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Worked Examples · Example 2
Q.

An economy producing only Guns and Butter can achieve the following combinations when its resources are fully and efficiently employed:

CombinationGuns (units)Butter (units)
A050
B147
C242
D334
E424
F50

Calculate the opportunity cost (in units of Butter) of producing each successive Gun, moving from A to F. What does the pattern in these opportunity costs tell you about the shape of the economy's Production Possibility Curve?

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The opportunity cost of each successive Gun is the amount of Butter given up in moving from one combination to the next:

A→B: 50−47=3 units of Butter for the 1st GunA\to B:\ 50-47=3 \text{ units of Butter for the 1st Gun}

B→C: 47−42=5 units of Butter for the 2nd GunB\to C:\ 47-42=5 \text{ units of Butter for the 2nd Gun}

C→D: 42−34=8 units of Butter for the 3rd GunC\to D:\ 42-34=8 \text{ units of Butter for the 3rd Gun}

D→E: 34−24=10 units of Butter for the 4th GunD\to E:\ 34-24=10 \text{ units of Butter for the 4th Gun}

E→F: 24−0=24 units of Butter for the 5th GunE\to F:\ 24-0=24 \text{ units of Butter for the 5th Gun}

The sequence of opportunity costs — 3, 5, 8, 10, 24 — keeps RISING as more Guns are produced. This is the Law of Increasing Marginal Opportunity Cost: as resources are progressively shifted from Butter production into Gun production, the resources being shifted are less and less suited to producing Guns (and were better suited to Butter), so each additional Gun costs more Butter than the one before it. This rising-cost pattern is precisely why the Production Possibility Curve is drawn CONCAVE to the origin …

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