Is the last unit of input increases total product we know that marginal product is?

Change in output resulting from employing one more unit of a particular input

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] as:

M P = Δ Y Δ X {\displaystyle MP={\frac {\Delta Y}{\Delta X}}}

where Δ X {\displaystyle \Delta X}

Δ Y {\displaystyle \Delta Y}

Y {\displaystyle Y}

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, respectively). Then the marginal product of capital (MPK) and marginal product of labor (MPL) are given by:

M P K = ∂ F ∂ K {\displaystyle MPK={\frac {\partial F}{\partial K}}}

M P L = ∂ 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.[3]

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

References

1. ^ Brewer, Anthony (2010). The Making of the Classical Theory of Economic Growth. Routledge. ISBN 978-0415486200.
2. ^ Mukherjee, Sampat; Mukherjee, Mallinath; Ghose, Amitava (2003). Microeconomics. New Delhi: Prentice-Hall of India. ISBN 81-203-2318-1.
3. ^ Kurz, Heinz D. and Neri Salvadori (1995) Theory of Production: A Long-Period Analysis. Cambridge University Press.

• 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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The law of diminishing marginal productivity is an economic principle usually considered by managers in productivity management. Generally, it states that advantages gained from slight improvement on the input side of the production equation will only advance marginally per unit and may level off or even decrease after a specific point. 

• Diminishing marginal productivity typically occurs when advantageous changes are made to input variables affecting total productivity.
• The law of diminishing marginal productivity states that when an advantage is gained in a factor of production, the productivity gained from each subsequent unit produced will only increase marginally from one unit to the next.
• Production managers consider the law of diminishing marginal productivity when improving variable inputs for increased production and profitability.

The law of diminishing marginal productivity involves marginal increases in production return per unit produced. It can also be known as the law of diminishing marginal product or the law of diminishing marginal return. In general, it aligns with most economic theories using marginal analysis. Marginal increases are commonly found in economics, showing a diminishing rate of satisfaction or gain obtained from additional units of consumption or production.

The law of diminishing marginal productivity suggests that managers find a marginally diminishing rate of production return per unit produced after making advantageous adjustments to inputs driving production. When mathematically graphed this creates a concave chart showing total production return gained from aggregate unit production gradually increasing until leveling off and potentially starting to fall.

Different than some other economic laws, the law of diminishing marginal productivity involves marginal product calculations that can usually be relatively easy to quantify. Companies may choose to alter various inputs in the factors of production for various reasons, many of which are focused on costs. In some situations, it may be more cost-efficient to alter the inputs of one variable while keeping others constant. However, in practice, all changes to input variables require close analysis. The law of diminishing marginal productivity says that these changes to inputs will have a marginally positive effect on outputs. Thus, each additional unit produced will report a marginally smaller production return than the unit before it as production goes on.

The law of diminishing marginal productivity is also known as the law of diminishing marginal returns.

Marginal productivity or marginal product refers to the extra output, return, or profit yielded per unit by advantages from production inputs. Inputs can include things like labor and raw materials. The law of diminishing marginal returns states that when an advantage is gained in a factor of production, the marginal productivity will typically diminish as production increases. This means that the cost advantage usually diminishes for each additional unit of output produced.

In its most simplified form, diminishing marginal productivity is typically identified when a single input variable presents a decrease in input cost. A decrease in the labor costs involved with manufacturing a car, for example, would lead to marginal improvements in profitability per car. However, the law of diminishing marginal productivity suggests that for every unit of production, managers will experience a diminishing productivity improvement. This usually translates to a diminishing level of profitability per car.

Diminishing marginal productivity can also involve a benefit threshold being exceeded. For example, consider a farmer using fertilizer as an input in the process for growing corn. Each unit of added fertilizer will only increase production return marginally up to a threshold. At the threshold level, the added fertilizer does not improve production and may harm production.

In another scenario consider a business with a high level of customer traffic during certain hours. The business could increase the number of workers available to help customers but at a certain threshold, the addition of workers will not improve total sales and can even cause a decrease in sales.

Economies of scale can be studied in conjunction with the law of diminishing marginal productivity. Economies of scale show that a company can usually increase their profit per unit of production when they produce goods in mass quantities. Mass production involves several important factors of production like labor, electricity, equipment usage, and more. When these factors are adjusted, economies of scale still allow a company to produce goods at a lower relative per unit cost. However, adjusting production inputs advantageously will usually result in diminishing marginal productivity because each advantageous adjustment can only offer so much of a benefit. Economic theory suggests that the benefit obtained is not constant per additional units produced but rather diminishes.

Diminishing marginal productivity can also be associated with diseconomies of scale. Diminishing marginal productivity can potentially lead to a loss of profit after breaching a threshold. If diseconomies of scale occur, companies don’t see a cost improvement per unit at all with production increases. Instead, there is no return gained for units produced and losses can mount as more units are produced.