Marginal product describes how total product changes as a variable input changes, so it corresponds to the slope of the production relationship. With discrete observations, firms compare the change in output with the change in input quantity. In a production function, the same relationship can be represented mathematically by the relevant partial derivative.
Marginal product may decline because additional units of a variable input must operate alongside fixed resources. As the variable input grows while those resources remain unchanged, each added unit can contribute less additional output than the previous one. This pattern is the law of diminishing marginal returns and is especially relevant to short-run production decisions.
The relevant variable input can be labor, machinery, or raw materials, so marginal product evaluates the additional output associated with one more unit of whichever resource is being examined. Comparing these measures helps a firm assess where an additional resource may contribute most to production, while recognizing that the other inputs remain held constant in each analysis.
A calculation requires two observations of input quantity and the corresponding total-product levels. Subtract the earlier output from the later output, then divide that change by the change in the variable input. This procedure works with measured production data and identifies the additional output associated with the input increase without changing the other inputs.
Firms can use marginal product to evaluate whether additional workers, machinery, or raw materials are contributing meaningful increases in output. Comparing the additional output associated with alternative resources supports resource-allocation and hiring decisions. The analysis also reveals when adding more of a variable input produces smaller gains because fixed resources limit its contribution.
In the short run, some production resources remain fixed while a firm changes a variable input. If the marginal product of that input declines, each additional unit contributes less output under those fixed conditions. This production pattern helps explain why short-run cost behavior is connected to the productivity of variable resources.