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04_PRODUCTION FUNCTION (Returns to Factor) class 12



It refers to the technological relationship between output and various combinations of inputs. It is written as : Q = f(F1, F2, F3 …. Fn)

Where         Q = output

f = function of

F1, F2, F3 …. Fn are the different factors.



Production function can be explained in 2 difference periods.

  1. Short Run

In the short period, some factors of production are fixed while others are variable. Hence every factor of production cannot be varied. The production can be increased only by increasing the amount of variable inputs. The firm cannot change the fixed factors like plants, land and building etc. thus, a short run is time period which is the less than the minimum required to bring out changes in the fixed factors.


  1. Long Run

It refers to a time period in which a firm can changes all of its factors of production including building, machines etc. the distinction between fixed and variable factors disappears in the long run.

Distinction between Short Run and Long Run

Basic Short Run Long Run
1. Meaning It is the time period which is less than the min. required to bring about the changes in the fixed factors It is a time period in which all the factors can be changed
2. Output Output can only be increased by change the quantity of variable factors Output can be increased by making the changes in the quantity of both fixed as well as variable factors of production.
3. Classification of factors of prod Factors of production are two types

1.    Fixed

2.    Variable

Distinction between fixed and variable factors disappears
4. Effect on Price Demand plays a dominant role in the determination of price of the commodity Supply can be adjusted according to any. Change in demand so DD and SS plays equal role in price determination.


Types of Factors :

  1. Variable Factors :Variable factors are the factors inputs can be changed as output changes e.g. Labour.
  2. Fixed Factors :Factors whose quantity cannot be changed as the output           changes.


Level of Production

Level of production is related to short run. It can be changed by changing the quantity. Of variable factors like raw material, fuel electricity etc.


Scale of Production

Scale of production is a long run concept. it can be changed by changing the quantity of all the factor of production.



Product (or output) implies the amount of goods produced by a firm during a given period of time.

These 3 concepts of product.

  1. Total Product or Total Physical Product

Total physical product refers to the total amount of goods produced by a firm with given inputs during a specific period of time.


TPP can also be defined as the sum total of all the marginal products of different units of factors or it is the average product multiplied by the no. of units of the factors employed.

where N = no. of factors employed

TPPx=  APPx × N


  1. Marginal Product or Marginal Physical Product

Marginal product is the net addition to the total product when one more unit of the variable factor is employed.

For e.g. : When 10 labourers are employed on a piece of land produces 2500 kg of wheat. When one more labour is employed the production increases to 2700 kg.

Marginal  product is 200 kg as it is the addition made to the total production.

MPP = T PPn – TPPn – 1

(where n : n units of factors

MP rises in the beginning and falls when more units are employed for production.



  1. AverageProduct or Average Physical Product

          Average product is the per unit production of the variable factors.


It rises in the beginning, then it falls when more units are employed but remain five.

Land 2 acres



Units TP AP MP
1 2 2 2
2 5 2.5 3
3 9 3 4
4 12 3 3
5 14 2.8 2
6 15 2.5 1
7 15 2.14 0
8 14 1.75 -1



1.       As we increases the units of variable factor (labour) on the land which is a fixed factor TP rises at on further increase in the variable factor, make the TP rises at diminishing rate (upto the  6th unit). At 7th unit, it reaches the maximum point. After this, the further increase in variable factor, makes it falls.


2.       When the units of the variable factor is increased, in the beginning, both APP and MPP rises. After reaching, their maximum points, they start falling, MPP can  be zero or negative. But APP can never be zero or negative.


Relationship between AP and MP

1.       AP increase, when the MP is greater           than the AP.

2.       When AP and MP are equal, AP           reaches the maximum point i.e. at           the point e.

3.       AP falls, when MP is less than AP.





Relationship between TP and MP

1.       When TP increases at increasing           rate, MP also         rises.

2.       When TP rises at diminishing rate,           MP falls       but remains positive.

3.       When TP is maximum, MP becomes           zero i.e.        cuts x-axis

4.       When TP falls, MP falls and becomes           negative.



          There are two types of production function :

  1. Short Run Production Function

It is a situation where only one input is variable and all the other are kept constant. The relationship between the variable inputs and the output is called in short run production function or returns to factor or law of variable proportion.

