that moves out by 2% a year doubles in about 35 years.
This is why growth matters so much to the people of a country, and why its costs matter too. Someone must decide how much to give up today for tomorrow, and which point on the frontier to choose. In some economies, millions of buyers and sellers make these choices through prices. In others, a government plan makes them. The next lecture asks how different economies answer these questions.
- The PPF shifts outward when an economy gains more land, labour, capital or enterprise, or when its resources become more productive through better technology or human capital.
- Moving from inside towards the frontier is short-run growth, and moving the frontier itself outward is long-run growth.
- A change that helps only one good pivots the frontier, and it still frees resources to produce more of the other good.
- The frontier shifts inward when resources are destroyed or lost, but unemployment only moves the economy's point inside it.
- Producing more capital goods now means fewer consumer goods now, in exchange for a frontier that moves out further later.