Chapter 7: Problem 15

Each potential short-run average total cost curve is tangent to the long-run average cost curve at a. the level of output that minimizes short-run average total cost. b. the minimum point of the average total cost curve. c. the minimum point of the long-run average cost curve. d. a single point on the short-run average total cost curve.

Short Answer

Expert verified

Each potential short-run average total cost curve is tangent to the long-run average cost curve at the level of output that minimizes short-run average total cost, the minimum point of the average total cost curve, the minimum point of the long-run average cost curve, and occurs at a single point on the short-run average total cost curve. All the statements (a, b, c, and d) are true regarding the tangency point.

Step by step solution

Understanding Short-run and Long-run Average Total Cost

Short-run average total cost (SRATC) curves represent the average total cost of production for a firm in a certain period of time, considering that some factors of production, such as capital, are fixed. On the other hand, long-run average total cost (LRATC) curves represent the average total cost of production when all factors of production can be adjusted. The LRATC curve is drawn by enveloping all the units of SRATC curves.

Identifying Tangency Point

The point of tangency between a short-run average total cost curve and the long-run average total cost curve represents the point where the firm achieves the minimum possible average total cost in both the short-run and the long run. At this point, the firm is both operationally and economically efficient. Now, let's analyze each of the given options.

Option a

Each potential short-run average total cost curve is tangent to the long-run average cost curve at the level of output that minimizes short-run average total cost. This statement is true, as the tangency point represents the minimum average total cost achievable in both the short run and the long run.

Option b

Each potential short-run average total cost curve is tangent to the long-run average cost curve at the minimum point of the average total cost curve. This option is similar to option a and also true, since the tangency point represents where both curves achieve their minimum average total cost.

Option c

Each potential short-run average total cost curve is tangent to the long-run average cost curve at the minimum point of the long-run average cost curve. This statement is also true, as the tangency point represents the minimum average total cost achievable in both the short run and the long run.

Option d

Each potential short-run average total cost curve is tangent to the long-run average cost curve at a single point on the short-run average total cost curve. This statement is true, as each short-run average total cost curve is tangent to the long-run average total cost curve at only one point.

Conclusion

All the statements (a, b, c, and d) are true regarding at which point each potential short-run average total cost curve is tangent to the long-run average cost curve. The tangency point is the level of output that minimizes short-run average total cost, the minimum point of the average total cost curve, the minimum point of the long-run average cost curve, and occurs at a single point on the short-run average total cost curve.

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