The document discusses managerial economics and the law of variable proportions. It covers three stages: increasing returns, diminishing returns, and negative returns. It also examines total product, average product, and marginal product during these stages. Additional topics include returns to scale, internal and external economies, isoquants, marginal rate of technical substitution, and the properties of isoquants.

1. Managerial Economics
Prepared by : - Amit Maisuriya

2. Stages of the law of Variable Proportions
1. Stage of Increasing Returns
2. Stage of diminishing returns
3. Stage of Negative returns : -
Addition of more and
more units of variable factors are added to a fixed
factor, beyond a certain point, output increases at a
diminishing rate and ultimately turns out to be
negative.
E.g.. Overdose of Fertilizers.

3. Behavioral Pattern of TP,AP,MP during 3 Stages
Stage Total Product Marginal Product Average Product
Stage – I Increases of an Increases and Increases, but at a
increasing rate reaches its maximum lower rate than
marginal product
and reaches its
maximum
Stage – II Increases at Start diminishing and Starts diminishing
diminishing rate and become zero
becomes maximum
Stage – III Reaches its Continues to decline Continues to decline
maximum, becomes and become negative but not up to zero
constant, and than level
start falling

4. Conclusion
• Economic efficiency rises during stage - 1
• During 2 stage average product and marginal product
decline but total product continue to increase.
• In 3 stage is ruled out as all the three outputs,
namely total product, marginal product and average
product are decline marginal product becomes
negative.

5. Return to scale
• It mean the behavior of production scale or returns
when all the factors are increased or decreased
simultaneously in the same proportion.
• The percentage or proportionate increase in output
when all inputs are changed in the same proportion is
known as return to scale.
• Return to scale due to the increase in the scale of
operations namely increase in size, additional technical
and management personnel.

6. Phases of return to scale
1. Increasing returns to scale: -
 Indivisibility of the factors
 Division of labor leading to specialization
 Dimensional economics
2. Constant return to scale:-
Increase in same proportion as
increase in input.
3. Diminishing returns to scale: -
Out put increase in smaller
proportion than increase in all inputs.

7. Internal Economies
 They arise within or inside the firm
 They arise due to improvement in internal factors
 They arise due to specific efforts of one firm
 They are particular to a firm an enjoyed by only one firm
 They arise due to an increase in the scale of production.
 They are dependent on the size of the firm
 They can be effectively controlled by the management of
a firm
 They are called as “ Business Secrets” of a firm.

8. External Economies
• The following imp. Aspects of external economies…
1. They arise out side the firm
2. They arise due to improvements in external factors
3. They arise due to collective efforts of an industry
4. They are general, common and enjoyed by all firms
5. They arise due to over all development expansion and
growth of an industry or a region.
6. They are dependent on the size of industry
7. They are beyond the control of management of the firm
8. They are called as open secrets of the firm.

9. Production function with two variable Inputs
• In this chapter, we shall study production function
when two factors are taken as variables factors and
which are substitutes for each other.
• This technique is known as iso-quants or iso-product
curve which are similar to indifference curve
technique of the theory of consumption.

10. What are Iso-quants?
 An Iso-quants may be defined as a curve representing
various combinations of two inputs that produce the
same level of output.
 An iso-quant is also known as an iso-product curve or an
equal product curve or production indifference curve.
 On an indifference curve shows the same level of
satisfaction to the consumer
 Similarly every point on an iso-quant would indicate the
same amount of output.
 “An Iso-quants may be defined as a curve which shows
the different combinations of the two inputs producing
the same level of output.”

11. Illustration of iso-quant with the help of
table and curve
Iso-quant Schedule
Combination Units of Units of Total output
labour Capital (in units)
A 1 12 100
B 2 8 100
C 3 5 100
D 4 3 100
E 5 2 100

12. Iso-quant curve
ISO-QUANT
14
A
12
C
A 10
P 8 B
I
T 6 C UNITS OF CAPITAL
A
L 4 D
E
2
0
1 2 3 4 5
LABOUR

13. Iso-quant Map
 An iso-quant map is a set of iso-quants representing
different levels of output.
 A higher iso-quant indicates higher level of output.

