Total Product, Average Product, Marginal Products, Law of Variable Proportions

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Total Product, Average Product and Marginal Products in Production Function  

Productivity of an input is generally measured in terms of total, average and marginal products.

Total Product (TP)

The total quantity output produced by

A firm or an industry makes total quantity output by making various input units such as labour, materials, machine etc.

It is the sum of all successive marginal products of that input.

It can be found by multiplying the average product by the units of input.

TP is expressed as:

TP_L = AP_L × L

Where:

TP_L = total product

AP_L = average product

L = labour input

Similarly, we can calculate the total product of capital input.

 

Average Product (AP)

Average product is the per unit product of an input.

It can be calculated by dividing the total product of an input by the corresponding unit of labour input.

AP is expressed as:

AP_L = TP_L ÷ L

Where:

AP_L = average product

TP_L = total product

L = labour input

In the same way, the average physical product of capital is AP_K = TP_L ÷ C

 

Marginal Product (MP)

The additional output produced by a firm or an industry by using one more unit of an input is called marginal product.

Marginal product of an input is the addition to total output or product resulting from the addition of one unit of input while holding all other inputs constant.

Marginal product of labour is represented as:

MP_L = ΔTP ÷ ΔL      

Where:

Δ = change

MP_L = marginal product

L = labour

 

In other worlds, marginal physical product is the change in total product of an input in response to the change in input holding other inputs constant.

Alternatively, it is also expressed as:

MP_L = TP_n – TP_n–1

Where:

n = n^th unit of the input

MP_L = marginal product

TP_n = total product

Marginal product of capital can be calculated in the similar way.

 

The natural and relationship between total product (TP), average product (AP) and marginal product (MP) is further illustrated in table labour is assumed as the variable factor.

Total, Average and Marginal Product of Labour (L)

L	TP	MP = ΔTP/ΔL	AP = TP/L
0	0	–	–
1	5	5 – 0 = 5	5
2	16	16 – 5 = 11	8
3	24	24 – 16 = 8	8
4	28	28 – 24 = 4	7
5	28	28 – 28 = 0	5.6
6	24	24 – 28 = –4	4

 

In table, the first column represents the units of labour which is variable factor.

Likewise, the second, third and fourth columns represent TP, MP and AP respectively.

 

Along with increase in units of variable input (labour), total product initially increases at increasing rate, then at decreasing rate and become maximum corresponding to 5^th unit of labour.

Beyond this, total product starts to fall.

 

Similarly, marginal and average products also increase in the beginning, reaches to the maximum and start to fall.

When total product reaches to the maximum, marginal product become zero.

The concept of TP, AP and MP can also be shown graphically.

The concept of TP, AP and MP can also be shown graphically and this is done in figure in explaining the law of variable proportions or the law of diminishing marginal product.

 

We can draw figures that show the TP, AP and MP curves using the available data, for example the data given in table.

We explain the geometrical shapes of the TP, AP and MP curves and their relationships in explaining the law of variable proportions or the law of diminishing marginal returns.

 

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Law of Variable Proportions

The law of variable proportion is also known as the short run production.

The law of variable proportion is one of the economic laws used in the field of production.

It explains how output changes when one factor of production is made variable keeping the quantities of other factors constant.

In this law, output changes by varying the amount of the variable factor only.

As the producer increases the amount of variable factor, then the factor proportions vary.

The change in level of output with variable proportion of inputs follows a rule and this rule in economics is called the law of variable proportion.

As the amount of fixed factor (capital) is fixed, then fixed factor and variable factor (Labour) can be combined in varying proportions.

So, this law is called law of variable proportions.

 

 

Statement of the Law of Variable Proportions

If we increase the variable factor (labour) keeping the other factors (capital) constant, then the total product initially increase at increasing rate.

Then it increases at decreasing rate, becomes maximum and ultimately total product (TP) begins to fall.

Likewise, average product (AP) and marginal product (MP) also increase in the beginning become maximum then start to decrease. 

Let us consider few definitions of the law of variable proportions given by renowned economists.

 

According to Alfred Marshall, “An increase in the capital and labour applied in the cultivation of land causes in general a less than the proportionate increase in the amount of the product raised unless it happens to coincide with an improvement in an art of agriculture.”

 

Thus, in the words of Marshall, the law can be found in agriculture production.

If we keep the quantity of land fixed and goes on increasing the quantity of labour, eventually the marginal product declines.

 

According to P.A. Samuelson, “An increase in some inputs relative to other fixed inputs will, in a given state of technology, cause output to increase; but after a point the extra output resulting from the same additions of extra inputs will become less and less.”

 

According to George Joseph Stigler, “As equal increments of one input are added, the inputs of other productive services being held constant, beyond a certain point the resulting increments of product will decrease that is, the marginal products will diminish.”

