Q.(a) Why is the short run Marginal Cost curve U-shaped?

(a) 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 returns). In the short run, at least one factor of production is fixed—typically capital—while others like labor are variable.

Initially, when output is low, the fixed factor is underutilized. As we add more units of the variable factor, specialization and better utilization of the fixed factor cause marginal product to rise. Since $MC = \frac{w}{MP_L}$ (where $w$ is the wage rate and $MP_L$ is the marginal product of labor), a rising marginal product means marginal cost falls. This gives the downward-sloping portion of the MC curve.

Beyond a certain level of output, however, the fixed factor becomes a constraint. Adding more variable input leads to diminishing marginal returns—each additional unit of the variable factor adds less to total output than the previous one. The marginal product falls, so marginal cost rises. This creates the upward-sloping portion.

The result is a U-shaped MC curve: falling initially due to increasing marginal returns, reaching a minimum, then rising due to diminishing marginal returns.

(b) Relation between Average Cost (AC) and Marginal Cost (MC) curves

The relationship between AC and MC follows three key rules:

1. When MC < AC: Average cost is falling. Each additional unit costs less than the average of all previous units, pulling the average down. …

(a) Why is the short-run Marginal Cost curve U-shaped?

The U-shape of the short-run marginal cost curve flows directly from the law of variable proportions (also called the law of diminishing returns). In the short run, at least one factor of production—typically capital—is fixed. You can only vary the other inputs, usually labor.

When you start production with very little of the variable input relative to the fixed input, each additional worker has plenty of capital to work with. Productivity is low because the fixed factor is underutilized. As you add more workers, they can specialize, coordinate better, and use the fixed capital more efficiently. Marginal product of labor rises—each extra worker adds more output than the previous one. Because marginal cost is the cost of producing one more unit, and that unit now requires less additional labor (since MP is rising), marginal cost falls. This gives you the downward-sloping portion of the MC curve.

But this can't continue forever. Once you've added enough workers, the fixed capital becomes a constraint. Workers start getting in each other's way, machines are overused, and coordination becomes harder. Marginal product of labor begins to fall—each extra worker now adds less output than the previous one. To produce one more unit of output now requires more additional labor, so marginal cost rises. This is the upward-sloping portion.

The inverse relationship is clear: when $MP_L$ rises, $MC$ falls; when $MP_L$ falls, $MC$ rises. Since the law of variable proportions tells us that marginal product first rises, reaches a maximum, then falls, marginal cost must first fall, reach a minimum, then rise—tracing out a U.

(b) Relation between Average Cost (AC) and Marginal Cost (MC) curves

The relationship between AC and MC is one of the most elegant in microeconomics, and it rests on a simple mathematical truth about averages and marginals.

The conceptual link: Marginal cost tells you the cost of the next unit. Average cost tells you the cost per unit on average up to that point. Whenever the cost of the next unit (MC) is below the average (AC), producing that unit pulls the average down. Whenever MC is above AC, the next unit pulls the average up. And at the exact point where MC equals AC, the average is neither rising nor falling—it's at its minimum.

Think of it like a batsman's batting average. If your average is 50 and you score 30 in the next innings (marginal score below average), your average falls. If you score 70 (marginal above average), your average rises. If you score exactly 50, your average stays put.

The three regions

1. When MC < AC: Each additional unit costs less than the average of all previous units. This drags the average cost down. The AC curve is falling.

2. When MC = AC: The cost of the additional unit exactly equals the average. The average is stationary—neither rising nor falling. This is the minimum point of the AC curve.

3. When MC > AC: Each additional unit costs more than the average. This pushes the average cost up. The AC curve is rising.

The diagram (in words)

Both the MC and AC curves are U-shaped in the short run, but the MC curve is more sharply U-shaped and lies below AC initially. …