Diminishing Returns & the Shape of Marginal Cost

You’ll be able to

State the law of diminishing marginal returns and identify where it begins
Explain why marginal cost is the mirror image of marginal product
Distinguish diminishing returns from diseconomies of scale

Diminishing returns is a short-run idea

The law of diminishing marginal returns says that adding units of a variable input to a fixed input eventually raises output by progressively less. The fixed input is essential to the statement: with a fixed kitchen, the tenth cook adds less than the third. This is a short-run phenomenon, because in the long run every input can be scaled — which is why it must not be confused with diseconomies of scale.

Increasing then diminishing then negative

Marginal product often rises at first, because a second and third worker allow specialization that a lone worker cannot manage. Then it falls as the fixed input becomes crowded. It can even go negative — workers getting in each other's way, so total output actually drops. The exam expects you to locate the point where marginal product peaks, which is exactly where marginal cost bottoms out.

Why MC mirrors MP

MC = wage / MP_labor

The wage is fixed, so when marginal product rises, marginal cost falls, and vice versa. MC is MP turned upside down.

The mirror relationship, spelled out

If each worker costs the same wage, then the cost of one more unit of output is the wage divided by how much output that worker adds. So rising marginal product means falling marginal cost, and falling marginal product means rising marginal cost. Marginal cost reaches its minimum exactly where marginal product reaches its maximum. Once you see this, the U-shape of MC is not a separate fact to memorize — it is diminishing returns drawn upside down.

Worked example

A firm hires workers at $120 each. Output for 1 through 5 workers is 10, 25, 45, 60, 70 units. Find marginal product and marginal cost at each step and identify where diminishing returns begins.

1.Marginal products: 10, 15, 20, 15, 10.
2.Marginal product peaks at the third worker (20 units), so diminishing returns begins with the FOURTH worker.
3.Marginal cost per unit = $120 / MP: 12.00, 8.00, 6.00, 8.00, 12.00.
4.Marginal cost bottoms out at the third worker, exactly where marginal product peaks.

Answer: Diminishing returns begins with the fourth worker, whose marginal product of 15 is below the third's 20. Marginal cost is minimized at $6.00 per unit at the third worker — the mirror of the marginal product maximum.

Watch out

Diminishing returns begins at the worker AFTER the one with the highest marginal product, not at that worker. And diminishing marginal product does not mean total output is falling — total keeps rising while marginal product is positive.

Checkpoint

Marginal product for workers 1 to 5 is 8, 14, 18, 16, 11. Diminishing marginal returns begins with which worker?

Checkpoint

Marginal cost reaches its minimum at the output where:

Checkpoint

Diminishing marginal returns occurs because:

On the exam

When a table gives total product, write the marginal product column immediately, then divide the wage by each entry for marginal cost. Both columns are usually needed and computing them once saves recomputation under time pressure.

Answer the 3 checkpoints as you read.