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Figure 2-6

A production possibilities frontier line of sofas versus cars. The origin of the axis system is at (0, 0). The line starts on the Sofas axis at the maximum feasible value, then descends in a straight line to the maximum feasible value for cars on the Cars axis. Representative points are as follow. (0, 900), (200, 600), (400, 300), (600, 0). Four points, A, B, C, and D, are plotted as follows. Point A is at the maximum feasible value for sofas, (0, 900). Point B is on the production possibilities frontier at (200, 600). Point C is on the production possibilities frontier at (400, 300). Point D is is at the maximum feasible value for cars, (600, 0).

Refer to Figure 2-6. Consider the production possibilities frontier for an economy that produces only sofas and cars. The opportunity cost of each car is
a. the reciprocal of the slope of the production possibilities frontier, or 3/2 sofas.
b. the reciprocal of the slope of the production possibilities frontier, or 2/3 of a sofa.
c. the slope of the production possibilities frontier, or 2/3 of a sofa.
d. the slope of the production possibilities frontier, or 3/2 sofas.

1 answer

To determine the opportunity cost of each car on the production possibilities frontier (PPF) for sofas and cars, we first need to calculate the slope of the PPF.

From the given points on the PPF where:

  • Point A: (0, 900) - maximum sofas
  • Point B: (200, 600)
  • Point C: (400, 300)
  • Point D: (600, 0) - maximum cars

We can calculate the slope of the PPF section from Point B to Point C. The change in the number of cars (y-axis) is from 600 to 300, which is a decrease of 300 cars. The change in the number of sofas (x-axis) is from 200 to 400, which is an increase of 200 sofas.

The formula for slope (m) between two points (x1, y1) and (x2, y2) is:

\[ m = \frac{y2 - y1}{x2 - x1} \]

Using the points B (200, 600) and C (400, 300):

\[ m = \frac{300 - 600}{400 - 200} = \frac{-300}{200} = -\frac{3}{2} \]

The negative sign indicates a trade-off; as you produce more cars, you have to give up sofas. The absolute value of the slope, \( \frac{3}{2} \), represents the opportunity cost of producing one car.

Since here we need to calculate the opportunity cost of each car:

  1. The slope of the PPF from Point B to Point C indicates that for every car produced, you give up \( \frac{3}{2} \) sofas.
  2. Therefore, the opportunity cost of one car is \( \frac{3}{2} \) sofas.

This means that the correct answer is:

d. the slope of the production possibilities frontier, or 3/2 sofas.