Relationship between Marginal Product and Average Product

The marginal product curve crosses the average product curve at the maximum of the average product curve.

Marginal product focuses on the changes between production totals and the quantity of resources. Average product shows output at a specific level of input. The peak of the average product curve is the point at which the marginal product curve and average product curve intersect. For the points below (to the left of) this point, the marginal product of the extra input is higher than the average product. For example, if adding another worker increases output by more than the average product of the total labor force, then the marginal product of the new worker will raise the average product amount. Thus, the average product curve must be below the marginal product curve. Similarly, if the new worker adds less product than the average product amount, the average product curve will be above the marginal product curve (for all points to the right of the point of intersection of the two curves). At the point of intersection, the additional worker produces the same as the average product of the total workforce; there will be no change. The marginal product curve may fall to zero, showing that an additional worker will have no impact on production; for example, if there is no more space left to work in, or if machines are working at 100% capacity and all raw materials have been used up.

The marginal product (MP) curve crosses the average product (AP) curve at the point where the average product curve is at a maximum.