The PPF — what an economy can produce — Economics

Before this

This leads to

Economic growth — shifting the PPF outward
Market, planned and mixed economies
Comparative advantage · coming soon

Twenty volunteers and a school fair

The last lecture ended with a promise: the next lecture would draw the limit on what an economy can make as a curve. This is that lecture. It also keeps an older promise, from the opportunity cost lecture, to draw a graph of choices for a whole country.

Start small. Your school fair has exactly 20 volunteers. Each can work at the food stalls or run a games booth. More people on food means more plates served but fewer games, and the other way round.

Can the fair serve 200 plates and also run 10 games? With 20 volunteers, no. Serving 200 plates needs every volunteer on food, and 10 games need every volunteer on games. There is a limit, and a plan beyond it is impossible, however hard everyone works.

That limit can be drawn. Economists call the drawing the production possibility frontier, or PPF. Some books call it the production possibility curve. It puts scarcity, choice and opportunity cost into a single picture.

Building the frontier

Move from a school to a whole country. Imagine a country that produces only two things: rice and computers. (This country and its numbers are invented.) A real country produces thousands of goods, but two are enough to see the idea.

The country has a fixed amount of land, labour, capital and enterprise, and a fixed level of technology. If every resource goes into rice, it can grow 100 thousand tonnes of rice in a year, and make no computers. If every resource goes into computers, it can make 50 thousand computers, and grow no rice. In between, it can make many mixtures of the two. The table shows six of them.

Combination	Computers (thousands per year)	Rice (thousand tonnes per year)	Rice given up for the last 10 thousand computers
A	0	100	—
B	10	95	5
C	20	85	10
D	30	70	15
E	40	45	25
F	50	0	45

Each row is the most rice the country can grow for that number of computers, when it uses all its resources and uses them well. Plot the six combinations on a graph, with computers along the bottom and rice up the side, and join them. The line is the PPF.

The PPF for the invented rice-and-computers country. Points A to F are on the frontier. U is inside it, and X is outside it.

The production possibility frontier (PPF)

The PPF shows the maximum combinations of two goods that an economy can produce in a given time. It assumes that all resources are fully and efficiently used, with present resources and technology.

"Fully and efficiently used" means no worker is idle, no machine stands still, and every resource does the job it does best. "Present resources and technology" means the frontier is a picture of one moment. If resources or technology change, the frontier changes too, and that is the subject of the next lecture.

Before you read about the three regions of the graph, make a prediction about point U.

Predict, then reveal — more computers from point U

The country is at point U: 20 thousand computers and 60 thousand tonnes of rice, with many workers unemployed. The government wants 10 thousand more computers. How much rice must the country give up? Choose your prediction.

This box asks a question about point U, inside the frontier, and gives the answer.

The country is at U: 20 thousand computers and 60 thousand tonnes of rice, with many workers unemployed. It wants 10 thousand more computers. It need not give up any rice. The unemployed workers can make the computers. The new point, 30 thousand computers and 60 thousand tonnes of rice, is still possible, because the frontier at 30 thousand computers is at 70 thousand tonnes. Opportunity cost along the frontier applies only when every resource is already in use.

On, inside, outside

On the frontier (points A to F): the economy is using every resource, and using it well. Economists call this productive efficiency. From a point on the frontier, there is only one way to get more of one good: produce less of the other.

Inside the frontier (point U: 20 thousand computers and 60 thousand tonnes of rice): the economy is producing less than it could. Workers may be unemployed, for example in a recession, when spending falls across the whole economy. Factories may stand idle, or people may be doing jobs that do not suit them. Point C shows that the same 20 thousand computers could come with 85 thousand tonnes of rice, not 60. So 25 thousand tonnes of rice are being lost every year, for nothing in return.

Outside the frontier (point X: 40 thousand computers and 80 thousand tonnes of rice): with 40 thousand computers, the most rice the country can grow is 45 thousand tonnes. X is out of reach with its present resources and technology.

Now try the three regions yourself on the graph below.

Graph builder — choose a combination

Choose how many computers and how much rice the country should produce. The point appears on the graph. Read whether it is on, inside or outside the frontier, and what it costs.

Try:

Computers: 20 thousand

Rice: 60 thousand tonnes

This table tests five combinations against the frontier, with computers in thousands and rice in thousand tonnes. The frontier's rice for each number of computers comes from the table above, with straight lines between the listed points.

Computers	Rice chosen	Most rice	Verdict
20	60	85	Inside: 25 lost
20	85	85	On (point C)
25	77.5	77.5	On, between C and D
40	80	45	Outside (X): 35 over
45	20	22.5	Inside by 2.5

On the frontier, each extra 5 thousand computers costs more rice than the last: 2.5 thousand tonnes near A, but 22.5 thousand tonnes near F.

