In short run cost theory, what is the usual shape of the short run marginal cost curve for a firm as output increases?

Introduction / Context:
Short run marginal cost is one of the most frequently drawn curves in microeconomics. It indicates how the cost of producing one extra unit of output changes as the firm expands production. The typical shape of this curve summarises the impact of increasing and then diminishing returns to the variable factor. Recognising this shape is essential for understanding firm behaviour and cost minimisation.

Given Data / Assumptions:

• The firm operates in the short run with at least one fixed input.
• Input prices are constant.
• The production function exhibits increasing returns initially and then diminishing marginal returns.
• We focus on the shape of the short run marginal cost curve.

Concept / Approach:
Marginal cost is defined as the change in total cost when one extra unit of output is produced. When marginal product of the variable input is rising, each additional unit of input adds more to output, so the extra cost per unit of output tends to fall, leading to declining marginal cost. After a point, diminishing marginal returns set in; marginal product falls, and each extra unit of output requires more input and therefore more cost, causing marginal cost to rise. Together, these phases yield a U shaped marginal cost curve.

Step-by-Step Solution:
1. At low output levels, underutilised fixed inputs mean that adding more variable input increases efficiency.2. As efficiency improves, the cost of producing additional units declines, so marginal cost falls.3. Once capacity is better utilised, diminishing marginal returns occur because the fixed factor becomes a bottleneck.4. The firm must use much more variable input to produce extra units, so the extra cost per unit of output increases.5. Therefore, marginal cost first falls and then rises, giving the characteristic U shape.

Verification / Alternative check:
If we plot numerical values such as marginal cost equal to 12, 10, 9, 9, 10, 12, and 15 for successive units of output, the pattern clearly falls first and then rises. A continuous curve fitted through such points would look U shaped. This matches the standard diagrams used in textbooks where the marginal cost curve cuts the average variable cost and average total cost curves at their minimum points, further confirming the U shaped form.

Why Other Options Are Wrong:
Option B: A V shape implies a straight line down and then straight line up, which does not reflect the smooth curvature implied by production theory.
Option C: An X shape suggests two crossing lines, not the smooth U curve associated with marginal cost.
Option D: A W shape would indicate multiple phases of falling and rising cost, which is not part of the basic short run model.
Option E: A perfectly vertical curve would mean marginal cost is infinite at all output levels, which is neither realistic nor implied by the law of variable proportions.

Common Pitfalls:
Students sometimes misremember which curves are U shaped. A good rule is that, in the short run, marginal cost, average variable cost, and average total cost are all typically U shaped. Another mistake is to think marginal cost is always rising, but this ignores the initial phase of increasing returns. Connecting marginal cost behaviour to marginal product through the cost of the variable input helps keep the reasoning clear.

Final Answer:
The short run marginal cost curve for a firm is typically U shaped.