Production Analysis

Production Analysis Dr. Kishor Bhanushali Faculty – Economics IBS - Ahmedabad

Concepts………………………… Production is basically an activity of transformation of factor input to output Production Function is purely technical relationship between factor input and output Method of Production is a combination of the factor inputs required to produce one unit of output

The Production Function Production function is purely technical relations, which relates factor input and output The production function represent the technology of the firm or industry of the economy as a whole It gives the maximum amount of output that can be obtained by employing different inputs The method of production or process or activity is a combinations of the factors inputs required for the production of one unit of output The production process is technically efficient if it uses less of at least one factor or production and no more from the other factor, compared to any other process of production The production function can be constructed on the assumption that the technology is given and out put can be increased by increasing input

Production Function When technology changes, production function itself changes Selection of best input combination for the production of a particular output level depends upon input and output prices Q Q = f (K,L)

0

L

-

Production function depends on Quantities of resources used State of technology Size of the firm Nature of firms organization Relative prices of factors Combinations of factors of production

Average and Marginal Product Average product of a factor of production can be defined as its total productivity divided by its quantity Marginal product of a factor of production can be defined as the change in output resulting from a very small change in one factor input, keeping the other factor input constant

Law of Diminishing Returns or Law of Variable Proportions The law of diminishing returns states the with a given state of technology, if the quantity of one factor input is increased by equal increments, the quantities of other factor inputs remaining fixed, the resulting increment of the total product first increase but decrease after a particular point It is also known as the law of diminishing returns to factor. It state that as we go on employing more of one factor of production other factors remaining the same, its marginal productivity will diminish after some point. Three assumptions (1) State of technology is given (2) one factor to be kept constant (3) law is not applicable when to inputs are used in fixed proportion

Relation between TP, AP & MP No of Workers

TP

MP

AP

0

0

-

-

1

7

7

7.00

2

18

11

9.00

3

33

15

11.00

4

46

13

11.50

5

55

9

11.00

6

60

5

11.00

7

63

3

9.00

8

65

2

8.13

9

66

1

7.33

10

66

0

6.60

11

64

-1

5.82

12

60

-4

5.00

Production Curve & MP

Ridge Lines

Three Stages in Production Stage I –Average product is increasing and Marginal product is greater than average product (Stage of Increasing Returns) Stage II – Average product is decreasing and marginal product is also decreasing , but marginal product is positive (Stage of Decreasing Returns) State III- Total product is decreasing and the marginal product is negative (Stage of Negative Return)

In the first stage, the quantity of fixed factor of production is abundant relative to variable factor of production. Therefore when more and more units of variable factors is used, the fixed factor is used more intensively and efficiently. This cause production to increase at rapid rate implying increasing AP and MP

In the second stage variable factor is used at such a rate that ensures the efficient utilization of the fixed factor, any further increase in variable factor cause AP and MP to fall because the quantity of fixed factor is now become limiting compared to variable factor

In the Third Stage the quantity of variable factor is so large compared to fixed factor that the former comes in each other’s way reducing the efficiency of the fixed factor which results in a fall in total product instead of rising. This is the reasons behind the negative marginal product

The combinations of labor and capital attained maximum efficiency of labor at the boundary line between stage I and stage II and maximum efficiency of capital at boundary line between stage II and stage III The proportion in which labor and capital will be used will depend on their relative prices

Short Run and Long Run The short run is a period during which some inputs cannot be veried. The long run is a period of production that gives managers adequate time to vary all the imputs to produce goods

Returns to Scale By returns to scale we mean the behavior of production or returns when all factors are increased or decreased simultaneously in the same ratio. In returns to scale we analyze the effect of doubling, trebling, quadrupling and so on of all inputs of productive resources on the output of the product Constant returns to scale Increasing returns to scale Decreasing returns to scale

Returns to Scale Sr. No.

Inputs

TP

MP

Returns

1

1 L+3C

2

2

Increasing

2

2L+6C

5

3

Increasing

3

3L+9C

9

4

Increasing

4

4L+12C

14

5

Increasing

5

5L+15C

19

5

Constant

6

6L+18C

24

5

Constant

7

7L+21C

28

4

Decreasing

8

8L+24C

31

3

Decreasing

9

9L+27C

33

2

Decreasing

Underlying cause of the changing returns to scale is the possibility or otherwise of division of labor

Economies of Scale Efficient use of capital equipment Economy of specialized labor Better utilization and greater specialization in management Economies of buying and selling Economy of the overhead charges Economy in rent Experiment and research Advertisement and salesmanship Utilization of by-products Credit availability

Internal and External Economies Technical economies Managerial economies Commercial economies Risk bearing economies Economies of concentration Economies of information Economies of disintegration

Diseconomies of Scale Over worked management Individual tastes ignored No personal elements Cut throat competition Lack of adaptability

Technological Changes Production function shifts upwrd

Q

Higher level of output can be produced with a same level of input Q = f(L,K)

A Q = f(L,K) B New Product Improvement for existing products Better management

0

M

L

ISOQUANT or Equal Product Curves ISOQUANT shows all possible combinations of two inputs physically capable of producing the given level of output Combination A

Factor X 1

Factor Y 12

B

2

8

C

3

5

D

4

3

E

5

2

ISOQUANT Curve & Map ISOQUANT Curve

ISOQUANT Map Y

Y

a

A

a’

B

a”

C IQ

IQ 0

b b’ b”

X

0

IQ IQ X

Indifference Curve & Map Indifference Curve

Indifference Map Y

Y

a

A

a’

B

a”

C IC

IC 0

b b’ b”

X

0

IC IC X

K

Marginal Rate of Technical Substitution

P

Q

R

Combination

Factor X

Factor Y

MRTS of X for Y

A

1

12

-

B

2

8

4:1

C

3

5

3:1

D

4

3

2:1

E

5

2

1:1

S T

0

L

Marginal Rate of Technical Substitution Marginal rate of technical substitution of X for Y is the number of units of factor Y which can be replaced by one unit of factor X, quantity of output remaining unchanged MRTS = ∆X ∆Y

Equal Cost Lines Equal cost line shows various combinations of tow factors which can be purchased with a given amount of total money E Factor Y

C A

0

Factor X

Least Factor Combinations X Maximization of output subject to cost constraints

A

E IQ3 IQ2 IQ1

0

V

Least Factor Combinations X Minimization of cost for a given level of output

A

E

IQ

0

B

V

Numerical

Q = 4 L + 6 K − 2 LK w = 10 2

r = 10 C = 720

2

MPl = 8L-2K MPk = 12K-2L L = 1.4K 10L+10K =720 K = 30 L = 42 Q = 9936

Expansion Path