Economic production function

1. Unit - IV

2. Introduction
 Whatever be the objective of business firms, achieving
optimum efficiency in production or minimizing the cost
of production is one of the prime concerns of managers
today. Infact, the survival of the firms in a competitive
market depend on their ability to produce at a competitive
cost.

3. Production
 Refers to the transformation of resources into outputs
of goods and services.
 General motors hires workers who use machinery in
factories to transform steel, plastic, glass, rubber and
so on into automobiles.

4. Production Function

5. Production Function
 States the relationship between inputs and outputs
 Inputs – the factors of production classified as:
 Land – all natural resources of the earth.
 Price paid to acquire land = Rent
 Labour – all physical and mental human effort involved in
production
 Price paid to labour = Wages
 Capital – Money, buildings, machinery and equipment used for
the production.
 Price paid for capital = Interest

6. Production Function
Inputs Process Output
Land
Labour
Capital
Product or
service
generated
– value added

7. Fixed and Variable Inputs
 Variable Input : one whose quantity may be varied in
the short run and the long run.
 Fixed Input : one whose quantity may not be varied in
the short run, but may be varied in the long run.

8. Analysis of Production Function:
Short Run
 In the short run at least one factor supply is variable but all
other factors can be changed.
 Reflects ways in which firms respond to changes
in output (demand).
 Can increase or decrease output using more or less of some
factors but some likely to be easier to change than others
 Increase in total capacity only possible
in the long run

9. Analysing the Production Function: Long
Run
 The long run is defined as the period of time taken to vary all factors of
production
 By doing this, the firm is able to increase its total capacity – not just
short term capacity
 Associated with a change in the scale of production
 The period of time varies according to the firm
and the industry.
 In electricity supply, the time taken to build new capacity could be
many years; for a market stall holder, the ‘long run’ could be as little as
a few weeks or months!

10. Production Function
 Production function is defined as “the functional relationship
between physical inputs ( i.e., factors of production ) and
physical outputs, i.e., the quantity of goods produced”.
 Production function may be expressed as under:
Q = f ( K,L)
Where ;
Q = Output of commodity per
unit of time.
K = Capital.
L = Labour.
f = Functional Relationship.

11.  Production function depends on :
 Quantities of recourses used.
 State of technical knowledge.
 Possible process.
 Size of firms.
 Relative prices of factors of production.
 Combination of factors.

12.  The following points may be emphasized:
 Production function represents a purely technical
relationship.
 Output is the result of joint use of factors of
production.
 Combination of factors depend on the state of
technical knowledge.
 Every management has to make choice of the
production function which gives average cost and
maximum average profit.

13. Laws of Production
Laws of production are of two types:
 The law of variable proportions.
 Laws of returns to scale.

14. The Law of Variable Proportions
 Is the answer to the question: How will total
output change when all inputs are fixed except one
input.

 Two ways to illustrate the answer:
 Production schedule (chart)
 Production function (graph)
 Usually, as in this example, labor is the variable
input; all other are held constant.

15. Short Run Production Function: The Law of Variable
Proportions
Statement of the law:
“The law of variable proportions states that when more
and more units of the variable factor are added to a given
quantity of fixed factors, the total product may initially
increase at an increasing rate reach the maximum and
then decline”.

16. Tabular Presentation of Law of Variable Proportions
Units of Labour TP MP AP
I Stage
II Stage
III Stage
1 80 80 80
2 170 90 85
3 270 100 90
4 368 98 92
5 430 62 86
6 480 50 80
7 505 24 72
8 505 0 63
9 495 -9 55
10 470 -25 47

17. Diagrammatical Presentation of Law of Variable Proportions
Assumptions of the
law:
State of Technology
remains the same.
Input prices remain
unchanged,
Variable factors are
homogeneous.
AP
MP
AP
MP

18. Conclusions
 While adding units of an input (labor), the marginal
product goes through three stages:
 Stage I (Increasing returns): marginal product increases
throughout.
 This means that every additional unit increases
productivity as well as total output.
 This is shown on the graph by an increasing slope.

