In short run cost analysis, what is the typical shape of the average variable cost curve for a competitive firm?

Introduction / Context:
Short run cost curves such as the average variable cost (AVC) curve and average total cost (ATC) curve are central to microeconomics. Examinations frequently test whether students remember the typical shapes of these curves and understand the economic reasons behind them. The question asks specifically about the shape of the average variable cost curve in the short run.

Given Data / Assumptions:

• We are analysing a firm in the short run with at least one fixed factor.
• Input prices are assumed constant.
• Production initially experiences increasing returns and then diminishing returns.
• We are asked about the shape of the average variable cost curve.

Concept / Approach:
The average variable cost curve relates the variable cost per unit of output to the level of output. Due to the law of variable proportions or diminishing marginal returns, as a firm increases output, variable cost per unit initially falls because the fixed factor is used more efficiently. After a certain level, overcrowding and inefficiency start to appear and marginal cost rises, which pushes average variable cost upward. This combination of falling then rising values produces a U shaped curve for average variable cost.

Step-by-Step Solution:
1. At low levels of output, workers and variable inputs can use fixed capital more efficiently, so variable cost per unit declines.2. This causes the average variable cost to fall initially as output increases.3. After some point, diminishing marginal returns set in as more variable input is applied to the same fixed input.4. The additional cost of producing extra units rises, and marginal cost increases sharply.5. Because marginal cost eventually exceeds average variable cost, it pulls the average variable cost upward, creating the upward sloping portion of the U shape.6. Thus, the overall shape of the average variable cost curve is U shaped, first falling then rising.

Verification / Alternative check:
A numerical example helps verify this. Suppose variable cost for successive units of output is such that average variable cost falls from 10 to 8 to 7, and then begins to rise to 8 and 9 as output expands further. Plotting these values against output yields a curve that falls initially, reaches a minimum, and then rises again, clearly forming a U shape. This pattern is found in standard textbook diagrams of short run cost curves.

Why Other Options Are Wrong:
Option B: A V shaped curve implies that average variable cost falls or rises in a straight line, which is not how cost behaves in typical production functions.
Option C: An X shaped curve would suggest two turning points and complex behaviour, which is not supported by basic production theory.
Option D: A W shaped curve also suggests multiple local minima and maxima, which is not the standard shape in introductory analysis.
Option E: A perfectly horizontal curve would mean constant average variable cost regardless of output, which contradicts the law of variable proportions.

Common Pitfalls:
Students sometimes mix up the shapes of marginal cost, average variable cost, and average total cost. All three are typically U shaped in the short run, with marginal cost cutting both average curves at their minimum points. It is useful to remember that the underlying cause in each case is diminishing marginal returns after a certain level of output. Another pitfall is to assume strange shapes like W or X just because they appear in options; examining the logic of costs usually points back to the simple U shape.

Final Answer:
The average variable cost curve in the short run is typically U shaped.