You should have noticed two things. From inside the frontier, you could move up, right, or both. On the frontier, every step to the right had a price in rice, and the price kept changing.

Opportunity cost, made visible

From A to B, the country gains 10 thousand computers and gives up 5 thousand tonnes of rice. That rice is the opportunity cost of the computers, read straight off the graph.

Now keep going. From B to C, the next 10 thousand computers cost 10 thousand tonnes of rice. From C to D, they cost 15. From D to E, 25. And the last 10 thousand computers, from E to F, cost 45 thousand tonnes. Per computer, the first ones cost half a tonne of rice each, and the last ones cost 4.5 tonnes each.

Stop and think

The country uses the same workers, land and machines all the way from A to F. So why do the last 10 thousand computers cost nine times as much rice as the first 10 thousand?

Show the answer

Because resources are not equally good at everything. The first computers come from the resources best at computers and worst at rice, such as engineers and city factory sites, so little rice is lost. The last computers can come only from the best rice farmers and the most fertile fields. Moving them loses a lot of rice and gains few computers. The country uses its best-suited resources first.

This is why a PPF is usually drawn bowed outward, curving away from the corner where the axes meet. Some books call this shape "concave to the origin". The bend is not decoration. It shows increasing opportunity cost: the more of one good an economy makes, the more of the other it must give up for each extra unit.

That is it. That is the whole idea. The PPF is opportunity cost drawn as a curve. Its slope gives the price of one good in terms of the other, and its bend shows how unequal the resources are.

Why the curve bends: two people make a frontier

You can watch the bend appear with just two people. In the opportunity cost lecture, Mei and Kofi were making things for a school fair. In one hour, Mei can make 6 cakes or 2 scarves. In one hour, Kofi can make 4 cakes or 2 scarves. (This example is invented.) So one scarf costs Mei 3 cakes, and costs Kofi only 2 cakes.

Give each of them one hour. If both make cakes, they produce 10 cakes. If the pair wants 2 scarves, Kofi should make them, because his cost only 2 cakes each. That leaves 2 scarves and Mei's 6 cakes. For more scarves, Mei must switch too, at 3 cakes a scarf. At 4 scarves, no cakes are left.

Mei and Kofi's combined frontier for one hour each. Kofi's scarves cost 2 cakes each, so he switches first; Mei's cost 3 cakes each. The steeper second piece makes the frontier bow outward.

The frontier has a corner: a gentler piece at 2 cakes per scarf, then a steeper one at 3. A real country has millions of people, fields and machines, each with its own costs, so the corners become too small to see and the frontier becomes a smooth curve.

The figure shows one more point. If Mei makes the scarves and Kofi the cakes, they get 2 scarves and only 4 cakes. That point is inside the frontier, although both work the whole hour. The resources are simply in the wrong jobs. This cause of being inside the frontier is the easiest to miss.

If every scarf cost the same number of cakes whoever made it, the frontier would be a straight line. A straight PPF means a constant opportunity cost.

Which point is best?

Every point on the frontier is efficient, but they are not equally good for the people who live there. Point B has plenty of rice and few computers. Point E has many computers but much less food. The PPF shows what is possible. It does not say which possible point to choose.

Choosing a point is the first of the three basic questions from the scarcity lecture: what to produce. Some economies answer it through prices, set by millions of buyers and sellers. Others answer it by a government plan. A later lecture compares these systems.

The same picture fits a government moving money and workers from defence into healthcare. If its resources were fully used, more hospitals mean less defence. If some were wasted, it might get more of both.

Stop and think

A country has two problems. Many of its workers have no jobs. And it has few factories and few workers with technical skills. Which problem puts it inside its frontier, and which one makes the frontier itself small?

Show the answer

The unemployed workers put it inside the frontier: they are resources the country has but does not use. The lack of factories and skills is different. It makes the frontier itself small, close to the origin. Jobs move the economy out to the frontier. More factories and skills push the frontier outward, which is the next lecture's subject. The two problems need different cures.

Singapore in the early 1960s faced both problems at once. Unemployment was in double figures through the early 1960s, and in 1961 about 50 000 people were looking for work. Industry was small. The government set up the Economic Development Board on 1 August 1961, to attract factories from abroad and create jobs. (Sources: Singapore Government, SG101, "1959–1965: Early Economic Strategies"; speech by Lee Hsien Loong on the EDB's 30th anniversary, 1 August 1991, National Archives of Singapore.) In the language of this lecture, the new jobs moved Singapore towards its frontier, and the new factories and skills began to push the frontier out.

Worked examples

Worked Example 1 — The school fair

Back to the fair. With 20 volunteers, the organisers estimate these combinations. (These numbers are invented.)

