Production function
Production Function
Production function refers to a functional relationship between physical inputs used and physical output of a commodity produced by a firm.
Ox = f (i1, i2, i3 ………………………………………………… in)
(Where: Ox= Output of commodity x; i1, i2, …. = Inputs needed for production)
Short Run
Short run refers to a period in which output can be changed by changing only variable factors. In the short run, fixed inputs like plant, machinery, building, etc. cannot be changed. It means, production can be raised by increasing variable factors, but till the extent of capacity of fixed factors.
Long Run
Long run refers to a period in which output can be changed by changing all factors of production. Long run is a period, that is long enough for the firm to adjust all its inputs according to change in the conditions. In the long run, firm can change its factory size, switch to new techniques of production, purchase new machinery, etc.
Difference between Short Run and Long Run
| Short run | Long run |
| Short run refers to a period in which output can be changed by changing only variable factors. | Long run refers to a period in which output can be changed by changing all factors of production. |
| There are some fixed and some variable factors in the short run. | All factors are variable in the long run. |
VARIABLE FACTORS AND FIXED FACTORS
There are two types of factors of production namely: (i) Variable Factors; (ii) Fixed Factors.
Variable Factors
- Variable factors refer to those factors, which can be changed in the short run. For example, raw material, casual labour, power, fuel, etc.
- Variable factors vary directly with the level of output. As output increases, requirement for variable factors also rises and vice-versa.
- Variable factors are not required in case of zero output.
Fixed Factors
1. Fixed factors refer to those factors, which cannot be changed in the short run.
For example, plant and machinery, building, land, etc.
2. The quantity of fixed factors remain same in the short run irrespective of level of output,
i.e. they do not change, whether the level of output rises, falls or becomes zero.
Types of Production Function
The distinction between fixed and variable factors helps us to study the two types of production function:
Short Run Production Function :
- Short run production function refers to the effect on output when only one input is changed while keeping other inputs used in production fixed.
- As there is change in one variable input only, the ratio between different inputs tends to change at different levels of output.
- This relationship is explained by ‘Law of Variable Proportions‘ or ‘Returns to a factor’.
Long Run Production Function:
- Long run production function refers to the effect on output when all the inputs used in production are changed simultaneously and in the same proportion.
- As all inputs are variable in the long run, the ratio between different inputs tends to remain the same at different levels of output.
- This relationship is explained by the ‘Law of Returns to Scale’.
Total Product (TP) or Total Physical Product (TPP): Total product refers to the total quantity of output produced by a firm in relation to the variable input employed.
Average Product (AP) or Average Physical Product (APP): Average product refers to output per unit of variable input.
Average Product (AP) =
TP = AP x Units of Variable Input
Marginal Product (MP) or Marginal Physical Product (MPP)
Marginal product refers to addition to total product, when one more unit of variable input is employe
MPn = TPn – TPn-1
TP = ΣMP (Area under the MP curve is TP)
Where MP = Marginal product of nth unit of variable input
TPn = Total product of n units of variable input
TPn-1= Total product of (n -1) units of variable input
MP = ΔTP/ ΔVI
Where TP is Total Product and VI is units of variable input
MP is the rate of change of TP for a given change in variable input.
RETURNS TO A FACTOR
Returns to a factor refers to the increase in the total product (return) when only one input is increased, keeping all other factors fixed.
LAW OF VARIABLE PROPORTIONS
Law of Variable Proportions states that as we increase quantity of only one input keeping all other inputs fixed, total product (TP) initially increases at an increasing rate, then at a decreasing rate and finally falls.
Assumptions of Law of Variable Proportions
- It operates in short run, and factors are classified as variable and fixed factors.
- It is assumed that the factors of production become imperfect substitutes of each other beyond a certain limit.
- The state of technology is assumed to be constant .
- It is assumed that all units of variable factor are equally efficient.
| Variable Input | TP (units) | MP (units) | Phase |
| 1 | 10 | 10 | 1st Phase
(Increasing Returns to a Factor) |
| 2 | 30 | 20 | |
| 3 | 45 | 15 | 2nd Phase
(Diminishing Returns to a Factor) |
| 4 | 52 | 7 | |
| 5 | 52 | 0 | |
| 6 | 48 | – 4 | 3rd (Negative Returns –
Part of Diminishing Returns to a Factor) |
Phase I (Between O to Q) TP increases at an increasing rate and MP also increases (O to P).- Phase II (Between Q to M) TP increases at decreasing rate and MP falls but is positive (P to S). This phase ends when MP becomes zero (at S) and TP reaches its maximum point (at M).
- Phase III (Beyond point M) TP starts decreasing and MP not only falls, but also becomes negative (beyond S).
