Economics 9708/11 — October/November 2020

Background Concept

A Production Possibility Curve (PPC) illustrates the maximum possible output combinations of two goods an economy can achieve when all resources are fully and efficiently employed, given the current state of technology. The curve is typically bowed outward (concave to the origin) because of increasing opportunity cost: as production of one good expands, increasingly unsuitable resources must be transferred, raising the marginal cost. However, when the PPC is a straight line, as in this question, opportunity cost is constant. This means the economy gives up a fixed amount of the other good for each additional unit produced, regardless of the output mix. The slope of the PPC equals the opportunity cost of the good on the horizontal axis measured in terms of the good on the vertical axis.

Understanding the Question

The question presents a linear PPC with consumer goods on the vertical axis (maximum 1000 units) and capital goods on the horizontal axis (maximum 50 units). The economy is currently operating at a point where 80% of resources go to consumer goods and 20% to capital goods. The question asks what the result will be if the economy decides to double its output of capital goods. This requires calculating the opportunity cost of that reallocation in terms of lost consumer goods. The four options present different numerical outcomes, only one of which correctly reflects the trade-off shown by the diagram.

Approach

To solve this, follow these steps:

1. Convert the percentage allocation into actual quantities using the intercepts of the PPC.
2. Determine the new quantity of capital goods after doubling.
3. Use the constant opportunity cost (derived from the slope or the intercepts) to find how many consumer goods must be given up to produce the extra capital goods.
4. Compare the calculated loss with the options provided.

Because the PPC is linear, the opportunity cost per unit is constant at 20 consumer goods per capital good (1000/50). This makes the calculation straightforward arithmetic.

Step-by-Step Reasoning

First, identify the current production levels. The maximum possible output of consumer goods is 1000 and of capital goods is 50. If the economy allocates 80% of its resources to consumer goods, it produces 0.80 x 1000 = 800 consumer goods. Similarly, 20% of resources allocated to capital goods yields 0.20 x 50 = 10 capital goods.

Second, determine the new capital goods output. Doubling the current 10 units gives 20 units of capital goods.

Third, calculate the opportunity cost. Because the PPC is a straight line, the opportunity cost is constant. The slope is rise over run: -1000/50 = -20. This means that to produce one more unit of capital goods, the economy must give up 20 units of consumer goods. To increase capital goods from 10 to 20 units (an increase of 10 units), the economy gives up 10 x 20 = 200 consumer goods.

Alternatively, using the PPC equation: Consumer goods = 1000 - 20(Capital goods). At 20 capital goods, consumer goods = 1000 - 400 = 600. The fall from 800 to 600 is 200 consumer goods.

Finally, evaluate the options. Option A (gain of 20 capital goods) is incorrect because the gain is 10 units, not 20. Option B (gain of 40 capital goods) is also incorrect. Option D (loss of 600 consumer goods) would imply consumer goods fall to 200, which would require producing 40 capital goods, not 20. Only option C correctly identifies the loss of 200 consumer goods.

Key Takeaways

• A linear PPC implies constant opportunity cost, calculated as the ratio of the intercepts.
• When resources are reallocated along the PPC, the opportunity cost of the good being increased is found by multiplying the change in quantity by the constant marginal rate of transformation (the slope).
• Percentage allocations must be applied to the maximum possible outputs to find actual quantities before calculating trade-offs.

Common Mistakes

• Misreading the axes or percentages: Some students may apply the 80% to capital goods or the 20% to consumer goods, reversing the calculation.
• Incorrect slope calculation: Dividing 50 by 1000 instead of 1000 by 50 gives the reciprocal, leading to an opportunity cost of 0.05 rather than 20.
• Doubling the wrong base: The current output is 10 units (20% of 50), not 50 or 20. Doubling 10 gives 20, not 40.
• Confusing the gain with the loss: The question asks for the result of doubling capital goods; the relevant trade-off is the consumer goods lost, not the capital goods gained.

Things to Be Careful About

• Always verify which axis represents which good before calculating. Here, consumer goods are vertical and capital goods are horizontal.
• Check whether the PPC is linear or bowed. A linear curve means constant opportunity cost, simplifying the calculation to a single multiplication.
• Ensure the final answer matches the form of the options: the question asks for the result, and the correct option describes a loss of consumer goods, not a gain of capital goods.