14. Iso-quant map
140
120
100

15. Iso-quant map
An Iso-quant map is a set of iso-quant
representing different levels of output. A
higher iso-quant indicates higher level of
output.
Each combination on the same iso-quant gives
the same level of out put.
 however a higher iso-quant represent higher
level of output.

16. Types of Iso-quant
• Iso-quant may be different shapes depending
on the degree of elasticity of substitutability
of inputs.
1. Linear iso-quant
2. Input output iso-quant
3. Kinked iso-quant
4. Smooth convex iso-quant

17. Linear iso-quant
y
Electrical Power
Natural Gas
Q1 Q2 Q3
X
Diesel

18. Linear iso-quant
• This type of iso-quant assumes perfect
substitutability between different factors of
production. Thus, for example, a given output, say
100 units, may be produced by using only labour
capital. The shape of such an iso-quant shall as on
the left side.

19. Input output iso-quants
This type of Iso-Quant
assumes perfect
U
N iso-quants complementary or zero
I
T
substitutability between the
O inputs.
F
C When there is only one
A method of production for
P
I any product, its Iso-quant is
T
A of right-angled shape. This
l type of iso-quant is also
Units of labor
known as Leontief iso-quant.
Zero Substitutability

20. Kinked Iso-Quant
• This is also known as linear
U
Iso-quant
programming iso-quant.
N
I
A1
A2 • It assumes limited
T
A3
substitutability of labour and
O
F capital.
C
A4 • As there are only a few processes
A
P which are available for producing
I any commodity ( say
T
A A1, A2, A3, A4) substitutability of
l factors is possible only at kinks.
Units of labor This can be illustrated as on the
Linear Programming Iso-Quant left side.

21. Smooth Convex Iso-Quant
Convex Iso-Quant
Y  It assumes continuous
U substitutability of labour
N
I and capital only over a
T
O certain range, beyond
F
C which factors cannot be
A
P substituted for each
I
T other.
A
l  This iso-quant appears
Units of labor X as a smooth curve
Imperfect substitutability convex to origin.

22. Marginal Rate of Technical substitution
• The Principles of marginal rate of technical
substitution is based on the production
function where two factors can be substituted
in Variable proportions in such a way as to
produce a constant level of output.
• Marginal rate of technical substitution
indicates the rate at which factors can be
substituted at the margin without any change
in the level of output.

23. Conti…
• For Example.. The marginal rate of technical
substitution of labour for capital is the number of
units of capital which can be replaced by one unit of
labour without changing the level of output.
• The concept of marginal of technical substitution can
be easily understood from the table given below

24. Marginal rate of technical substitution
Factor Combination Units of Labour Units of Capital Marginal rate of technical
substitution of labour for
capital
A 1 12 --
B 2 8 4:1
C 3 5 3:1
D 4 3 2:1
E 5 2 1:1

25. Conti…
 It will be seen from the above table that the marginal
rate of technical substitution shows a decline.
 E.G. In factor combination B, 4 units of capital can be
replaced by 1 unit of labour without change in output.
 So, 4:1 is the marginal rate of technical substitution at
this stage.
 In factor combination c, 3 units of capital can be replaced
by 1 unit of labour without any loss of output and as such
the marginal rate of technical substitution is 3:1.
 Similarly, the marginal rate of technical substitution for
combinations D and E is 2:1 and 1:1 respectively.

26. Conti…
Marginal rate of
Technical Substitution = Labour Units
Capital Units

27. Conti..
A small movement
A downwards the iso-quant
U
N curve from A to B in the
I B figure given below say K is
T Iso-Quant substituted by an amount of
O labour say L without any
F
c
loss of output. The slope of
C D the iso-quant curve Q1 at
A
P point A, Therefore, equal to
I E K
T
A L
l
Units of labor

28. Conti…
 The marginal rate of technical
substitution is equal to the ratio of a
U marginal physical products of the two
N factors.
I
T
 since the definition, output remains the
O same on an iso-quant curve, the loss in
F physical output from a small reduction in
C units of capital will be equal to the gain in
A
P
physical output from increase in the units
I of labour.
T  Thus, the loss in output is equal to the
A marginal physical product of capital
l
multiplied by the amount of reduction in
capital.
Units of labor
 likewise, the gain in output is equal to the
MRTS = K = MPL
marginal physical product of labour
L MPk multiplied by increase in labour.

