marginal and average product
Total product tells you the size of the pile; these two measures tell you how well you are doing per worker. Average product is the pile divided by the number of workers — output per head. Marginal product is the extra output the latest worker added — what you gained by hiring just one more. Both ask 'is the next, or the typical, worker pulling their weight?', but in slightly different ways.
Take a kitchen. Output goes 0, 10, 22, 30, 35 as you hire the first, second, third and fourth cook. Marginal product is the gap between consecutive totals: the first cook adds 10, the second adds 12, the third adds 8, the fourth adds 5 (MP = 10, 12, 8, 5). Average product is the total divided by the headcount: with three cooks AP = 30 / 3 = 10 each. A neat rule links them: when the marginal product is above the average it pulls the average up; when it is below, it drags the average down — exactly like how scoring above your batting average raises that average. So the marginal product curve always cuts the average product curve at the average's highest point.
Marginal product is the more important of the two, because firms make decisions one step at a time — should I hire one more? The answer turns on whether that worker's marginal product, sold at the market price, brings in more than their wage. And the typical pattern — marginal product first rising (workers specialise and help each other) then falling (they start to crowd the fixed equipment) — is just the law of diminishing returns seen up close. It is the source of the upward-sloping marginal cost curve that drives the whole theory of supply.
Five workers in a bakery produce 100 loaves; a sixth pushes it to 108. The average product is 108 / 6 = 18 loaves per worker, but the marginal product of that sixth worker is only 8 loaves. Because 8 is below the average of 18, hiring the sixth worker pulled the average down.
Marginal = what the last one added; average = the typical one. Marginal pulls average toward itself.
Do not confuse the two: marginal product can be falling while average product is still rising (as long as marginal stays above average). A firm's hiring choices hinge on the marginal figure, not the average — the question is always about the next worker.