  1. Long Run Production Function

Long run production function refers to a situation where all the inputs used in the production are variable. It is also known as returns to scale.


Returns to a Factor or Law of Variables Proportion

Returns to factor refers to the input output relations (i.e. production function) in which one factor is variable while others are fixed. It is known as returns to factor because it analyses the effect of change in quantity of one factor on the output.

Short run production function can be :

It is also known as law of variable proportion because as more and more of the variable factors are used, keeping other factors fixed, the proportion in which different factors are used change.

According to this law as more and more units of the variable factors are applied with the fixed factors, in the beginning. Total output increase at the increasing rate. Beyond a certain point, it rises at a diminishing rate. And finally total production starts declining with  every increase in the variable factor.



State 1       (Increasing Returns to Factor)

In the beginning, total product, increase at the increasing rate. MP also increases. This stage starts from the origin to the point where MP is maximum.

Stage 2       (Diminishing Returns Origin to Factor)

As more units of variable factor increases, TP continues to increase but at a diminishing rate, MP falls but positive. This stage starts from the maximum point of MP and ends when TP is maximum or MP is zero.


Stage 3 – Stage of Negative Returns.

          At this stage, TP declines, MP becomes negative. This stage is also known as to stage of negative returns. In this stage the efficiency of fixed and variable factor of declines.


A rational producer would always like to operate in 2nd stage. He will not stay in the first stage because it is the stage of increasing returns. The producer, therefore will not stop the production he will not operate in the third stage because TP is falling.

Assumptions of the Law

  1. One factor in the production is variable while other are constant.
  2. It is possible to change factor proportion.
  3. All units of the variable factor are homogeneous.
  4. Technology is assumed to be constant
  5. Law applies only in the short period.
  6. Factors of production are not the perfect substitutes for each other.



  1. Better Utilization of Fixed Factors

The reason for increasing returns is that in the beginning the fixed factors is in a large quantity than the variable factors. When variable factors are applied to fixed factors, it get better utilized and production increases rapidly.


  1. Specialization

Another reason is the advantages offered by specialization greater is the quantity of variable factor, greater is the specialization. It includes better skills productivity, efficiency, avoidance of the waste of time in shifting from one work to another, employment person best suited to particular type of work.





  1. Optimum Proportion Already Achieved :Once the optimum proportion between the fixed and variable factor is already achieved, with further increase in variable factor, fixed factors become inadequate relative to quantity of variable factors.
  2. Diminishing returns to factor occurs because increasing efficiency of production after the maximum capacity of individual factors have reached and limit to specialization has crossed.
  3. This stage also occurs because firm has to use inferior inputs, once the superior factor inputs are used up.



  1. This stage occurs due to the fact that number of units of variable factors becomes too excessive in relation to the fixed factors, and they get in each other’s way.
  2. To large the number of variable factors, impairs the efficiency of fixed factors.          



As more and more units of variable factors are employed. Keeping fixed factors constant, marginal product of the variable factor must fall. It means that marginal returns diminishes

Land Labours MP TP
1 1 10 10
1 2 8 18
1 3 6 24
1 4 4 28

Law of variable proportion is an extension to the law of diminishing         marginal returns.