29. Why the marginal rate of technical
substitution diminishes?
• It will be seen from the above table and diagram that the
marginal rate of technical substitution diminishes and this
is its one important feature.
• in other words, a salient characteristic of the marginal rate
of technical substitution is that it diminishes as more and
more units of labour are substituted for capital.
• Thus, as the quantity of labour used is increased and the
quantity of a capital employed decreased,
• The units of capital that are required to be substituted by
an additional unit of labour diminishes.
• This is known as the principle of diminishing marginal rate
of technical substitution
• As a more and more units of labour are used to
compensate for the loss of the units of capital to maintain
the same level of out put.

30. Conti…
• The marginal physical productivity of labour
diminishes and the marginal physical productivity
of capital increases and therefore less and less
units of capital will be required to replace one
units of labour to maintain the same level of
output.
• Thus, the marginal rate of technical substitution
diminishes as labour is substituted for capital.
• It means that the iso-quant must be convex to
the origin at every point.

31. Properties of Iso-quants
1. An Iso-Quant curve like a an indifference
curve is a downward sloping curve towards
the right
2. A Higher Iso-Quant represents large output
3. No two Iso-Quant can intersect each other
4. Iso-Quant are convex to the origin
5. In between two iso-quants there may be
number of iso-quants
6. Units of output shown on iso-quant are
purely arbitrary

32. An Iso-Quant curve like a an indifference curve is a
downward sloping curve towards the right
• That means, it has a negative slope.
• This implies that if more of one factor is
used, less of other factor is needed for
producing the same output.
• Thus, when the quantity of say labour is
increased, the quantity of other factor , say
capital must be reduce so as to keep the
output constant on a given iso-quant.

33. Conti…
• The downward slope of an iso-quant follows from a valid
assumption that the marginal physical products of factors are
positive, that is, the use of additional units of a factors give positive
increments in output.
• And so, when one factor is increased yielding positive marginal
products, the other factor must be reduced to hold the level of
output constant or else the total output will increase and we will be
switching over to a higher iso-quant.
• It would be interesting to note here that if iso-quants do not have a
negative slope, certain logical absurdities would follow.
• Thus for example, if the iso-quant slops upwards to the right
• This means that inspite of having used more units of both labour
and capital, the total output remains the same which is just not
ppossible.

34. Conti…
• In this diagram factor combination T on
the iso-quant curve shows more units of
both labour and capital and therefore, it
will give more output than combination P
where less units of labour and capital are
used.
• As such, point P and T on the iso-quant
curve cannot indicate equal product.
• As said earlier, every point on iso-quant
curve shows the same level of output.
• An upward sloping iso-quant curve
cannot indicate the same level of output.

35. Conti..
• Likewise, Suppose iso-
quant of labour is combined
with more units of capital or
less units of capital; in that
case iso-quant cannot be a
constant product curve.

36. Conti…
• Similarly, if iso-quant is horizontal
to x-axis which means that a given
amount of capital is combined with
more units of labour or less units of
labour; and in this case too iso-
quant cannot be a constant product
curve.
• The iso-quant
curve, therefore, cannot be equal
product curve.
• From the above discussion, it
would be clear that iso-quant curve
must slope downwards to right.

37. The higher iso-quant represents large
output
 That is, higher the iso-quant, Greater
the output and vice versa.
 In the diagram the combination T on
iso quant curve, shows large output
(200 units) than point P on iso-quant
curve (100 units). Thus, the combination
of OA capital and OB of labour produces
100 units o output, while OC units of
capital and OD units of lobar produce
200 units. As such IQ1 which lies above
IQ2 to the right represents a large level
of output.