19. Conclusions, cont.
 Stage II (diminishing returns): marginal product
decreases throughout.
 This means that every additional unit decreases
productivity, though total output still increases.
 This is shown on the graph by a decreasing positive
slope.

20. Conclusions, cont.
 Stage III (negative returns): marginal product is
negative throughout.
 This means that each additional unit actually decreases
total output.
 a waste of money and resources.
 This is shown on the graph by a negative slope.

21. Conclusions, cont.
 The greatest productivity is at the end of Stage I.
 The greatest output is at the end of Stage II.
 Therefore, Stage II is ideal, because there is a balance
between productivity and total output.

22. Law of Diminishing Returns and Business Decisions
 A Rational producer will never choose to produce in stage III where
Marginal Productivity of variable factor is negative. It will stop at the end
of the second stage where Marginal Productivity of the variable factor is
Zero. At this point the producer is maximizing the total output and will
thus be making the maximum use of the available variable factors.
 A producer will also not choose to produce in Stage I where he will not be
making full use of the available resources as the average product of the
variable factor continues to increase in this stage.
 A producer will like to produce in the second stage. At this stage Marginal
and Average Product of the variable factor falls but the Total Product of
the variable factor is maximum at the end of this stage. Thus stage II
represents the stage of rational producer decision.

23. Key Concept: Marginal Product
 Marginal product is the amount that total output
increases by adding one more unit of an input.
 Marginal product is calculated by subtracting the most
recent total product (# of units produced) from the
new total product.

24. Law of Return to Scale
 The word scale refers to the long-run situation where
all inputs are changed in the same proportion.
 The results might be constant, increasing or
decreasing returns.

25. Constant Return to Scale
 Refers to the situation where output changes by the
same proportion as inputs
 Eg if all inputs are increased by 10%, output also rises
by 10%, Inputs are doubled then output is also doubled

26. Increasing Return to Scale
 Refers to the case where output changes by a larger
proportion than inputs
 Eg if all inputs are increased by 10%, output rises by
more than 10%, Inputs are doubled then output is
more than doubled
 Division of labour & Specialisation

27. Decreasing Returns to Scale
 Refers to the case where output changes by a smaller
proportion than inputs
 Eg if all inputs are increased by 10%, output rises by
less than 10%, Inputs are doubled then output is less
than doubled
 Managerial Diseconomies

28.  In their effort to minimize the cost of production, the fundamental
questions which managers are faced with, are:-
 How are the Production and Costs related ?
 Does substitution between the factors affects the Cost of
Production?
 How does the technology i.e., factor combination matters
in reducing the cost of production ?
 How can the least cost combination of inputs be achieved
?
 What happens to rate of return when more plants are
added to the firm ?
 What are the factors which create economies and
diseconomies for the firm ?
 The theory of production provide answers to these questions by
providing tools and techniques to analyze the production
conditions and to provide solution to the practical business
problems.

29. Long Run Production Function: The Returns to scale
 The long run production function is termed as returns to scale. In the long
run, the output can be increased by increasing all the factors in the same
proportions.
 The laws of returns to scale is explained by the help of Isoquant curves. An
Isoquant curve is the locus of points representing various combination of
two inputs, Capital & Labour, yielding the same output.
 There are three technical possibilities;
a) Total output may increase more than proportionately: Increasing
returns to scale,
b) Total output may increase at a constant rate: Constant Returns to Scale,
c) Total output may increase less than proportionately: Diminishing
returns to scale.

30. Three Stages of Law of Diminishing Returns
Increasing
Returns
Increasing
Returns
Constant Returns
Diminishing
Returns
Scale of Inputs
Marginal
Product

31. Isoquant is one way of presenting the production function where two
factors of production are shown.
It represents all possible input combinations of the two factors, which are
capable of producing the same level of output.
IQ
O
Y
X
a
b
c
d
LABOUR
C
A
P
I
T
A
L
ΔK
ΔL
ΔK
ΔL
ΔK
ΔL

32.  Marginal rate of technical substitution indicates the rate at which
factors can be substituted at margin in such a way that the total output
remains unaltered.
 MRTS of L for K is defined as the quantity of K which can be given up in
exchange for an additional unit of L, so that level of output remains the
same.
 The MRTS at a point on the isoquant can be measured by the slope of
isoquant at that point.
 Slope of IQ at point b = ΔK/ΔL.
 MRTS = Slope = ΔK/ΔL.
 MRTS can be known from the ratio of MPP of two factors.
 As output remains the same at every point of isoquants so loss in
physical output from a small reduction in K will be equal to the gain in
physical output from a small increment in L.