 

From the above definitions, it is clear that the law of variable proportions or the law of diminishing returns refers to the behaviour of output as the quantity of one factor is increased keeping the quantity of other factors fixed and further it state that the marginal and average product will ultimately decline.

 

Since, the amount of capital is fixed and the amount of labour is variable, capital and labor can be combined in varying proportions.

So, the production function or this law is also known as the law of variable proportions.

 

Suppose there are two factors used in a production process: Capital (C) and Labour (L).

In short run, labour only can be changed and capital remains fixed.

If we examine this input output relationship it is known as short run production function.

If L is only increased keeping K constant, the proportion or ratio of K and L varies as shown in table.

 

Changing Capital Labour Ratio

Capital (C) = >	10	10	10	10
Labour (L) = >	1	2	3	4
Ratio: C ÷ L	10 ÷ 1 = 10	10 ÷ 2 = 5	10 ÷ 3 = 3.33	10 ÷ 4 = 2.5

 

If the proportion of input varies, output also varies.

It is explained in the law of variable proportion.

 

The law states that as successive units of variable input (say labour) are added to a fixed input (say capital) then the marginal productivity of the variable input eventually declines.

In other words, if additional labour is applied to a given amount of capital, then eventually output will rise less than the proportion of the increase in the labour.

Since the marginal productivity of labour declines as the amount of labour employment increases the law is known as the law of diminishing marginal productivity or the law of diminishing returns.

 

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Assumptions of Law of Variable Proportions

The operation of the law is based on the following assumptions:

At least one factors of production should be fixed

For the operation of the law, it is necessary to hold at least one factor constant or fixed.

If the capital increases, it will cause to increase in the productivity of variable input labour instead of decline.

 

Inputs are used in varying proportion

In short run production, some inputs are fixed while some are variable.

For example, labour is variable and capital is fixed inputs.

In the process of production, when labour is increased keeping capital constant, inputs are used in varying proportion.

 

The technology is constant

The operation of the law of variable proportion or diminishing marginal returns requires constant production technology.

It is assumed that the production technology does not change due to short time period.

Changes are made in the variable inputs.

 

Short run production

Law of variable proportions is based on short run.

 

Variable inputs are homogeneous

It implies that each unit of the variable input is identical.

Here, as we have assumed that labour is variable input, all the labour used in the production are equally skillful.

 

Explanation of the Law of Variable Proportions

The law of variable proportion is illustrated in table with numerical data but the data do not relate any particular firm (i.e. the data are hypothetical).

The data are reproduced from table given in previous section.

Variable factor is labour input (L).

 

In table the numbers in column 2 indicate the total product (TP) which results by combining each level of labour input in column 1 with an assumed fixed amount of capital.

Column 3 shows the marginal product (MP) of labour which is the change in total output in response to one unit change in labour input, the variable factor.

 

The Law of Variable Proportions

L	TP	MP = ΔTP/ΔL	AP = TP ÷ L
0	0	–	–
1	5	5 – 0 = 5	5
2	16	16 – 5 = 11	8
3	24	24 – 16 = 8	8
4	28	28 – 24 = 4	7
5	28	28 – 28 = 0	5.6
6	24	24 – 28 = –4	4

 

With no labour inputs, total product is zero; without the active aid of human labour any mobilizes other factors production.

The first and second unit of labour reflects increasing returns, their marginal products being 5 and 11 units respectively.

But then, beginning with the third labour, marginal product-the increase in total product-diminishes continuously and actually becomes zero with the fifth unit of labour and negative with the sixth.

Average product or output per labour is shown in column 4.

It is calculated simply by dividing total product (column 2) by the corresponding number of labour (column 1).

 

The law of variable proportion or the law of diminishing marginal product is illustrated in figure.

 

In the figure, one of the important points to note is that as the marginal product of a factor (e.g. labour in our present case) is defined as the change in total product resulting from the change in the factor/input by one unit, the MPL is recorded halfway between two successive units of labour employed.

The MPL is marginal product curve of labour, which reflects the change in total product associated with each successive units of labour.

Geometrically, the marginal product is the slop of the total product curve MP_L = ΔTP/ΔL.

Note that, so long as marginal product is positive total product is increasing.

And when marginal product is zero, total product is at its peak.

Finally when marginal product becomes negative, total product is necessarily declining.

Increasing returns are reflected in a rising average physical product curve; diminishing returns, in a falling marginal physical product.

 

  

Average product also reflects the same general increasing-maximum-diminishing relationship between variable inputs of labour and output as shown by marginal product.

But note this technical point is concerned to the relationship between marginal product and average product: where marginal product exceeds average product, the latter must rise.

And wherever marginal product is less than average product, then average product must be declining.

It follows that marginal product intersects average product where the latter is at a maximum.

 

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