Volunteers on food	Volunteers on games	Plates served	Games running
20	0	200	0
15	5	150	3
10	10	100	6
5	15	50	8
0	20	0	10

(a) Find the opportunity cost of one game when the fair goes from 0 to 3 games, and when it goes from 8 to 10 games. (b) Is 6 games with 120 plates possible? (c) Is 4 games with 100 plates on the frontier?

Think first. Divide the plates given up by the games gained.

(a) From 0 to 3 games, plates fall from 200 to 150. So 3 games cost 50 plates, and one game costs $50 \div 3 \approx 16.7$ plates. From 8 to 10 games, plates fall from 50 to 0. So 2 games cost 50 plates, and one game costs $50 \div 2 = 25$ plates. The cost per game rises, so this frontier bows outward.

(b) No. With 6 games, the most plates is 100. So 120 plates and 6 games is outside the frontier.

(c) No, it is inside. The fair can run 6 games with 100 plates, so 4 games with 100 plates wastes volunteers' time: 2 more games could run for free.

Check. Every row uses exactly 20 volunteers. An inside point always allows more of something without giving anything up. ✓

Real case — Guns and consumer goods: the United States, 1940–1944

The situation. In 1940, the United States had still not recovered from the Great Depression of the 1930s. By the official measure, 14.6% of its workers were unemployed, and many factories were working below capacity. In the language of this lecture, the economy was well inside its frontier.

The policy. From 1940 the country began to re-arm. After it entered the Second World War in December 1941, it turned a huge share of its factories and workers to weapons, ships and aircraft.

The prediction. Put "war goods" on one axis of a PPF and "civilian goods" on the other. From inside the frontier, the PPF predicts two stages: first both rise, as idle workers and machines are put to work; then, once the frontier is reached, more war goods cost civilian goods.

What happened. By 1944, official unemployment had fallen to 1.2%. Estimates by the economic historian Hugh Rockoff show civilian and military production rising together in 1941. In 1942, once the country was fully at war, civilian production fell. No new cars were made for civilians during the war. How much ordinary people lost is still debated. By the official figures, real spending per person on consumer goods was slightly higher in 1944 than in 1940. The economist Robert Higgs argued that price controls hid the true rise in prices, and his adjusted figures show real consumption per person falling by more than 6% between 1941 and 1943. (Sources: R. Higgs, "Wartime Prosperity? A Reassessment of the U.S. Economy in the 1940s", Journal of Economic History, 1992; H. Rockoff, "The United States: from ploughshares into swords", in M. Harrison (ed.), The Economics of World War II, 1998, as summarised by J. W. Mason.)

United States	1940	1944
Unemployment rate (official measure)	14.6%	1.2%

Verdict. The two-stage prediction fits well. In 1941, from deep inside the frontier, the economy made more weapons and more civilian goods together. Once the idle resources were used up, the trade-off appeared, and new cars for civilians disappeared. Economists disagree about the size of the civilian loss, not about whether the trade-off existed. During the war, many more people also joined the workforce. That added resources, which shifts the frontier itself, as the next lecture explains.

Three traps

Trap 1 — "Inside the frontier means people are not working hard"

An economy is inside its frontier when resources are idle or badly used. Mei and Kofi were inside the frontier while both worked the whole hour. Describe the cause, such as unemployment or resources in the wrong jobs, not a lack of effort.

Trap 2 — "More of one good always means less of the other"

That is true only on the frontier. From inside, an economy can have more of both, as the United States did in 1941. Say where the economy starts before you say what a change costs.

Trap 3 — "A point outside the frontier is impossible forever"

A point outside is impossible with today's resources and technology. With more resources or better technology, the frontier moves outward, and the point can come within reach.

Try it yourself

Work each one on paper first. Open a hint only when you are stuck.

An invented country can produce these combinations of buses and bicycles in a year: (0 buses, 60 thousand bicycles), (1 thousand, 56 thousand), (2 thousand, 48 thousand), (3 thousand, 34 thousand), (4 thousand, 0). (a) Find the opportunity cost of the third thousand buses. (b) Is (2 thousand buses, 40 thousand bicycles) on, inside or outside the frontier? (c) What about (3 thousand buses, 40 thousand bicycles)?

Hint 1
The third thousand buses take the country from 2 thousand to 3 thousand buses. Look at what happens to bicycles.

Hint 2
For (b) and (c), compare the bicycles with the most bicycles possible for that number of buses.

Full answer
(a) Bicycles fall from 48 thousand to 34 thousand, so the third thousand buses cost $48 - 34 = 14$ thousand bicycles. (b) With 2 thousand buses, up to 48 thousand bicycles are possible. Only 40 thousand are made, so the point is inside: 8 thousand bicycles are being lost. (c) With 3 thousand buses, the most is 34 thousand bicycles, so 40 thousand is outside. Check: the costs of each thousand buses are 4, 8, 14 and 34 thousand bicycles. They rise, so this frontier bows outward. ✓
For each event, say whether the economy moves along its frontier, moves to a point inside it, or moves from inside towards the frontier. (a) A recession closes many shops, and their workers lose their jobs. (b) With everyone still employed, workers move from farms to factories. (c) After a recession, unemployed workers find jobs again.

