Where does the marginal product curve intersect with the average product curve?

In order to better understand the difference between total production and marginal production one needs to focus attention on the concept of diminishing returns and how it applies to production.

The total amount of production by a firm is a function of the levels of input used by the firm. A simple version of this relationship is provided in a table below where the relationship that exists between output for the planned labor use, holds other inputs and technology constant expressed by the ratio:

The table indicates how output matches the planed level of labor use but as more labor is added production increases by smaller and smaller increments. This example depicts that output even decreases at higher levels of labor use. It can be observed output declines from 275 to 270 when the level of labor use increases from 40 to 45 from 7.86 to 6. While average production is between 5 and 10 inputs of labor.

This is a consequence of the law of diminishing returns as expressed by the ratio of marginal production.

According to this law, the MP of a variable input declines as more of it is employed with a given quantity of other fixed inputs. At some point, the ratio of labor to other factors decreases. The firm can add more workers but there’s only so much these workers can do without additional capital i.e., add more space, tools or electricity as more labor alone cannot increase output.

The marginal product (MP) is another useful and important concept. MP is defined as the additional output that results from the use of an additional unit of a variable input, holding other inputs constant. It is measured as the ratio of the change in output total production (TP) to the change in the quantity of labor used. In a graph this can be expressed as: