To determine the opportunity cost of producing one car in an economy that produces sofas and cars, we need to consider the concept of the production possibilities frontier (PPF) and how its slope represents opportunity cost.
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Understanding the Slope of the PPF: The slope of the PPF indicates how many sofas must be given up to produce one additional car. If the slope of the PPF is negative and represents a trade-off between two goods, we can find the opportunity cost accordingly.
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Opportunity Cost Calculation: If the slope of the PPF is, for example, -2/3, this means for each car produced, the economy loses 2/3 of a sofa. The opportunity cost of one car would thus be represented as 2/3 of a sofa.
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Reciprocal of the Slope: The reciprocal of the slope shows the opportunity cost in terms of cars per sofa. If the slope is -2/3, the reciprocal is -3/2, meaning producing 1 sofa costs 1.5 cars.
Given these points, let's analyze each option:
- Option a: "the reciprocal of the slope of the production possibilities frontier, or 2/3 of a sofa." (Incorrect)
- Option b: "the slope of the production possibilities frontier, or 2/3 of a sofa." (Correct if the slope represents that trade-off)
- Option c: "the slope of the production possibilities frontier, or 3/2 sofas." (Incorrect)
- Option d: "the reciprocal of the slope of the production possibilities frontier, or 3/2 sofas." (Incorrect)
Therefore, the correct answer is: b. the slope of the production possibilities frontier, or 2/3 of a sofa.