Q.Why is the short run marginal cost curve 'U'-shaped?

The short-run marginal cost curve is U-shaped because of the law of variable proportions (also called the law of diminishing marginal product) operating in the short run.

In the short run, at least one factor of production—typically capital—is fixed. When a firm increases output by employing more of the variable factor (say, labor), it initially experiences increasing returns: each additional unit of the variable input adds more to total output than the previous one. During this phase, the marginal product of the variable factor rises, which means the cost of producing one more unit (marginal cost) falls. This gives the downward-sloping portion of the MC curve. …

The economic intuition

Marginal cost measures the addition to total cost when you produce one more unit of output. In the short run, at least one factor of production (typically capital) is fixed, while others (like labor) are variable. The shape of the MC curve is entirely driven by how productively that variable factor is being used at different output levels.

Think about a factory with a fixed number of machines. When you start production with just a few workers, each additional worker has plenty of equipment to work with and can specialize in specific tasks. Coordination improves, the assembly line runs smoothly, and each extra worker adds more to output than the previous one. This is the phase of increasing returns to the variable factor. When the marginal product of labor is rising, the cost of producing an additional unit—the marginal cost—is falling. You're getting more output per rupee spent on labor.

But this cannot continue indefinitely. Once you've hired enough workers to fully utilize the fixed capital, adding even more workers means they start getting in each other's way. Machines must be shared, workspace becomes crowded, and coordination becomes harder. Now each additional worker adds less to total output than the one before—diminishing returns have set in. When the marginal product of labor falls, marginal cost rises. You need progressively more labor (and hence more cost) to produce each additional unit.

The relationship between marginal product and marginal cost

The mathematical link makes this precise. If $w$ is the wage rate (price of the variable factor) and $MP_L$ is the marginal product of labor, then:

This inverse relationship is the key. When $MP_L$ is rising (increasing returns), $MC$ is falling. When $MP_L$ reaches its maximum, $MC$ reaches its minimum. When $MP_L$ starts falling (diminishing returns), $MC$ starts rising.

The three stages unfold as follows:

| Stage | Returns to Variable Factor | Marginal Product | Marginal Cost | …