The law of variable proportions

The law of variable proportions (the law of diminishing marginal product): as more and more of a variable input is added to a fixed input, its marginal product first rises, and after some point falls.

Why? Think of a fixed plot of land. With one worker, there is too much land for him to farm well; adding workers improves the proportion of labour to land, so each extra worker adds more than the last. But after a point, the land becomes crowded: each extra worker has less land to work with, and adds less and less.

So the TP curve rises, first faster and then more slowly; the MP and AP curves are inverse-U shaped (rising, then falling).

Teachers often split the law into three stages:

• Stage 1: MP rises, so TP rises faster and faster (increasing returns to the factor). The point where MP is at its peak, and TP stops speeding up, is the point of inflexion.
• Stage 2: MP is falling but still positive, so TP still rises, more slowly, until it reaches its maximum where MP = 0.
• Stage 3: MP is negative, so TP falls: extra workers only get in each other's way.

A sensible, profit-seeking producer works in stage 2. In stage 3 she would be paying workers who reduce output. Note that MP can become negative, but AP never does, because TP itself stays positive.

MP and AP are linked like a new mark and your average mark:

• while MP > AP, each new worker pulls the average up, so AP rises;
• when MP < AP, AP falls.

So the MP curve cuts the AP curve from above at AP's maximum. In the table of the last lesson, at 3 workers MP (16) is above AP (12), so AP is still rising; the 4th worker's MP is 8, below AP, so AP falls to 11.