In economics and in particular neoclassical economics, the marginal product or marginal physical product of an input (factor of production) is the extra output that can be produced by using one more unit of the input (for instance, the difference in output when a firm's labor usage is increased from five to six units), assuming that the quantities of no other inputs to production change.
The marginal product of a given input can be expressed as:
where is the change in the firm's use of the input (conventionally a one-unit change) and is the change in quantity of output produced. Note that the quantity of the "product" is typically defined ignoring external costs and benefits.
If the output and the input are infinitely divisible, so the marginal "units" are infinitesimal, the marginal product is the mathematical derivative of the production function with respect to that input. Suppose a firm's output Y is given by the production function where K and L are inputs to production (say, capital and labor). Then the marginal product of capital (MPK) and marginal product of labor (MPL) are given by:
In the "law" of diminishing marginal returns, the marginal product of one input is assumed to fall as one considers higher and higher starting points for the quantity of that input. The marginal product of labor is the slope of the total product curve, which is the production function plotted against labor usage for a fixed level of usage of the capital input.
In the neoclassical theory of competitive markets, the marginal product of labor equals the real wage. In aggregate models of perfect competition, in which a single good is produced and that good is used both in consumption and as a capital good, the marginal product of capital equals its rate of return. As was shown in the Cambridge capital controversy, this proposition about the marginal product of capital cannot generally be sustained in multicommodity models in which capital and consumption goods are distinguished.
Famous quotes containing the words marginal and/or product:
“In realms of knowledge, we bequeath our books,
And woe pursue who to a master quotes
The funnier of our witty marginal notes.”
—Philip Larkin (1922–1986)
“Culture is a sham if it is only a sort of Gothic front put on an iron building—like Tower Bridge—or a classical front put on a steel frame—like the Daily Telegraph building in Fleet Street. Culture, if it is to be a real thing and a holy thing, must be the product of what we actually do for a living—not something added, like sugar on a pill.”
—Eric Gill (1882–1940)