7 – Laws of Production

Introduction

In the short run, the law of diminishing returns states that as more units of a variable input (such as labour or raw materials) are added to fixed amounts of land and capital, the change in total output will rise at first and then fall. When the marginal product of labour begins to fall, this is referred to as diminishing returns to labour. This means that total output will continue to rise, but at a slower rate as more workers are hired. In the long run, all production factors are variable. Returns to scale refers to how a business’s output responds to a change in factor inputs.

7.1 Factor’s Law of Diminishing Returns (Law of Variable Proportions)

If a firm’s inputs are fixed and only the number of labour services used varies, then any decrease or increase in output is achieved through changes in the number of labour services used. When the firm only changes the amount of labour services, the proportion between the fixed and variable inputs changes. As the firm changes this proportion by changing the amount of labour, it encounters the law of variable proportions, also known as diminishing marginal returns. This law states that as more of the factor input is used while all other input quantities remain constant, a point is reached where additional quantities of varying input produce diminishing marginal contributions to the total product.

Production Function with One Variable Input

Number of Labour Units (L) (1)	Total Product of Labour (TPL) (2)	Average Product of Labour (APL) (3 = 1 + 2)	Marginal Product of Labour (MPL) (4)
1	100	100	–
2	210	105	110
3	330	110	120
4	430	107.5	100
5	520	104	90
6	600	100	80
7	670	95.7	70
8	720	90	50
9	750	83.3	30
10	760	76	10

The MP begins to fall before the AP. The reason for this is that the AP attributes the increase in TP equally to all units of the variable factor, whereas the MP, by definition, attributes the increase in TP to the variable factor’s marginal unit.

If the MP exceeds the AP, the AP rises; if the MP is less than the AP, the AP falls. If the batsman’s next (or marginal) score is higher than his average score, his average score rises; if his next (or marginal) score is lower than his average score, his average score falls.

This implies that when the MP equals the AP, the AP is at its maximum. The reason for this is that when AP increases, MP is above it, pulling it up; when AP is at its maximum and constant, AP equals MP; and when AP decreases, MP is below it, pulling it down.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7.1.1 Three Production Stages

The total and marginal product curves can be used to visualise diminishing returns to a factor. The TPP curve in the above figure rises at an increasing rate in stage I and then at a decreasing rate in stage II. The TPP remains constant at stage II. Thus, until X units of labour are employed, total output increases more than proportionately; between X and Y units of labour used, total output increases less than proportionately with each additional unit of labour. When the number of labour units exceeds level Y, total output begins to fall. When TPP rises at an increasing rate, the MPP and APP curves rise; when TPP rises at a decreasing rate, the MPP and APP curves fall. MPP becomes zero at Y, where TPP becomes constant, and additional labour beyond Y makes MPP negative.

No company will choose to operate in Stage I or Stage III. In Stage I, the marginal physical product is increasing, which means that each additional unit of the variable factor contributes to output more than previous units of the factor; it is thus profitable for the firm to continue increasing its use of labour. In Stage III, the marginal contribution to the output of each additional unit of labour is negative; therefore, using any additional labour is not recommended. Even if the cost of labour is zero, moving into Stage III is still unprofitable. Thus, in a competitive situation, Stage II is the only important range for a rational firm. However, the precise number of labour units hired can be determined only when wage rate data is available.

7.1.2 Optimal Use of Variable Input

The company must determine how much labour it should use to maximise profits. The firm should hire an additional unit of labour as long as the additional revenue generated from the sale of the output produced exceeds the additional cost of hiring the unit of labour, i.e. until the extra revenue equals the extra cost.

Thus, if an additional unit of labour generates Rs. 300 in extra revenue while costing an extra Rs. 200, the firm will benefit from hiring this unit of labour as its total profit rises. This is an example of the general optimization principle in action.

