Marginal product
Encyclopedia
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.
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
and in particular neoclassical economics
Neoclassical economics
Neoclassical economics is a term variously used for approaches to economics focusing on the determination of prices, outputs, and income distributions in markets through supply and demand, often mediated through a hypothesized maximization of utility by income-constrained individuals and of profits...
, 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
Derivative
In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...
of the production function
Production function
In microeconomics and macroeconomics, a production function is a function that specifies the output of a firm, an industry, or an entire economy for all combinations of inputs...
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
Diminishing returns
In economics, diminishing returns is the decrease in the marginal output of a production process as the amount of a single factor of production is increased, while the amounts of all other factors of production stay constant.The law of diminishing returns In economics, diminishing returns (also...
, 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
Perfect competition
In economic theory, perfect competition describes markets such that no participants are large enough to have the market power to set the price of a homogeneous product. Because the conditions for perfect competition are strict, there are few if any perfectly competitive markets...
, the marginal product of labor
Marginal product of labor
In economics, the marginal product of labor also known as MPL is the change in output that result from employing an added unit of labor. More generally, in defining marginal product, other inputs to production are held constant...
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
Marginal product of capital
Marginal product of capital is the additional output resulting from the use of an additional unit of capital . It equals 1 divided by the Incremental capital-output ratio...
equals its rate of return
Rate of profit
In economics and finance, the profit rate is the relative profitability of an investment project, of a capitalist enterprise, or of the capitalist economy as a whole...
. As was shown in the Cambridge capital controversy
Cambridge capital controversy
The Cambridge capital controversy – sometimes simply called "the capital controversy" – refers to a theoretical and mathematical debate during the 1960s among economists concerning the nature and role of capital goods and the critique of the dominant neoclassical vision of aggregate...
, this proposition about the marginal product of capital cannot generally be sustained in multicommodity models in which capital and consumption goods are distinguished.