In short run cost analysis, what is the usual overall shape of the short run average cost (SAC) curve for a firm?

Introduction / Context:
The short run average cost curve is a fundamental concept in microeconomics. It combines average fixed cost and average variable cost to show total cost per unit at different output levels. Understanding its shape helps to explain how firms experience economies and diseconomies of scale in the short run and how they decide on optimal output levels.

Given Data / Assumptions:

• We are analysing a single firm in the short run.
• At least one factor, such as capital, is fixed, while others, such as labour, vary.
• Average cost per unit is calculated as total cost divided by quantity produced.
• The firm experiences increasing returns initially and diminishing returns later.

Concept / Approach:
In the short run, average fixed cost falls continuously as output increases because the fixed cost is spread over more units. Average variable cost falls at first due to better utilisation and specialisation but eventually rises due to diminishing marginal returns. The short run average cost curve is the sum of average fixed cost and average variable cost at each output level, and it typically falls at first, reaches a minimum, and then rises, forming a U shape.

Step-by-Step Solution:
1. At low output levels, fixed cost is spread over very few units, so average cost is high. 2. As output increases, average fixed cost falls sharply and average variable cost also falls due to improved efficiency and specialisation. 3. This combined effect makes short run average cost decline in the initial range. 4. Beyond a certain level, diminishing marginal returns to the variable factor cause average variable cost to rise. 5. When the increase in average variable cost outweighs the decline in average fixed cost, short run average cost starts to rise, creating a U shaped curve.

Verification / Alternative check:
Standard diagrams in microeconomics textbooks always show the short run average cost curve as U shaped, with marginal cost intersecting it at its minimum point. Numerically, you can verify this by computing average cost at different output levels when fixed cost is constant and variable cost per unit first falls and then rises.

Why Other Options Are Wrong:
Option B and C: V and X shapes do not capture the initial fall and later rise of costs in a smooth pattern; they suggest different or abrupt behaviours.
Option D: A W shape would mean costs fall, rise, fall and rise again, which is not the standard outcome described by the law of variable proportions.
Option E: A horizontal line would imply that average cost is constant regardless of output, which is inconsistent with the underlying cost structure in the short run.

Common Pitfalls:
Students may confuse the short run average cost curve with the long run average cost curve, which may also appear U shaped but for different reasons related to economies and diseconomies of scale. Another mistake is to focus only on variable cost and ignore the effect of spreading fixed costs. Always remember that in the short run, the combination of falling average fixed cost and changing average variable cost gives the U shaped average cost curve.

Final Answer:
U shape