In short run cost analysis, what is the usual overall shape of the short run marginal cost (SMC) curve?

Introduction / Context:
The short run marginal cost curve plays a central role in microeconomic analysis of firm behaviour. It shows the additional cost of producing one more unit of output. Its shape is linked to the law of diminishing marginal returns and is crucial for understanding how firms decide on output levels and how average cost behaves.

Given Data / Assumptions:

• We consider a single firm in the short run with at least one fixed input.
• Marginal cost is the change in total cost when output is increased by one unit.
• The firm experiences rising marginal productivity initially and then diminishing marginal returns.
• Cost curves are smooth and continuous.

Concept / Approach:
When a firm begins production, adding more units of the variable input such as labour to a fixed amount of capital initially leads to more efficient use of resources and rising marginal product, so marginal cost falls. After a certain point, adding more units of the variable input leads to congestion and diminishing returns, so marginal product falls and marginal cost rises. This combination of initial decline and later increase in marginal cost gives the short run marginal cost curve a U shape.

Step-by-Step Solution:
1. Marginal cost is inversely related to marginal product when input prices are constant. 2. At low levels of production, marginal product increases due to better utilisation of fixed inputs and division of labour. 3. Higher marginal product means more output from each additional unit of input, so the extra cost per unit of output falls and marginal cost declines. 4. Eventually, the law of diminishing marginal returns sets in and marginal product begins to decrease. 5. As marginal product falls, more input is needed to produce an extra unit, so the cost of that extra unit rises, and marginal cost increases, completing the U shape.

Verification / Alternative check:
If you plot marginal product and marginal cost together, marginal cost is falling when marginal product is rising and rising when marginal product is falling, provided the wage rate or variable input price is constant. This relationship is derived mathematically, but conceptually it follows from the idea that each extra worker adds less and less to total output beyond a certain point, which makes each additional unit of output more expensive to produce.

Why Other Options Are Wrong:
Option B and C: V and X shapes do not accurately represent the gradual fall and rise in marginal cost associated with the law of variable proportions.
Option D: A W shaped marginal cost curve would imply multiple cycles of falling and rising marginal cost, which is not the standard assumption in basic microeconomic theory.
Option E: A horizontal marginal cost curve would mean that each extra unit of output costs exactly the same, which does not reflect the usual effects of diminishing returns in the short run.

Common Pitfalls:
Students sometimes mix up the shapes of average and marginal cost curves, but it is important to know that both are typically U shaped in the short run for similar reasons related to diminishing returns. Another mistake is to think that marginal cost must start at zero or negative values, but in practice it starts at some positive level and then falls and rises as production expands.

Final Answer:
U shape