33.  Marginal rate of technical substitution indicates the rate at which
factors can be substituted at margin in such a way that the total output
remains unaltered.
 MRTS of L for K is defined as the quantity of K which can be given up in
exchange for an additional unit of L, so that level of output remains the
same.
 The MRTS at a point on the isoquant can be measured by the slope of
isoquant at that point.
 Slope of IQ at point b = ΔK/ΔL.
 MRTS = Slope = ΔK/ΔL.
 MRTS can be known from the ratio of MPP of two factors.
 As output remains the same at every point of isoquants so loss in
physical output from a small reduction in K will be equal to the gain in
physical output from a small increment in L.

34.  Thus,
Loss of output = Gain of output
i.e. [(Reduction in K ) X (MPP of K)] = [(Increment in L) X (MPP of
L)]
OR,
ΔK X MPK = ΔL X MPL
ΔK = MPL
ΔL MPK
OR,
MRTSLK = MPL ( By definition ΔK = MRTS LK = Slope of isoquant at
that point )MPK ΔL
Thus, MRTSLK is the ratio of marginal physical productivities of the
two factors.

35. Combinations Labour (L) Capital (K) MRTS L K
A
B
C
D
E
1
2
3
4
5
12
8
5
3
2
-
4:1
3:1
2:1
1:1
Tabular Presentation of MRTSLK

36. Iso-Cost Lines
 It shows all the combinations of the two factors ( say labour and
Capital) that the firm can buy with a given set of prices of two factors.
 It plays an important role to determine combinations of factors, the
firms will choose for production ultimately to minimize cost.
O
X
Y
PRICE OF LABOUR
P
R
I
C
E
OF
C
A
P
I
T
A
L
A
B
C
D E
E F

37. Producers Equilibrium or the Least Cost Combination of
Factors
 A producer desires to minimise his cost of production for producing a
given level of output with the least cost combination of factors.
E
P
R
S
T
IQ
IQ1
IQ2
LABOUR
C
A
P
I
T
A
L
A
B
O X
Y
How producers ultimately arrives the
point of equilibrium ?
•The equilibrium is achieved at the point
Where MRTS LK = PL/PK ie
• The slope of isoquant =Slope of
isocost
•Or , MRTS LY = MPL = PX
MPK PY
Or, MPL = MPK
PX PY

38. Expansion Path
 The Line joining the least cost combinations like a, b, c, d.
 Expansion Path may be defined as the locus of efficient combinations
of the factors.
Expansion Path
y
o x
a
b
c
IC
IC1
IC2
LABOUR
C
A
P
I
T
A
L
A
B
C
D E F

39. a) Increasing Returns to Scale:
Causes:
 Indivisibilities of Factors,
 High degree of specialization,
Labour
C
A
P
I
T
A
L

40. b) Constant Returns to Scale
Causes:
 Factors of production fully
utilised.
 Technology remains unchanged
C
A
P
I
T
A
L

41. c) Diminishing Returns to Scale
Causes:
 Managerial Diseconomies.
 Scarce and Exhaustible
resources.
Labour
C
A
P
I
T
A
L

42. Economies & Diseconomies of Scale
The Factors which cause the operations of the
Laws of Returns to Scale are grouped as under;
Economies of Scale, relates to profit accruing to
a business firm. Economies of scale are
classified as;
Internal economies
External economies,

43. Internal Economies
 Economies in production
• Technical advantages,
• Advantages of division of Labour and
specialization
 Economies in Marketing
 Managerial Economies
 Economies in Transportation & storage

44. External Economies to large size firms arise
from the discounts available to it due to;
 Large scale of purchase of raw material,
 Finance at low rate of interest,
 Low advertising cost,
 Low Transportation cost.
Diseconomies of scale are the losses accruing
to a business firm as a result of large scale
production.