- Point of Inflexion (Point Q) Point ‘Q’ is known as point of inflexion as curvature of TP curve changes at this point. Till point Q, TP is convex to x axis and beyond point Q, TP becomes concave to x -axis.
According to the Law of Variable Proportions, the changes in TP and MP can be classified into following three Phases:
Phase I: TP rises at increasing rate. MP increases (Increasing Returns to a Factor)
Reasons for Phase I: In the first phase,(till 2nd unit of variable input) every additional variable factor adds more and more to the total output.
[In phase I, TP increases at increasing rate (till point ‘Q’) and MP rises till it reaches its maximum point ‘P’, which marks the end of first phase.]
- Better Utilization of the fixed factor: In the first phase, the supply of the fixed factor (say, land) is too large, whereas variable factors are too few. So, the fixed factor is not fully utilised. When variable factors are increased and combined with fixed factor, then fixed factor is better utilised and output increases at an increasing rate.
- Specialisation of variable factor: When variable factors are increased and combined with the fixed factor, there is greater cooperation and high degree of specialization between different units of the variable factor, as a result efficiency of variable factor increases.
NOTE: Phase II and III together constitute Diminishing Returns to a Factor
Phase II: TP rises at decreasing rate. MP decreases but is positive. (DRF)
Reasons for Phase II : In the second phase (from 2 units to 5 units of variable input), every additional variable factor adds lesser and lesser to the total output.
[In phase II, TP increases at a decreasing rate from Q to M and ends where TP is maximum (point ‘M’) at 52 units and at point ‘S’, when MP is zero.]
- Use beyond optimum combination of factors: Among the different combinations between variable and fixed factor, there is one optimum combination, at which marginal product is maximum. Beyond this combination, the marginal product begins to diminish.
- Over-utilisation of fixed factor: As we keep on increasing the variable factor with the other factors fixed, eventually a point comes when over-utilisation of fixed factor starts giving diminishing returns.
- Imperfect Substitutes: Diminishing returns to a factor occurs because fixed and variable factors are imperfect substitutes of one another. There is a limit to the extent of which one factor of production can be substituted for another. But, beyond the optimum limit, they become imperfect substitutes of one another, which leads to diminishing returns.
Phase III: TP falls. MP falls and turns negative. (DRF – Negative returns to factor)
Reasons for Phase III: In the third phase (after the 5th unit of variable input), the employment of additional variable factor causes TP to decline.
[The phase III starts after point ‘S’ on MP curve and after point ‘M’ on TP curve.]
- Excessive pressure on fixed factors: The negative returns to a factor apply because some factors of production are of fixed nature, which cannot be increased with increase in variable factor in the short run. Hence the per unit availability of fixed input for each variable factor keeps on declining leading to negative MP.
- Decrease in efficiency of variable factor: With continuous increase in variable factor, the advantages of specialization and division of labour start diminishing. It results in inefficiencies of variable factor, which is another reason for the negative returns to eventually set in.
Phase of operation by a rational producer
A rational producer will always seek to operate in Phase II of Law of Variable Proportions.
- In Phase I, employment of every additional unit of variable factor gives more and more output i.e. marginal product increases. It means, there is scope for more profits, if production is increased with more units of variable factor.
- In Phase III, marginal product of each variable factor is negative. So, this phase is ruled out on the ground of technical inefficiency and a rational producer will never produce in the third phase.
LAW OF DIMINISHING RETURNS
RelationsLaw of diminishing returns states that when more and more units of a variable input are employed along with fixed inputs, then marginal product of the variable factor must fall.
It includes Phase II and Phase III of Law of Variable Proportions
The difference between Law of Variable Proportion and Law of Diminishing Returns is that the Law of Variable Proportions includes Phase I of increasing returns to factor which is not included in the latter.
hip between AP and MP
- When MP is greater than AP, AP rises.
- When MP is equal to AP, AP is constant and maximum.
- When MP is less than AP, AP falls.
At what point does the MP curve cut AP curve?
The MP curve cuts AP curve from above at its maximum point. This is because as long as MP is greater than AP, AP increases.
Similarly, when MP is less than AP, AP falls. It, therefore, follows that MP curve cuts AP curve from above at its maximum point where MP is equal to AP and AP is constant and maximum.
Relationship between TP and MP
Marginal products (MP) are additions to total product (TP), therefore, at any level of employment of an input, TP is the sum of MPs of all units of that input, i.e., TP = ΣMP.
- When MP increases , TP increases at an increasing rate.
- When MP decreases but remains positive , TP increases at a decreasing rate.
- When MP becomes zero, TP is maximum.
- When MP falls and becomes negative, TP also falls.