38. No two iso-quant can intersect each
other
 if two iso-quant intersect of touch
each other, this means that there will be
a common point on the two curve as
shown in the diagram.
 This implies that the same factor
combination.
(labour and capital) which can
produce say 100 units of output at one
iso-quant can also produce 150 units of
output at the other iso-quant.
 This is quite absurd because the
same factor combination cannot
produce two different of output.

39. Iso-Quant are convex to the origin
 The convexity of an iso-quant
curve implies that the slope of
the iso-quant curve moves
downwards from let to right
along the curve.
 thus, foe example, as more
and more units of labour are
employed to produce 100 unites
of the product, lesser and lesser
units of capital are used.
 this is because the marginal
rate of technical substitution
between two factors diminishes.

40. In between two iso-quants there may
be a number of iso-quants
• it showing various levels of output which the
combination of two factors can give.
• Thus, for example in between 100 units and
200 units of output shown on IQ and IQ1
respectively ,
• There may be iso-quant showing
120,135,150,175 units of output.

41. Units of output shown on iso-quant
are purely arbitrary
• Thus, for example the various units of output
like 100,150,220,300 etc. shown on isoquant
map are arbitrary.
• Instead of these units any other number of
units of output say like 10,25,35,45, or
1000,1500,2000 etc. can also be assumed.

42. Difference between iso-quant and
Indifference curve
• As said earlier, iso-quants are very much similar
to indifference curves of the theory of demand in
the sense that :
1. Just as indifference curves assume two
commodities, iso-quant also consider two
factors or inputs, say like labour capital
2. All points or combinations on indifference curve
show equal level of satisfaction to the
consumer, likewise all combination on an iso-
quant show equal level of production.
3. The main properties of indifference curve are
also similar to the properties of iso-quants.

43. However, there are certain difference
also between these two techniques:
1) An indifference curve indicates satisfaction to consume, which
however, cannot be measured in physical units, while in the case
of an iso-quant the product can be measured in physical units.
2) in difference map only indicates that a higher indifference curve
gives more satisfaction than a lower one; but it does not say how
much more or how much less satisfaction the consumer would
derive. On the other hand, in the case of an iso-quant map one
can say how much output is more on an iso-quant as compared to
lower iso-quant.
3) As satisfaction on indifference curves cannot be measured In
physical units, we give arbitrary numbers say like 1,2,3,4 etc on
the other hand, on iso-quants we can indicates physical units say
like 100,200,250,300 etc. to indicate the level of output to which
each curve corresponds.

44. Iso-Cost Curve
• Having discussed the properties of iso-quants, we turn to the
prices of the two inputs as represented on the iso-quant map by
the iso-cost curves.
• As iso-cost curve is also known as the price line or outlay line
showing the price of the actor in terms of another factor.
• each iso-cost curve represents the different combination of two
inputs which a firm can buy for a given amount of money at the
given price of each input.
• In other words, the iso-cost curves represent the locus of all
combination of the two input factors which result in the same
total cost.
• E.G. if the unit cost of labour (L) is P and the unit cost of a capital C
is q, then the ,
Total cost (TC) = pL + qC

45. Iso-cost line
• The combination of the factors , say labour and capital – with
which a firm produces a given output depends on the prices of the
factors and the amount of money which a firm is willing to spend.
• An iso-quant line indicates the prices of factors and the total sum
of money which a firm wants to spend.
• Each iso-quant line shows various combination of two inputs which
can be purchased with a given amount of money.
• An iso-quant line may, therefore, be defined as the locus of various
combinations of factors which a firm can buy with a constant outlay.
• As said earlier , the iso-quant is also known as price line or outlay
line.

46. Conti…
• E.G. A firm has Rs. 1000/- to spend and the price
per unit of a labour and capital is Rs. 50/- and Rs.
100/- respectively.
• Now, if the firm spends the entire amount on labour
it has a combination of 20 units of labour + Zero (0)
capital.
• Alternatively, if it spend the entire amount on capital
its has a combination of zero (0) labour + 10 units of
capital.
• There are many possible combination of these two
factors representing equal expenditure.

