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Average Physical Product (APP), Marginal Physical Product (MPP)

In economics and in particular neoclassical economics, the marginal product or marginal physical productivity of an input (factor of production) is the change in output resulting from employing one more unit of a particular input (for instance, the change in output when a firm’s labor is increased from five to six units), assuming that the quantities of other inputs are kept constant.[1]

The marginal product of a given input can be expressed[2]

MP=ΔYΔX{\displaystyle MP={\frac {\Delta Y}{\Delta X}}}

where ΔX{\displaystyle \Delta X} is the change in the firm’s use of the input (conventionally a one-unit change) and ΔY{\displaystyle \Delta Y} is the change in quantity of output produced (resulting from the change in the input). Note that the quantity Y{\displaystyle Y} 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:

Y=F(K,L){\displaystyle Y=F(K,L)}

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:

MPK=∂F∂K{\displaystyle MPK={\frac {\partial F}{\partial K}}}MPL=∂F∂L{\displaystyle MPL={\frac {\partial F}{\partial L}}}

In the “law” of diminishing marginal returns, the marginal product initially increases when more of an input (say labor) is employed, keeping the other input (say capital) constant. Here, labor is the variable input and capital is the fixed input (in a hypothetical two-inputs model). As more and more of variable input (labor) is employed, marginal product starts to fall. Finally, after a certain point, the marginal product becomes negative, implying that the additional unit of labor has decreased the output, rather than increasing it. The reason behind this is the diminishing marginal productivity of labor.

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 multi-commodity models in which capital and consumption goods are distinguished.

Relationship of marginal product (MPP) with the total product (TPP)

The relationship can be explained in three phases-
(1) Initially, as the quantity of variable input is increased, TPP rises at an increasing rate. In this phase, MPP also rises.
(2) As more and more quantities of the variable inputs are employed, TPP increases at a diminishing rate. In this phase, MPP starts to fall.
(3) When the TPP reaches its maximum, MPP is zero. Beyond this point, TPP starts to fall and MPP becomes negative.

See also

Marginal product of labor
Marginal product of capital
Marginal revenue productivity theory of wages
Marginal cost
Production theory
Average product
Cost of production
Shadow price


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^ Mukherjee, Sampat; Mukherjee, Mallinath; Ghose, Amitava (2003). Microeconomics. New Delhi: Prentice-Hall of India. ISBN 81-203-2318-1.

Beck, Bernhard (2008). Volkswirtschaft verstehen. ISBN 9783728132079.
Rothbard, Murray N. (1995). Classical Economics: An Austrian Perspective on the History of Economic Thought Volume II (PDF). Auburn, Alabama: Ludwig von Mises Institute. ISBN 0-945466-48-X.
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Marginal Revenue Product (MRP) Definition

Marginal Revenue Product (MRP) Definition – The marginal revenue product is calculated by multiplying the marginal physical product (MPP) of the resource by the marginal revenue (MR) generated. The MRP assumes that the expenditures on other factors remain unchanged and helps determine the optimal level of a resource.the marginal product of labor (MPL) is the change in output that results from employing an added unit of labor. It is a feature of the production function, and depends on the amounts of physical capital and labor already in use…Marginal physical product, usually abbreviated MPP, is found by dividing the change in total physical product by the change in the variable input. What is the marginal product examples? Definition. The term "marginal productivity" refers to the extra output gained by adding one unit of labor; all other…

the marginal physical productivity of labour is defined as – – If the marginal physical product (MPP) is continuously decreasing, then the value of marginal cost will increase continuously…Marginal product is any input in the production process is the increase in the quantity of output obtained from on additional unit of the input. Average product is the output produced when one more unit of the variable factor is employed The relationship is state as: If labour's marginal product…Marginal cost (MC) has a very clear relationship with marginal physical product (MP). Consider only labor (the same relationships will exist for any variable input in the short run, since the marginal cost will be equated across variable inputs), where ^ = "change," Q = physical output, w = wage, L…

the marginal physical productivity of labour is defined as -

What is the formula for marginal physical product? | AnswersDrive – The marginal physical product of the second worker is the difference between the total output corresponding to the second worker and the total TABLE 4.2: APP L and MPP L EXERCISE Units of capital Number of workers Output Average Physical Product of Labor Marginal Physical Product of…Marginal Physical Product: This is another term for marginal product which serves to emphasize that production is measured in physical units rather than The proper economic interpretation of marginal revenue product is the contribution of the last unit of variable input to total revenue.The marginal revenue product is the value of marginal physical product, and you calculate it by multiplying marginal physical product times the unit price of the pair of jeans.

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