PRODUCTION FUNCTION: RETURNS TO A FACTOR AND RETURNS TO SCALE

1.       Production requires use of certain inputs like land, labour, capital, raw materials, etc. these inputs are classified as:

(i)                  Factor inputs and

(ii)                Non-factor inputs

Factor inputs include factors of production such as land, labour, capital and enterprise, whereas non-factor inputs include raw material and fuels. These inputs are further classified as

(i)                  Fixed inputs and

(ii)                Variable inputs

A fixed input is one whose supply cannot be increased in the short run such as, land whereas a variable input is one whose supply can be increased in the short run, such as labour.

2.       A production function expresses the technical relationship between inputs and output of a firm. It tells the maximum quantity of output that can be produced with any given quantities of inputs. If there are two factor inputs : labour (l) and capital (k), then the production function can be written as

Q= f(l,k) where Q is the quantity of output and l,k the units of labour and capital.

3.       There are mainly three concepts relating to production.

(i)                  Total product or total physical product, denoted by TPP;

(ii)                Average product or average physical product, denoted by APP and

(iii)               Marginal product or marginal physical product, denoted by MPP.

4.       Total physical product (TPP) refers to the total output of a commodity at a particular level of employment of an input (say labour) when the employment of all other inputs ( say labour or capital) is unchanged.

5.       Average physical product (APP) is obtained by dividing the total physical product (TPP) by the number of units of variable inputs, i.e, APP= TPP/L where L is labour input. The APP curve is generally inverted U-shape.

6.       Marginal physical product (MPP) is defined as an addition made to TPP by employing an additional unit of a variable input, keeping the other inputs as unchanged, i.e., MPP=TPP_n- TPP_n-1 or MPP= ΔTPP/ΔL. The MPP curve is generally inverted U-shape.

7.       Total physical product (TPP) can also be derived from the MMP.TPP is the sum total of marginal physical product corresponding to various units of the varaible inputs,i.e., TPP=MPP₁+MPP₂+……….+MPP_n=∑MPP.TPP can also be obtained as: TPP=APP x L.

8.       The total physical product (TPP) changes with the change in the marginal physical product (MMP) of an input.

9.       Ther is a relationship between TPP and MPP:

(i)                  When MPP prises, TPP rises at an increasing rate,

(ii)                When MPP falls but positive, TPP rises at decreasing rate

(iii)               When MPP is zero, TPP is maximum and

(iv)              When MPP falls but negative, TPP falls.

10.   There is also a relationship between APP and MPP:

(i)                  When APP rises, MPP>APP

(ii)                When APP is maximum, APP=MPP and

(iii)               When APP declines, MPP

11.   Laws of returns are studied under two heads:

(i)                  Law of variable proportions and

(ii)                Law of returns to scale.

12.   Law of variable proportions states that if we go on using more units of a variable factor (labour) with a fixed factor (land), the total output initially increases at an increasing at an increasing rate but beyond a certain point, it increases at a diminishing rate and finally it falls.

13.   Law of variable proportions can also be stated in terms of the behaviour of marginal product. The law states that if we go on using more and more units of a variable factor (labour) with a fixed factor (land), the marginal product initially increases but beyond a certain point, it starts diminishing but remains positive and finally it becomes negative.

14.   Ther are generally three stages of law of variable proportions; (i) stage 1 (ii) stage 2 (iii) satge 3.

fig.1 law of variable proportions

15.   In phase 1, TPP increases at an increasing rate, MPP rises. In this phase, we get increasing returns to a variable factor because greater use of the variable factor makes it possible to utilise the fixed indivisible factors more fully and also to introduce a greater degree of division of labour. In phase 2, TPP increases at decreasing rate. It means MPP starts failing but remains positive. In the second phase, we get diminishing returns to a factor because in this stage the proportion between the variable factor and the fixed factor has crossed the optimum proportion between them and a variable factor such as labour has less and less fixed factor to work. In phase 3, TPP starts failing, MPP not only continues to fall but also becomes negative. Phase 3 is also called phase of negative returns in the third phase, the variable factor becomes too much relative to fixed factor which obstructs the production process and as a result there is a fall in total product.

16.   Law of diminishing returns to a factor states that as we use more and more units of labour with fixed quantity of land, the total production increases at a diminishing rate, i.e., marginal product is diminishing.

17.   Returns to scale to the behaiviour of output to change in all the factors of production in the same proportion. There are three phases/stages of returns to scale (i) increasing returns to scale, (ii) constant returns to scale and (iii) diminishing returns to scale.

18.   Increasing returns to scale means that a given percentage increase in all factor inputs causes proportionately greater increase in output. They are due to internal economics of scale.

19.   constant returns to scale means that a given percentage increase in all factors inputs causes equal percentage increase in output.

20.   Diminishing returns to scale means that a given percentage increase in all factor inputs causes proportionately less increase in output. They are due to internal dis economics of scale.

21.   The cobb-douglas production function is given by Q=AK^αL^β. It is to be noted that the type of returns to scale of this function will depend on the magnitude of α+β. If α+β=1, the production function exhibits constant returns to scale. If α+β>1, it exhibits increasing returns to scale and if α+β<1 diminishing="" exhibits="" it="" o:p="" returns="" scale.="" to="">

22.   There is a difference between returns to factor and returns to scale:

(i)                  Returns to factor apply when one factor alone is variable and other factors remain fixed, while returns to scale apply when all factors of production are variable,

(ii)                Returns to factor describes the behaviour of output to change in one factor alone whereas returns to scale describes the behaivour of output to change in all the factors in the same proportions,

(iii)               Returns to factor relates to short period whereas returns to scale is concerned with long period.

Also read:

What is demand?

Price elasticity of demand