Question

In a famous article [J. Viner, "Cost Curves and Supply Curves," Zeilschríl fur Nationalokonomie \(3 \text { (September } 1931 \text { ): } 23-46]\), Viner criticized his draftsman who could not draw a family of \(S A T C\) curves whose points of tangency with the U-shaped \(A C\) curve were also the minimum points on each \(S A T C\) curve. The draftsman protested that such a drawing was impossible to construct. Whom would you support in this debate? \\[

Short answer

Answer: No, it is not possible to draw a family of SATC curves with points of tangency to the U-shaped AC curve at their respective minimum points. The tangency points on the AC curve represent the lowest average total cost but not necessarily at the minimum points of the respective SATC curves.

Step-by-step solution

- Understand the AC and SATC curves

The Average Cost (AC) curve represents the costs of a firm per unit of output. Its shape is usually U-shaped, indicating that at first, average costs decrease as the output expands, reaching a minimum point, and then increase the output. The SATC curves refer to the short-run average total costs at different scales of production. As the firm expands or contracts, the SATC curves shift.

- Relationship between AC and SATC curves

To clarify the debate, we need to understand the relationship between AC and SATC curves. The AC curve is the envelope of the family of SATC curves. In other words, for any given level of output, the AC curve represents the lowest possible average total cost.

- Visualize the scenario

Imagine a U-shaped AC curve, which represents the firm's lowest average costs at different output levels. The family of SATC curves should show varying shapes following the envelope the AC curve creates. The student can draw a U-shaped AC curve on a graph paper and then try to draw some SATC curves tangent to the AC curve at different points. They'll notice that at the minimum points of each SATC curve, they will not necessarily be tangent to the AC curve.

- Reach a conclusion

Based on the understanding of the relationship between the AC and SATC curves, the draftsman is correct. It is not possible to draw a family of SATC curves whose points of tangency with the U-shaped AC curve are also the minimum points on each SATC curve. The tangency points on the AC curve represent the lowest average total cost but not necessarily at the minimum points of the respective SATC curves.

Key concepts

Average Cost (AC) Curve

The Average Cost (AC) curve is a crucial concept in economics, representing the average cost per unit of output for a firm. When plotted on a graph, this curve typically has a U-shape.
In the initial stages of production, as the output increases, the average costs decline due to more efficient utilization of resources. This is because fixed costs, such as rent and salaries, get distributed over a larger number of goods.
However, after reaching a certain point, expanding production results in higher average costs. Factors such as overtime payment for workers or the need to maintain machinery contribute to this rise.
Therefore, understanding the U-shaped AC curve helps businesses determine the most cost-effective level of production. By operating at the minimum point of the AC curve, a firm achieves the lowest possible average cost.

Short-Run Average Total Cost (SATC) Curve

The Short-Run Average Total Cost (SATC) curve illustrates the average total cost a firm incurs over a short time period at various levels of output. Each SATC curve corresponds to a specific level of fixed resources that do not change in the short run.
As production scales up or down, these SATC curves shift position, reflecting changes in average costs due to adjustments in variable resources, like labor or materials.
Unlike the AC curve, each SATC reflects cost conditions specific to a certain scale of operation, characterized by fixed inputs. Firms can analyze these curves to decide on temporary production levels that optimize their short-term operations.
This insight is pivotal for businesses as they navigate short-term fluctuations in demand and supply and strive for efficient operations without fully altering their resource base.

U-Shaped Cost Curve

The concept of a U-Shaped Cost Curve appears in both AC and SATC curves. This shape emerges due to the relationship between fixed and variable costs during production. Initially, costs drop because of higher efficiency and spreading out fixed costs.
Yet, as production continues to expand, diminishing returns set in. The U-shape reflects that there is an optimal level of production where costs are minimized.
In graphical representations, this is depicted by the downward and then upward swoop of the curve. At the bottom, or the minimum point, firms find the most efficient scale of production, balancing both fixed and variable costs.
Comprehending this shape aids in strategic planning, allowing firms to adjust resources and outputs in a way that aligns with their financial and production goals for maximum efficiency.