47. Conti…
Combination Units of Units of Total
Labour Capital expenditure
A 20 + 0 Rs. 1000-00
B 10 + 5 Rs. 1000-00
C 00 + 10 Rs. 1000-00

48. Conti…
 in this diagram plotting the points. A,B,C
etc. we get a line AC which is budget line or
an iso-cost line.
 every point on the budget line iso-cost
curve shows the same amount of
expenditure.
 if the total outlay ( expenditure) of the
firm and the prices of the two factors are
given .
 an iso-cost curve indicates all possible
combinations of the two factors which the
firm can have.
 Clearly the budget line or an iso-cost is
the counter-part of the price-line in
indifference curve analysis.

49. Conti…
 Now, if the firm decides to increase the total
expenditure on two factors to Rs. 2000/- it can
purchase more of both the factor.
 Thus, as a result of the increase in total outlay to
Rs. 2000/- the iso-cost line will shift towards the right.
 Likewise, with a total outlay being increased to Rs.
3000/- the iso-cost line will further move to the right.
 The diagram on the left side shows the shift in iso-
cost line from AB to CD TO EF resulting from increase
in outlay or total cost.
The slope of the iso-cost line is the ratio of the price
of a unit of labour to the price of unit of capital.
 in case, the price of any of the input
changes, ,there would be corresponding changes In
the iso-cost curve and the equilibrium position too
would shift.

50. Least Cost - Combination of Factors
 The firm tries to attain equilibrium position by
working for the most economical or least cost
combination of the factors of production.
 Just as a consumer when faced with making a
choice between different combination of two
commodities aims at achieving maximum profits.
 And for this purpose, the firm has to choose the
factor combination in a most economic or
optimum manner, that is, the firm would try to
attain least cost combination of the factorof
production.

51. Conti…
• In other words, it may be said that in order to
produce a given output, there are various
combinations of the factors of production and the
firm
• Naturally would choose that combination of
factors which minimizes its cost of production, for
only then that the firm can get maximum profits.
• Thus, the firm will try to produce a given level of
output with least cost combination of factors.
• This least cost combination will be the optimum
point for the firm.

52. Returns to scale: Iso-Quant
• Return to scale, i.e. increase in scale of operation of the firm
• we have to vary not only the variable factor (s) but also fixed factor (s).
• if all factors are increased in same proportion and output increase in
the same proportion,
• we have a case of constant returns to scale
• If output increases more than proportionately
• we have a case of increasing returns to scale and
• If output increases less than proportionately, we have a case of
diminishing returns to scale.
• when increasing returns to scale are available , the firm is realizing
certain advantages of large scale operation; in the opposite case there
are disadvantages.

53. Conti…
• When advantages and disadvantages of scale are
balanced, there are constant returns to scale.
• This can be explained by the technique of iso-quants.
• An iso-quant is an equal quantity curve on which all
points show the same level of output.
• A higher iso-quant shows the higher level of output
and lower level iso-quant lower level of output.
• In the diagram IQ1,IQ2,IQ3 etc. are iso-
quants, showing for example, 1000 units, 2000
units, and 3000 units of output.
• Line OP shows the output at different levels on various
iso-quant curves.

54. Increasing Returns to Scale
 IN Figure. MN<LM, which means
that with less increase in
inputs, same quantity of output can
be achieved
 In other words, of factors of
production are doubled the output
will be more than doubled.
 The returns to scale increase.
 The firm enjoys increasing
returns to scale

55. Diminishing Returns To Scale
 In figure. OP is the scale line.
In this case MN>LM
 Which shows that the
inputs, are rising faster, but the
increase in output is the same.
 In other words, the doubling
factors will result in less than
double the amount of output.

56. Constant Returns to Scale
 If the factor of the production vary in
the same proportion and output also
varies in the same proportion, there are
constant returns to scale.
 in Figure MN = LM indicating that
increase in input is the same at every stage
, and the consequent increase in output is
in, the same proportion.
 Thus, if the factors are doubled output
also is doubled.
 This is known as the operation of the lay
of constant returns.

