this would be helpful for KU students

2. In This Lecture…
 Production with two Variable
Inputs : Production Isoquants,
Isocost Lines, Least Cost
Combination Factors, MRTS
and two Special Cases of
Production Functions – Perfect
Substitutes and Perfect
Complements
 Introduction to Law of Returns
to Scale

3. Production with Two Variable
Inputs
 In the long run, all factors of Production are
variable.
 One of the decisions a firm can face in the long run
is which combination of factors of production to
use.
 Economic efficiency involves choosing those
factors so that the cost of production is at
minimum.
 If the firm uses two inputs – labor and capital,
both of which are variable, then the long run
production functions are of type---- X = f (L,K)

4. Isoquant/Isocost Analysis
 In analyzing least cost combination of
factors, graphical analysis of Isoquant and
Isocost Analysis is required.

5. Concept of Isoquant
 Isoquant or Iso-product curve shows
different combinations of labor and
capital with which a firm can produce a
specific desired quantity of output.
 It is the locus of all the technically
efficient combinations of inputs which
yield a given amount of output.
 It shows firm’s flexibility when making
production decisions.

6. Isoquant Map
 Isoquant or Iso-product map is the set of
Isoquants family.
Qk
O
III = 150 units
II = 100 units
I = 50 units
QL
The further away the Isoquant from the origin the higher will be the
level of output

7. Isoquant
 The Isoquant I shows 50 units of output
that can be produced by many different
combinations of labor and capital. The
producer is indifferent between these
combinations of labor and capital as he
will be on the same level of output no
matter whatever the combination of
capital and labor.
 The Isoquant II shows 100 units of output
 The Isoquant III shows 150 units of output

8. Features of Isoquant
 The Isoquants are always downward
sloping meaning that if a firm wants to
use more of labor then it must use less of
capital to produce the same level of
output or to remain on the same Isoquant.
 The isoquants never intersect each other.
 The Isoquants are convex to the origin
due to diminishing Marginal Rate of
Technical Substitution (MRTS)

9. What is MRTS?
 The slope of an isoquant is called MRTS
of labor for capital.
 The slope measures the degree of
substitutability of the factors or in other
words it means that within limits, labor
and capital can be substituted for each
other.
 MRTS is defined as the amount of capital
that the firm is willing to give up in
exchange for labor, so that output level
remains constant.

10. Diminishing MRTS
 The slope of an Isoquant decreases as we move
down along an Isoquant showing increasing
difficulty in replacing capital for labor as they
are imperfect substitutes..
QK
ΔY1/ ΔX1 > ΔY2 / ΔX2 > ………. > ΔYn/ ΔXn
ΔY1
ΔX1
ΔY2
ΔX2
O
QL

11. Two Special Cases of Production
Functions
 Perfect Substitutes : In case when labor
and capital are perfect substitutes, MRTS
is constant and the isoquants are straight
lines. It means the rate at which capital
and labor can be substituted for each
other is same no matter whatever the
level of inputs are being used.

12. Two Special Cases of Production
Functions : Perfect Substitutes
Capital per month
A
B
C
q1 q2
O
q3
Labor per month
 Points A,B and c are three different capital-labor combinations that
generate the same output q3.

13. Two Special Cases of Production
Functions
 Perfect Complements : When the isoquants
are L-shaped, only one combination of labor
and capital can be used to produce a given
output. Additional output cannot be
obtained unless more capital and labor are
added in specific proportions. Adding more
capital alone or labor alone does not increase
output. This implies that the methods of
production are limited.
 In this case the production function will be
of fixed proportions.

14. Two Special Cases of Production
Functions : Perfect Complements
Capital per month
C
q3
B
A
q2
q1
O
Labor per month
 Points A,B and C are three different capital-labor combinations at
fixed proportion to increase the level of output.

15. Isocost Lines
 Isocost line is a line that shows the
different possible combinations of two
inputs, which a producer can buy that
yields him the same cost irrespective of
the combination he chooses given his
budget and the prices of factor inputs.
 Anywhere on the isocost line a producer is
spending his entire budget either on
capital or on labor or the combination of
both.

16. Isocost Lines
 Say labor costs $5 per unit and machinery costs
$3 per unit and that the firm has chosen to
spend $30.Then Isocost line will be as follows:machinery
10
4
0
2
4
6
labor

17. Shifts in Isocost Lines
 With a change in the spending of the firm. If the
spending increases then Isocost line will shift as
follows:machinery
10
4
0
2
4
6
labor

18. Shifts in Isocost Lines
 With a change in the price of any of the factors.
If the price of labor decreases then Isocost line
will shift as follows:machinery
10
4
0
2
4
6
labor

19. Economic Efficiency
 Economic efficiency with least cost combination
of factors will be attained when Isocost line is at
tangency with a Isoquants.
machinery
10
E
III= 150 units
II=100 units
I=50 units
4
0
2
4
labor

20. Economic Efficiency and
Expansion Path
In the expansion path from the origin through points A,
B and C shows the lowest cost combination of labor and
capital that can be used to produce each level of output
in the long run.
Capital
expansion path
q3
q2
q1
O
Labor

21. Economic Efficiency and Input
Substitution when price changes
With an increase in the price of labor, the isocost curve
becomes steeper and the producer will substitute OK2 ,
OL2 combination of capital and labor instead of OK1, OL1
to produce the same level of output
Capital
K2 B
A
K1
q1
O L2
L1
Labor

22. Economic Efficiency and Input
Substitution when expenditure changes
With an increase in the expenditure of a firm, the isocost
curve shifts to the right and the producer will substitute
OK2 , OL2 combination of capital and labor instead of
OK1, OL1 to produce the same level of output
Capital
K2
K1
q2
q1
O
L 1 L2
Labor

23. Law of Returns
 The law of returns to scale states that
when all factors of production are
increased in same proportion, the output
will increase but the increase may be at an
increasing rate or constant rate or
decreasing rate.

24. Three Aspects of Law of Returns
to Scale
 Increasing Returns to Scale (IRS)
 Constant Returns to Scale (CRS)
 Decreasing Returns to Scale (DRS)

25. Increasing Returns to Scale
 Increasing Returns to Scale (IRS)
When percentage increase in output is
more to that of the percentage increase in
input – Increasing Returns to Scale
operates.

26. Increasing Returns to Scale –
Graphical Representation
Capital
30
20
10
0
Labor
The isoquants move closer together as inputs are increased along
the line.

27. Constant Returns to Scale
 Constant Returns to Scale (CRS)
When percentage increase in output is
equal to that of the percentage increase in
input – Constant Returns to Scale
operates.

28. Constant Returns to Scale –
Graphical Representation
Capital
30
20
10
0
Labor
The isoquants are equally spaced together as inputs are increased
along the line.

29. Decreasing Returns to Scale
 Constant Returns to Scale (DRS)
When percentage increase in output is
less than that of the percentage increase in
input – Decreasing Returns to Scale
operates.

30. Decreasing Returns to Scale –
Graphical Representation
Capital
30
20
10
0
Labor
The isoquants move further away as inputs are increased along the
line.

31. NEXT