Production Possibilities Curve: Study Guide (Microeconomics 1.3)

The problem the model solves

Every economy faces scarcity: its resources (land, labour, capital and entrepreneurship) are limited, but the things people want are not. So using resources to make one good means not using them to make something else. The production possibilities curve (PPC) is a simple model that shows this trade-off on a graph.

Throughout this guide we use Kestrel Island, a fictional economy that makes only two goods:

• wheat, measured in thousand tonnes per year (on the horizontal axis);
• bicycles, measured in thousands per year (on the vertical axis).

Assumptions of the model

A PPC is drawn for a given moment, with these assumptions:

1. Two goods only. (One may stand for “all other goods”.)
2. Fixed quantity and quality of resources. No new land, workers or machines appear while we read the curve.
3. Fixed technology. The methods of production do not change.
4. Full employment and efficient use. Points on the curve assume all resources are in use and none is wasted.

If any of assumptions 2 or 3 changes, the whole curve moves. If assumption 4 fails, the economy is at a point inside the curve.

Reading a PPC

Kestrel Island’s production possibilities are:

Point	Wheat (thousand tonnes per year)	Bicycles (thousands per year)
A	0	50
B	10	48
C	20	42
D	30	32
E	40	18
F	50	0

Each point tells you something different:

• On the curve (A to F): efficient. All resources are used and none is wasted. To get more of one good, Kestrel must give up some of the other. That forced choice is the trade-off.
• Inside the curve (G: 20 wheat, 30 bicycles): inefficient. At 20 thousand tonnes of wheat, Kestrel could make 42 thousand bicycles, but it makes only 30. Some resources are unemployed or used badly. The curve itself shows scarcity; a point inside shows underused resources.
• Outside the curve (H: 40 wheat, 32 bicycles): unattainable. With 40 thousand tonnes of wheat, the most Kestrel can make is 18 thousand bicycles. H cannot be reached with today’s resources and technology.

Opportunity cost from a PPC

The opportunity cost of a choice is the value of the next best alternative given up. On a PPC, it is the amount of the other good you must give up.

Opportunity cost of 1 more unit of X = (units of Y given up) ÷ (extra units of X gained)

Always say what the cost is measured in: the opportunity cost of wheat is measured in bicycles, and the opportunity cost of bicycles is measured in wheat. The two are reciprocals of each other.

Move	Extra wheat (thousand t)	Bicycles given up (thousand)	Opportunity cost of 1 thousand t of wheat
A → B	10	2	0.2 thousand bicycles
B → C	10	6	0.6 thousand bicycles
C → D	10	10	1.0 thousand bicycles
D → E	10	14	1.4 thousand bicycles
E → F	10	18	1.8 thousand bicycles

The cost of each extra block of wheat rises. This is increasing opportunity cost.

Why the curve bows outward

Resources are not equally suited to every use. Kestrel’s flat, fertile farmland is excellent for wheat. Its skilled metalworkers and factories are excellent for bicycles. When Kestrel makes its first wheat, it moves the resources best suited to farming and least useful in factories, so few bicycles are lost. As it makes more and more wheat, it must use factory workers and land that are poor at farming. Each extra tonne of wheat then costs many more bicycles. This rising cost makes the curve bowed outward (concave to the origin).

There are three possible shapes:

Shape	Opportunity cost as you produce more of one good	When it fits
Straight line (linear)	constant	resources are equally good at making both goods
Bowed outward	increasing	resources are specialised (the usual case)
Bowed inward	decreasing	rare; sometimes used when producing more makes each extra unit cheaper

The slope of the PPC (ignoring the minus sign) between two points is the opportunity cost of the good on the horizontal axis.

Shifts of the curve versus movements along it

This is where students lose the most marks. Ask: has the economy’s ability to produce changed, or only its choice?

Change	What happens on the graph	Why
Kestrel decides to make more wheat and fewer bicycles	movement along the PPC (e.g. C → D)	resources and technology are unchanged; only the mix changes
Unemployed workers find jobs	movement from inside towards the PPC (e.g. G → C)	the economy uses resources it already had; the curve does not move
More workers, more machines (capital), more usable land, or better-educated workers	outward shift: economic growth	the economy can now produce more of both goods
Better technology in both industries	outward shift of the whole curve	productivity rises everywhere
Better technology in one industry only	the curve pivots outward on that good’s axis only	maximum of the other good does not change
A disaster destroys land or factories; the workforce shrinks	inward shift: contraction	fewer resources are available

Notice that reducing unemployment is not economic growth in this model. It moves the economy to a point it could always have reached. Growth means the boundary itself moves out.

Worked example 1: increasing opportunity cost on Kestrel Island

Question. Use the Kestrel Island table. (a) What is the opportunity cost of moving from C to D? Express it per thousand tonnes of wheat. (b) Compare it with the move from D to E. What does the comparison show? (c) What is the opportunity cost of 1 thousand bicycles when moving from E back to D? (d) What is the opportunity cost of moving from G to C?

(a) From C (20, 42) to D (30, 32):

1. Extra wheat = 30 − 20 = 10 thousand tonnes.
2. Bicycles given up = 42 − 32 = 10 thousand.
3. Opportunity cost = 10 ÷ 10 = 1.0 thousand bicycles per thousand tonnes of wheat (1 bicycle per tonne).

(b) From D (30, 32) to E (40, 18):

1. Extra wheat = 40 − 30 = 10 thousand tonnes.
2. Bicycles given up = 32 − 18 = 14 thousand.
3. Opportunity cost = 14 ÷ 10 = 1.4 thousand bicycles per thousand tonnes of wheat.

The same 10 thousand tonnes of extra wheat costs more bicycles the further Kestrel moves towards wheat. This is increasing opportunity cost, which is why the curve is bowed outward.

(c) From E (40, 18) to D (30, 32): Kestrel gains 14 thousand bicycles and gives up 10 thousand tonnes of wheat. Opportunity cost of 1 thousand bicycles = 10 ÷ 14 = 0.71 thousand tonnes of wheat (to 2 decimal places). This is the reciprocal of 1.4.

(d) From G (20, 30) to C (20, 42): wheat stays at 20, bicycles rise by 42 − 30 = 12 thousand. Nothing is given up, so the opportunity cost is zero.

Check. The units in (a) are “bicycles per tonne of wheat”: the good given up per unit of the good gained. In (d), a zero cost makes sense: G was wasting resources, so using them costs nothing.

Worked example 2: constant opportunity cost and a pivot

Question. Marisol is a second fictional economy. If it uses all its resources on wheat, it can make 20 thousand tonnes per year; if it uses them all on bicycles, 40 thousand per year. Its resources are equally good at both, so its PPC is a straight line. (a) Find the opportunity cost of each good. (b) Classify J (5 wheat, 20 bicycles), K (10, 20) and L (15, 20). (c) A new bicycle technology doubles the number of bicycles Marisol can make. Wheat production is unaffected. Describe the new PPC and find the new opportunity cost of wheat. Is L now attainable?

(a)

1. Giving up all 40 thousand bicycles gains 20 thousand tonnes of wheat.
2. Opportunity cost of 1 thousand tonnes of wheat = 40 ÷ 20 = 2 thousand bicycles.
3. Opportunity cost of 1 thousand bicycles = 20 ÷ 40 = 0.5 thousand tonnes of wheat.
4. The line is straight, so these costs are the same everywhere on it: constant opportunity cost.

(b) The equation of the line is bicycles = 40 − 2 × wheat. At 20 thousand bicycles, the line gives wheat = (40 − 20) ÷ 2 = 10.

• J (5, 20): at 5 wheat, the maximum is 40 − 10 = 30 bicycles. 20 < 30, so J is inside: inefficient.
• K (10, 20): 40 − 20 = 20. K is on the curve: efficient.
• L (15, 20): the maximum is 40 − 30 = 10 bicycles. 20 > 10, so L is outside: unattainable.

(c) The bicycle intercept doubles to 80; the wheat intercept stays at 20. The PPC pivots outward around the wheat intercept. New opportunity cost of 1 thousand tonnes of wheat = 80 ÷ 20 = 4 thousand bicycles (it was 2). Each tonne of wheat now costs more bicycles, because Marisol’s resources have become better at making bicycles.

On the new line, bicycles = 80 − 4 × wheat. At 15 wheat: 80 − 60 = 20. So L is now on the new PPC: it is attainable and efficient.

Interpretation. Technology that helps only one industry still lets the economy have more of both goods at most points, because resources can move. But it changes the trade-off between the goods.

Common misconceptions

• “A point inside the PPC is impossible.” It is possible but inefficient. Points outside are unattainable.
• “Lower unemployment shifts the PPC outward.” It moves the economy from inside towards the curve. The curve shifts only if resources or technology change.
• “A change in what people want shifts the PPC.” Preferences change which point is chosen (a movement along the curve), not what is possible.
• “Opportunity cost is the total amount of the other good.” It is the amount given up: the change, not the level. From C to D, the cost is 10 thousand bicycles, not 32 thousand.
• “Opportunity cost is measured in money.” In the PPC model, it is measured in units of the other good.
• “Better technology for one good shifts the whole curve out evenly.” It pivots the curve on that good’s axis only.
• “The PPC bows out because of diminishing demand or rising prices.” The shape comes from resources being unequally suited to the two goods, not from prices.

Where this leads

The PPC is the first model in the course. Next you will use opportunity cost to compare producers and explain gains from trade (Topic 1.4), and to weigh costs against benefits (Topic 1.5). Test yourself with the practice questions, then use the revision notes and the checklist to consolidate.