Hint 1
Ask in each case: are any resources idle, before and after?

Hint 2
A move along the frontier keeps every resource in use but changes the mix of goods.

Full answer
(a) A move to a point inside: workers and shops become idle, so the economy produces less than it could. (b) A move along the frontier: all resources are still used, but the mix changes, with fewer farm goods and more factory goods. (c) A move from inside towards the frontier: idle workers are used again, so the economy can produce more of both. Check: only (b) has an opportunity cost in goods. In (a) the country loses output for nothing, and in (c) it gains output without giving anything up. ✓
On an invented island, there are 10 workers. In one day, each worker can catch 4 fish or pick 12 coconuts, and every worker is equally good at both. (a) Find the most fish, and the most coconuts, the island can get in a day. (b) What is the opportunity cost of one fish? (c) What shape is the island's frontier, and why?

Hint 1
For (a), put all 10 workers on one task.

Hint 2
For (b), one worker gives up 12 coconuts to catch 4 fish. Does it matter which worker moves?

Full answer
(a) All on fish: $10 \times 4 = 40$ fish. All on coconuts: $10 \times 12 = 120$ coconuts. (b) Each worker who moves gives up 12 coconuts for 4 fish, so one fish costs $12 \div 4 = 3$ coconuts. (c) A straight line from 40 fish to 120 coconuts. Every worker has the same cost, so the cost of a fish stays 3 coconuts all the way along. Check: half the workers on each task gives 20 fish and 60 coconuts, and $120 - 3 \times 20 = 60$ . ✓ The PPF bows outward only when resources differ.
A stretch. Ravi and Lucia grow vegetables on two invented farms. In one day, Ravi can grow 8 kg of tomatoes or 4 kg of beans. Lucia can grow 6 kg of tomatoes or 6 kg of beans. Each works one day. (a) Find each person's opportunity cost of 1 kg of beans. (b) Draw their combined frontier, with beans along the bottom. (c) If Ravi grows only beans and Lucia only tomatoes, where is their point? Explain what is wrong with it.

Hint 1
For (a), Ravi gives up 8 kg of tomatoes for 4 kg of beans. For (b), the first beans should come from the person whose beans cost less.

Hint 2
The corners of the frontier are: both on tomatoes, the cheaper bean grower on beans and the other on tomatoes, and both on beans.

Full answer
(a) Ravi: $8 \div 4 = 2$ kg of tomatoes per kg of beans. Lucia: $6 \div 6 = 1$ kg of tomatoes per kg of beans. (b) Both on tomatoes: 0 kg of beans and $8 + 6 = 14$ kg of tomatoes. Lucia's beans are cheaper, so she switches first: 6 kg of beans and Ravi's 8 kg of tomatoes. Then Ravi switches too: $6 + 4 = 10$ kg of beans and no tomatoes. The frontier joins (0, 14), (6, 8) and (10, 0), with a gentler slope of 1 and then a steeper slope of 2, so it bows outward. (c) Ravi's 4 kg of beans and Lucia's 6 kg of tomatoes give the point (4, 6). On the frontier, 4 kg of beans could come with $14 - 4 \times 1 = 10$ kg of tomatoes, all from Lucia's cheaper beans. So (4, 6) is inside the frontier, and 4 kg of tomatoes are lost, although both of them work all day. Check: at (6, 8), $14 - 6 = 8$ ✓. Giving each task to the person with the lower opportunity cost is called comparative advantage, and it is the reason people and countries trade.

The bigger idea

The PPF turns three ideas from the earlier lectures into one picture. Scarcity is the frontier itself: a boundary that wants can push against but cannot cross. Choice is the point the economy picks on it. Opportunity cost is the slope, read off as you move along it.

It also shows the two ways a country can become better off. It can move out to the frontier, by using idle or badly matched resources. Or it can move the frontier itself. The first stops once every resource is in use. The second has no such limit, and it is how countries have become richer over centuries. The next lecture is about that second way.

Key concepts in this lesson

The production possibility frontier (PPF) shows the maximum combinations of two goods an economy can produce with all its present resources fully and efficiently used.
Points on the frontier are productively efficient, points inside waste resources, and points outside cannot be reached with today's resources and technology.
Moving along the frontier shows opportunity cost: more of one good means less of the other, measured in the goods given up.
The frontier bows outward because resources are not equally suited to both goods, so the opportunity cost of each extra unit rises.
An economy can be inside its frontier because of unemployment, idle capital or resources in the wrong jobs, and from there it can produce more of both goods.