Note on Concept of Production Function

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 Production:

Simply, production is the creation of utility. In other word, production is the process of transforming factor of production is not only production of physical goods but it imcludes other activities like writing a book, writing an artical, engineering, etc.

Production Function:

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It is the functional relationship between quality input & quality output. Those factor which are essential for the production of goods are input & final form of production is called output. Therefore the production function is purely engineering relationship which connect input & output. Algebrically, it is represented as;

Q = f (Ld, L, K, T, E)

Where,

Q = Quantity

Ld = Land

L = Labour

K = Capital

T = Technology

E = Efficiency

Types of production function

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source:slideplayer.com

1) Short-run production function:
In economics short run is defined as the time period in which some factor of production afre supposed to be constant & some are supposed to be variable. Some factor like labour, raw materials, fuel, etc can be changed even in short run but some factor like land, building, machine, technology, management, etc cannot be changed in shot run. Therefore, short run production fucntion is the functional relation between fixed & variable input & output. Mathmatically, it is expressed as;
                      Q = f( \bar{K} , L )

Where, Q = Quantity Output
            f = Function
  \bar{K} = Capital input as variable factor
            L = Land & input as fixed factor

2) Long-run production function:

Long-run is defined as the period in which all factors are variable. Producer has sufficient time for necessary adjustment in production in long time period. Therefore, we can change every factor including; land, building, techonolgy, administration, management, etc in long run. Therefore, in long run production all variable input & output. Algeberically, it is expressed as;
                            Q = f ( K, L )

Where,
Q = Quantity Output
f  = Function
K = Capital input as a variable factor
L = Land input as a variable factor

 

Concept of Total Product, Average Product, and Marginal Product

Total Product (TP)

Total product is the total quality of a goods that can be produced by using variable factor within specific period of time.  In other word, total product is obtained by average product multiplying by the number of varialbe factor. Algebrically it is;

TP = MP1 + MP2…..+ MPn

where, TP = Total product,

MP1 = Marginal product from 1st of input

MP2 = Marginal product from 2nd of input

 By the help of following table & diagram, we can drive TP curve:

Units of labour

Total Product

1

10

2

30

3

60

4

80

5

90

6

90

7

80

 

In above table, different stages of production are shown. In 1st unit, the total production is 10 and it increases up to 3rd stage. In 4th stage, it increases up to 80 and when one labour is added it become 90 and remains constant and it decreases and become 80 in the 7th unit.

 

Average Product (AP)

Average product can be obtained from total product dividing by the number of variable factor. It is also called per unit product. Symbolically, it is expressed as :

AP = \(\frac{TP}{L}\)

Where,

AP = Average product

TP = Total product

L   = No. of variable factor

This can be explained with help of the following table:

 

Units

Total Product

Average Product

Stage

1

10

10

1st

2

30

15

3

60

20

2nd

4

80

20

5

90

18

 

3rd

6

90

15

7

80

11.4

 

In the above table, the AP is 10 when the input is 1. As the inputs are continuously added the TP increases rapidly in increasing order and AP is 15 which is also increasing at the first rate. Up to the 3rd unit, AP increases rapidly but after that, it remains constant for a while in the 4thunit. Then, it slowly starts to decreases. At last, AP becomes 11.4 at the 7th input.

Marginal Product (MP)

Marginal product is the net additional product to the total product made by added unit of other input. In another word, it is the increasing total product due to the change in fashion of production.

MP  = \(\frac{ΔTP}{ΔL}\)

Where,

MP  = Marginal product

ΔTP = Change in Total product

ΔL   = Change in unit of labour

This can be explained with the help of the following table:

 

Units

Total Product

Marginal Product

Stage

1

10

10

1st

2

30

20

3

60

30

2nd

4

80

20

5

90

10

3rd

6

90

0

7

80

-10

 

In the table, when the input is 1, the MP is 10. Here along with the increase in input, the MP also continuously increases but in a slow rate. Up to 3rd input, the MP increases from 10 to 30 but from 4th input, MP decreases from 30 to 20 and to 10 at the 5th unit of input. Then, in a sixth input, MP becomes zero. When one more input is added to 7th input, the MP becomes negative.

 

 

 

 

 

 

 

 

 

(Karna, Khanal, and Chaulagain)(Khanal, Khatiwada, and Thapa)(Jha, Bhusal, and Bista)

Bibliography

Jha, P.K., et al. Economics II. Kalimati, Kathmandu: Dreamland Publication, 2011.

Karna, Dr.Surendra Labh, Bhawani Prasad Khanal and Neelam Prasad Chaulagain. Economics. Kathmandu: Jupiter Publisher and Distributors Pvt. Ltd, 2070.

Khanal, Dr. Rajesh Keshar, et al. Economics II. Kathmandu: Januka Publication Pvt. Ltd., 2013.

 

 

 

  1. The theory of production explains the relationship between input and output.
  2. The sum of the total quantity of goods and services produce by a firm in a given period of time by using various inputs is called total product. 
  3. Total product divided by the total input is called average product.
  4. Marginal product is the net additional product to the total product made by added unit of other input. 
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