Multiple Choice Questions

  1. Returns to factor is the phenomena of

          (a) Law of returns to scale                 (b) Law of variable proportion

(c) Both (a) and (b)                             (d) None of the above


  1. Marginal product is net addition to the total product, when one more unit is

          (a) consumed                                     (b) produced

(c) sold                                               (d) employed


  1. __________ is the extension to the law of diminishing marginal returns

          (a) Law of demand                             (b) Law of supply

(c) Law of variable proportion            (d) Law of returns to scale


  1. Identify the phase in which TP increases at diminishing rate

          (a) Diminishing returns to factor

          (b) Increasing returns to factor

(c) Negative returns to factors

(d) None of these


  1. When arrange product increases, marginal product is

          (a) Less than average product

(b) More than average product

(c) Equal to average product

(d) None of these


  1. What happens to MP, when MP is more than AP

          (a) AP rises                                        (b) AP falls

(c) AP remains constant                     (d) None of these


  1. A rational producer always operate in_____________ of law of variable proportion

          (a) 1st Phase                                       (b) 2nd Phase

(c) 3rd Phase                                       (d) None of these


  1. Increasing returns to factor is because of

          (a) Optimum combination of fixed and variable factor

(b) Better utilization of fixed factors

(c) Mis-management between variable factors

(d) All of the above


  1. Marginal product is

          (a) product from last unit of labour employed

(b) net addition to total product

(c) TPn – TPn – 1

(d) All of the above



  1. In short run, changes in production is determined by

(a) Level of production                       (b) Scale of production

(c) Both (a) and (b)                             (d) None of these


  1. Law of variable proportion explains

          (a) Productivity of various factors of production

(b) Emotional relation between input and output

(c) Technical relation between input and output

(d) None of these


  1. Arrange product can have

          (a) Only positive values                      (b) Only negative values

(c) Both positive and negative values (d) Neither positive or negative values


  1. At the point of inflexion

          (a) MP is zero                                     (b) MP is maximum

(c) TP is maximum                             (d) AP is maximum


  1. Which of the following is not the phase of law of variable proportion

          (a) Increasing returns to factor          (b) Diminishing returns to factor

(c) Constant returns to factor            (d) Negative returns to factor


  1. The total output generated by first four units of variable factors is 400, 500, 550 and 625 units what is the marginal product of 3rd unit

          (a) 100 unit                                       (b) 50 units

(c) 75 units                                        (d) 550 units

  1. Production per unit of labour employed is

(a) MP                                                (b) AP

(c) TP                                                 (d) None of these


Numeric Questions

  1. Calculate AP and MP Schedule of labour
Labour 0 1 2 3 4 5
TP 0 15 55 50 40 48


  1. Calculate TP and AP Schedule of labour
Labour 1 2 3 4 5 6
TP 3 6 7 5 3 1
  1. Calculate TP and AP Schedule of the labour
Labour 1 2 3 4 5 6
MP 50 110 150 180 180 150


  1. Determine TP and MP schedule
Labour 1 2 3 4 5
AP 50 45 40 55 30



  1. Complete the following table
Labour 0 1 2 3 4 5 6
TPP 0 20 88
MPP 0 22 17
APP 0 22 20


  1. Identify different phrases of the law of variable proportion from the following table. Given reasons.
Unit of variable factor 1 2 3 4 5
TP 4 9 13 15 12


  1. Identify various phrases of the law of variable proportion from the following table :


Unit of variable factor 1 2 3 4 5 6
TP 50 110 150 180 180 150


Unit of variable factor 1 2 3 4 5
TP 10 22 30 35 30


Unit of factor 1 2 3 4 5
TPP 20 50 70 80 60

(d)      Complete the following table assuming that there are increasing returns   to a factor throughout

Unit of variable factor 1 2 3 4
TP 100


One Mark Questions :

  1. A firm can change its labour and raw material but cannot change the available plant and machinery. What economic time period is the firm operating in?
  2. Can total product even decline?      
  3. Whathappens to TP when MP increases?
  4. What is the value of MP, when TP is at its maximum value?
  5. State the law of diminishing marginal returns to factor.
  6. Calculate the output produced under the production function Q = 10 L + 5K. If the firm employees 3 units of labour and 5 units of capital?                
  7. When MPP is falling and positive, at what rate TPP is changing?
  8. When MPP is greater than APP, what can you say about APP?
  9. When MPP is less than APP, what can you say about AP?
  10. When MPP is equal to APP, what can you say about AP?
  11. When APP falls, what is the relationship between MPP and APP.
  12. To increase the production, only one factor input is variable, while other are kept constant, explain the effect on TPP? Give reasons?
  13. 4 units of the labour produces 100 units of output and 5 units of labour produces 120 units of output, calculate MPP.

Three – 4 Marks Questions :

  1. Explain the relationship between TPP and MPP?
  2. Explain the relationship between APP and MPP with the help of a diagram?
  3. What is meant by returns to a factor? Explain the law of diminishing marginal returns?
  4. Explain the effect on output, when only one input is increased and all other inputs are held constant?
  5. Explain the meaning of increasing returns to factors with the help of TPP schedule and TPP curve?
  6. What do you mean by returns to factor? What leads to diminishing returns to a factor?

Six Marks Questions :

  1. What is meant by returns to factors? State the there phrases of law of variable proportion?
  2. Explain the law of variable proportion with the help of total and marginal physical product curve and schedule?
  3. State and explain the law of diminishing return to a factor?




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