Final answer:
Geometrically, the marginal product is the slope of the total product curve at any given point. It is calculated as the change in total product divided by the change in labor and illustrates the Law of Diminishing Marginal Product, where initial increases in labor can lead to increased output, but beyond a certain point, additional labor contributes to less output.
Step-by-step explanation:
Geometrically, the marginal product at any point is the slope of the total product curve at that point. Mathematically, this is calculated as the change in total product (ΔTP) divided by the change in labor (ΔL). To illustrate with an example, if initially zero workers produce no output, and then one worker can produce four units of output, the marginal product of the first worker is four units per labor input. If another worker is added and the total output increases by six units, the marginal product of the second worker would be six units.
This change in production output, as more units of labor are utilized, demonstrates the concept known as the Law of Diminishing Marginal Product. Initially, the marginal product may increase with additional labor due to more efficient use of capital, but eventually, the addition of further labor may lead to a decreasing marginal product, indicating that each subsequent worker is contributing less to output than the previous one. This phenomenon occurs due to the fixed capital that cannot be proportionally increased with the labor.