Economic Systems and Production Possibility Curves: Question 2

Worked solution

Part (a): Opportunity cost of R $\to$ S

Between combination R (20 tonnes of food, 85 units of machinery) and combination S (30 tonnes of food, 70 units of machinery), food output rises by 10 tonnes, and machinery output falls by: $85 - 70 = 15$

So the opportunity cost of increasing food output from 20 to 30 tonnes is 15 units of machinery.

Part (b): Opportunity cost of S $\to$ T, and the shape of the PPC

Between combination S (30 tonnes of food, 70 units of machinery) and combination T (40 tonnes of food, 50 units of machinery), food output again rises by 10 tonnes, and machinery output falls by: $70 - 50 = 20$

So the opportunity cost of increasing food output from 30 to 40 tonnes is 20 units of machinery.

Comparing the two results: the opportunity cost of an extra 10 tonnes of food rose from 15 units of machinery (R $\to$ S) to 20 units of machinery (S $\to$ T). In fact, working through the whole table the same way gives opportunity costs of 5, 10, 15 and 20 units of machinery for each successive 10-tonne increase in food (P$\to$Q, Q$\to$R, R$\to$S, S$\to$T), a steadily rising opportunity cost.

This rising, or increasing, opportunity cost means the PPC is bowed outward (concave to the origin), not a straight line. This happens because factors of production are not equally suited to producing both goods: as more resources are shifted out of machinery and into food production, resources that are progressively less suited to growing food (but were highly suited to producing machinery) have to be used, so each extra tonne of food costs more and more machinery given up. A straight-line PPC, by contrast, would show a constant opportunity cost at every point.

Part (c): Is (15 tonnes, 60 units) on, inside, or beyond the PPC?

Combinations Q (10 tonnes of food, 95 units of machinery) and R (20 tonnes of food, 85 units of machinery) both lie on the PPC and bracket 15 tonnes of food. Because the curve is bowed outward, the maximum machinery obtainable at 15 tonnes of food must be at least as high as a straight line joining Q and R would suggest, roughly $(95+85)/2 = 90$ units, or slightly more.

The economy is actually producing only 60 units of machinery at 15 tonnes of food, which is well below this 85-95 unit range. So the combination (15, 60) lies inside the PPC: some resources in this economy must currently be unemployed, or not being used to their full productive potential, since more machinery (and/or food) could be produced from the same resources.

Part (d): Effect of the irrigation technology on the PPC

The new irrigation technology raises the amount of food that can be grown from a given area of land, with no effect on machinery production. This means:

• The maximum food output the economy could achieve (if it devoted all resources to food, producing no machinery) increases.
• The maximum machinery output the economy could achieve (if it devoted all resources to machinery, producing no food) is unchanged, since the technology only affects food production.

The PPC therefore shifts outward, representing economic growth in the economy’s productive capacity, but it is not a simple parallel shift in every direction. The curve stretches out mainly along the food axis, becoming flatter/wider on the food side, while the machinery-axis intercept stays roughly where it was.

Final answers

• (a) Opportunity cost of R $\to$ S $=$ 15 units of machinery
• (b) Opportunity cost of S $\to$ T $=$ 20 units of machinery; the rising opportunity cost (15 then 20) shows the PPC is bowed outward (concave to the origin)
• (c) (15 tonnes food, 60 units machinery) lies inside the PPC. Resources are unemployed or underused
• (d) The PPC shifts outward, stretching mainly along the food axis, since the technology raises maximum food output but leaves maximum machinery output unchanged