Question

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

Short answer

I would support the draftsman; creating such a drawing is impractical.

Step-by-step solution

Understand the Concepts

We need to review the concepts of short-run average cost (SAC) curves and the long-run average cost (AC) curve. The SAC curves are typically U-shaped due to fixed costs in the short run, while the AC curve represents the lower envelope of SAC curves in the long run, where all costs become variable.

Identify Tangency Points

In this problem, we need to check if it's possible for SAC curves to be tangent to the AC curve exactly at their minimum points. Tangency at a minimum implies that the slope of the SAC curve is zero at that point, matching the slope of the AC curve, which must also be zero.

Analyze the Commonality of Tangency and Minimum Points

Consider the nature of SAC and the AC curves. For SAC to be tangent to AC at its minimum, each minimum would have to lie on the AC curve, suggesting that both slopes (derivatives) are equal and zero simultaneously at these points. This conforms to mathematical tangency.

Evaluate the Possibility of Construction

Think about the mathematical construction and drawing. Tangency does not necessarily imply the SAC maintains its minimum tangent to a specific portion across various AC levels due to different economies of scale affecting the cost curves. Thus, maintaining tangencies at minimums for all curves simultaneously is impractical to construct in real scenarios.

Key concepts

Short-run Average Cost

Short-run average cost (SAC) curves capture a key idea in economics. They are typically U-shaped. This shape is due to the way costs behave in the short run, where some costs are fixed. Fixed costs remain constant regardless of the output level. Initially, as production increases, these fixed costs spread over more units, decreasing the average cost.
However, after a certain point, producing more units may lead to inefficiencies, increasing the average cost again. This causes the SAC curve to slope upward.
In the short run, businesses can change only some inputs, like labor, but not others, like plant size or major equipment. As a result, they experience increasing marginal costs due to limited flexibility. This affects the shape of the SAC curve, reinforcing its U-form. Understanding this is crucial when analyzing the relationship between production scale and cost efficiency.

Long-run Average Cost

The long-run average cost (AC) curve represents a different concept. It shows the lowest possible cost at which any level of output can be produced when all inputs are variable. Unlike short-run conditions, all resources can be adjusted. This means plants can expand or contract in size, equipment can be adapted, and workforce numbers can vary as needed.
The AC curve is often called the 'envelope curve'. This is because it forms the lower boundary of all possible SAC curves. By adjusting factors fully and flexibly, the firm minimizes costs across different production scales.
In essence, the long-run AC curve helps us to understand the most efficient scale of production. By operating at any point on this curve, a firm ensures that it can produce its output level at the least cost possible. This is due to the flexibility of adjusting all factors of production.

Economies of Scale

Economies of scale are a central concept explaining cost efficiency as firms increase production. They occur when average costs decrease as output increases. This happens because larger production scales lead to lower costs per unit.
Reasons for economies of scale include:

• Bulk buying of materials which reduces per-unit cost.
• More efficient use of larger equipment.
• Better specialization and division of labor.

These factors contribute to a firm's ability to enjoy lower costs at higher output levels in the long run. They're visualized as a downward-sloping section of the AC curve. Understanding economies of scale helps us comprehend why firms aim for growth. By expanding their operations, they can achieve lower unit costs and potentially increase profits. This concept also underpins why some firms become dominant in their industries.