7.2 Returns to Scale (Law of Returns to Scale)

If all inputs are changed at the same time (possible only in the long run), and assume they are increased proportionately, the concept of returns to scale must be used to understand output behaviour. When all factors of production are changed in the same direction and proportion, the output behaviour is studied.

In the long run, increasing the ‘scale of operations can increase output. When we say “increase the scale of operations,” we mean “increase all factors at the same time and in the same proportion.” In a factory, for example, the scale of operations can be increased in the long run by doubling the labour and capital inputs. The laws that govern the scale of operation are known as the laws of scale returns.

The laws of returns to scale always refer to the long run because all production factors are variable only in the long run. In other words, changing all of the factors of production is only possible in the long run. Therefore, the laws of returns to scale refer to a future time when changes in output result from increasing all inputs at the same time and in the same proportion.

Scale returns are classified as follows:

1. Increasing Returns to Scale (IRS): When output increases more than proportionally to all input increases.

2. Constant Returns to Scale (CRS) states that if all inputs increase by a certain percentage, the output will also increase by that same percentage.

3. Decreased Returns to Scale (DRS): When an increase in output is less than proportional to an increase in all inputs.

For example, if all production factors are doubled and output increases by more than two times, the situation is one of increasing returns to scale. Conversely, if output does not double despite a 100% increase in input factors, we have diminishing returns to scale.

The general production function is expressed as $Q=f(L,K)$. When both land (K) and labour (L) are multiplied by a factor $ℎ$

h and the resulting output Q increases accordingly, the production function becomes $Q=f(hL,hK)$. The nature of returns to scale—whether constant, increasing, or decreasing—depends on whether $ℎ$

h is equal to, greater than, or less than 1.

For instance, if all inputs are doubled, there are constant returns to scale; if output more than doubles, there are increasing returns to scale; and if output is less than double, there are decreasing returns to scale. This is illustrated when the firm increases its inputs from 3 to 6 units (K, L), resulting in either double output (point B), more than double output (point C), or less than double output (point D), as depicted in the accompanying figure.

Returns to Scale

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Increasing returns to scale occur as the scale of operation increases, allowing for greater division of labour and specialisation, as well as the use of more specialised and productive machinery. Decreasing returns to scale occur primarily because managing the firm becomes more difficult as the firm’s scale of operation increases. In the real world, the forces of increasing and decreasing returns to scale frequently coexist, with the former usually outweighing the latter at low levels of output and the reverse occurring at very high levels of output.

When all of the factors of production are increased in a specific proportion and output increases in the same proportion, the production function is said to exhibit CRS. Thus, if labour and capital are increased by 10% while output increases by 10%, the production function is CRS.

 

 

 

 

 

 

 

 

 

 

The figure shows that to produce X units of output, L units of labour and K units of capital are required (point a). If labour and capital are now doubled (as is possible in the long run), so that there are 2L units of labour and 2K units of capital, output is exactly doubled, equalling 2X. (point b). Similarly, trebling the input results in trebling the output, and so on.

If all of the production factors are increased in a specific proportion and output increases by more than that proportion, the production function is said to exhibit IRS. For example, in many industrial processes, doubling all inputs allows factories to run more efficiently and effectively, effectively more than doubling output. Figure depicts this. L units of labour and K units of output are required to produce X units of output. When labour is doubled to 2L units and capital is doubled to 2K units, output exceeds 2X. (Point c lies on a higher isoquant than point b).

 

 

 

 

 

 

 

 

 

 

 

 

The production function is said to exhibit DRS if the factors of production are increased in a specific proportion and the output increases by less than that proportion. For example, if capital and labour are increased by 10% but output increases by less than 10%, the production function is said to have decreasing returns to scale.

The figure below shows that to produce X units of output, L units of labour and K units of capital are required. When the input is doubled, the output increases by less than twice its original level. For example, if the inputs are 2L and 2K, the output level ‘a’ is reached, which is lower than the one displaying 2X.