57. Conti…
• If may be noted that increasing returns to scale
are due to internal economies accruing to the
firm on account of increase in the scale of
operation of the firm.
• diminishing returns are due to internal
diseconomies which is nothing but increasing
inefficiency in operation beyond and optimum
size of the firm.
• Similarly, if internal economies and diseconomies
are balanced, we have a case of operation if
constant returns to scale.

58. Expansion Path
 The indifference curve analysis and the Iso-quant/iso-
cost analysis come to identical conclusions.
 A consumer attains equilibrium when the marginal
ratio of substitution between two commodities is equal
to the price of the two commodities.
 Similarly, the firm attains equilibrium when Marginal
rate of technical substitution between two factors is
equal to the price ratio of the two factors.
 This is the condition of equilibrium of a consumer and
firm.

59. Conti…
 Now let us explain the expansion path of a firm with the help
of iso-quant/iso-cost curves.
 “ Expansion Path is a line or a curve on which every point is
an equilibrium point i.e. minimum cost combination of two
factors at various level of output.
 As the firm tries to expand its output, it will try to see that it
attains equilibrium at the lowest cost at that output.
 This is nothing but the concept of minimizing cost an
maximizing profit.
 we assume that the prices of two factors are given and the
map of iso-quants (i.e., equal quantity curves) is also given.
 Each higher iso-cost line shows higher level of cost (i.e.
outlay) but the prices of two variable factors (i.e. X and Y or
labour & Capital) remain constant.

60. Conti…
 The between iso-cost and iso-quant indicates
equilibrium which shifts as the firm moves
form lower to higher level of production.
 A firm receiving maximum profit will produce
at one or the other point on expansion
path, because any other point, outside will
mean less than maximum profit.

61. Conti…
 In this above diagram, iso-quants are given as
IQ1, IQ2, IQ3 etc. and iso-costs are presented as
AB, CD, EF etc.
 The slopes of iso-costs are constant because the prices
of two factors remain constant.
 Iso-quants are indicated by figures 100,200,300 etc.
 points P,Q and R show equilibrium positions of the firm
at different level of output.
 As the firm expands its output, the combination of
factors will change as indicated by points on the
expansion path.
 it may be noted here that the expansion path shown
above is based on the assumption that the prices of two
factors remain constant .
 if the price of any one factor changes or if both the
prices change, in different proportions
 The expansion path too will change.
 Here the shape of expansion is not necessarily the

62. Conti..
 similarly, if the iso-quants are more or less
convex to the origin than what they are shown
In the above diagram
 the tangency points will change and hence
the expansion path too will change.
 The shape of iso-quants depend on the
degree of substitutability or
complementarities between the two factors.

63. Economic Region and Ridge - Lines
 We are familiar with the shape of a an iso-
quant.
 it is generally convex to the origin
 But there may be exceptional iso-
quant, which may bend backwards at the
upper end and slope upwards at the lower
end.
 As shown beside …..

64. Conti…
 In this diagram iso-quant is
abnormal beyond A1 and B1.
 Between these two points it is
normal i.e. convex toe the origin.
 the firm will produce only
between A1 and B1.
 If the firm uses more of both
the factors, it will produce less
than the output indicated by the
IQ1 i.e. 100 Units.

65. Conti…
 In this diagram we have different iso-quants indicating
different levels of output.
 In this diagram OA and OB are called Ridge lines.
 Ridge lines show the limits within which the firm will
operate for production because outside the ridge
lines, production will be uneconomic.
 It may be noted that the area within the ridge lines is the
area wherein the iso-quant are normal i.e. convex to the
origin.
 outside his area, the iso-quants are not convex
 the area between the ridge lines i.e. OA and OB is called
the economic region.
 In the economic region, certain units of labour and capital
can be employed to produce 100,200,300 units as shown by
respective iso-quants.
 Any point out side the economic region is called
uneconomic because less output will be produced by a
combination of two factors one o=r both of which are more
than required for production.

66. Conti…
 This is clearly waste and therefore the firm
will always try to remain in the economic
region which lies within the two Ridge-lines.
 Obviously the firm will not produce at any
point above OA or below OB lines.
 The above analysis shows relevance of that
portion of the iso-quants which the firm
would always like to keep in mind while taking
production decisions.