Question

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

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.

Key concepts

Short-run Average Total Cost

The Short-run Average Total Cost (SRATC) curve plays a crucial role in understanding the cost of production within a fixed period. In the short run, certain inputs like capital are fixed while others can vary. This fixed nature of some inputs defines the SRATC curve.
It represents the cost per unit of output when the production period is not long enough to change all input levels. As production scales up, each SRATC curve shows how costs fluctuate based on the production level, typically forming a U-shape.
The short-run cost structure reflects factors like labor adjustments and overtime costs that differ based on the output level. Together, these factors help determine the efficiency and cost management strategies in the short run.

Long-run Average Total Cost

In contrast to the short-run, the Long-run Average Total Cost (LRATC) curve illustrates cost behavior when a firm can adjust all inputs.
This curve acts as an envelope for all possible SRATC curves and represents the lowest possible cost of production for each output level when firms can fully optimize all factors.
Adjusting factors such as the scale of operation and technology allows the LRATC to show what is achievable with full flexibility, often leading to economies or diseconomies of scale.
The LRATC therefore acts as a guide for firms to understand their performance and planning efficiency over long periods when production dynamics can fully adapt.

Tangency Point

The concept of the tangency point is crucial when assessing the interaction of SRATC and LRATC curves. It is at these tangency points that SRATC curves touch the LRATC curve.
These points suggest that the firm is achieving the most efficient cost levels possible for both short and long-term production levels simultaneously.
At the tangency point, the cost levels are minimized as it aligns with optimal output. It signifies the best performance where production adjustments meet market conditions and internal efficiencies.
This highlights a firm's ability to switch smoothly from short-run constraints to optimal long-run planning, maintaining economic efficiency.

Economic Efficiency

Economic efficiency in production occurs when resources are optimized to achieve the lowest cost output. Both SRATC and LRATC curves play a role in realizing this efficiency.
By hitting the tangency point, a firm attains economic efficiency where the cost of producing an additional unit is minimized, ensuring resources aren't wasted.
This efficiency must address the optimal allocation of resources like labor and capital while maximizing the output from available resources.
Achieving this state ties closely with competitive pricing and business sustainability, where firms strive to operate at minimum average total costs over time, ensuring long-term success.