The basic function of a firm is to produce one or more goods and /or services and sell them in the market. Production requires employment of various factors of production, which are substitutes among themselves to certain extent. Thus, every firm has to decide what combination of various factors of production, also called inputs, to choose to produce a certain fixed or variable quantities of a particular good. The problem is referred to as “ how to produce?”

1. Production
Analysis
BY: MILAN PADARIYA
Pharma MBA

2. Meaning of Production
• The basic function of a firm is to produce one or
more goods and /or services and sell them in the
market.
• Production requires employment of various factors
of production, which are substitutes among
themselves to certain extent.
• Thus, every firm has to decide what combination
of various factors of production, also called inputs,
to choose to produce a certain fixed or variable
quantities of a particular good.
• The problem is referred to as “ how to produce?”

3. Meaning of Production
• Production has a broad meaning in economics.
• Production means presenting an item for sale,
where the item could be a tangible good or an
intangible good.
• Tangible goods could be presented for sale
through either their manufacturing or through just
trading in them.
• Production include activities such as transporting,
storing, and packaging of goods.
• Thus, people who are engaged in transporting, say,
wheat from Haryana to Kerala, are also considered
as producers of wheat.

4. Meaning of Production
• Firms which procure wheat from the market,
convert it into wheat flour and then pack it in bags
under their brand name are also producers of
wheat.
• In case of services, however, intermediaries do not
exist and their production comes through
manufacturing only.

5. Production Fuction
• A production function expresses the technological
or engineering relationship between output of a
good and inputs used in the production, namely
land, labour, capital and
management(organization)
• Traditionally, production functions are defined in
terms of quantities of output and inputs.

6. • The production function could be written as
Q = f (Ld, L, K, M, T)
= f1, f2, f3, f4, f5 > 0
Where
Q = output in physical units of good X
Ld = land units employed in the production of Q
L = Labour units employed in the production of Q
K = capital units employed in the production of Q
M = managerial units employed in the production of Q
T = technology employed in the production of Q
f = unspecified function
fi = partial derivation of Q with respect to i th input

7. • This function assumes that output is an
increasing function of all inputs. This is generally
true.
• This function gives the maximum possible
output that can be produced from a given
amount of various inputs, or, alternatively, the
minimum quantity of inputs necessary to
produce a given level of output.
• The relative importance of various inputs in
production varies from product to product.

8. • For ex, production functions for agricultural
products generally have inputs as land,
fertilizer, rainfall, seeds, etc.
• In contrast, the production function for
industrial products have inputs as labour,
capital, management and technology.
• Land is an important factor of production in
agriculture, while labour is an important factor
of production for industry.

9. • If the two inputs considered are labour and
capital, the production function reduces to
Q = f (L, K)
= f1, f2 > 0
Short run is the period during which atleast one
of the factors of production is available in a
fixed quantity.
Thus , during such a period, production could be
increased or decreased by changes in other
inputs only.

10. • For ex, in a given season, a farmer might have
a fixed quantity of land to grow wheat, but he
could still produce more or less wheat by using
more or less fertilizer.
• Similarly, Maruti Udyog has a fixed capacity to
manufacture cars but it could still vary its
production by scheduling work on one shift
instead of two shifts or on all the three shifts
instead of two shifts.

11. • How short is the short-run?
• It depends! In the case of a farmer, the short-run
could be just about a year, while in the case of
Maruti Udyog, it could well be around five years.
• This is beacause, land is not fixed for the cultivation
of wheat beyond a perticular season, and the next
season would come after one year only. In
constrast, Maruti udyog would need aroung five
years to add to its capacity, fund raising, assets
purchasing and installation, etc.

12. • Thus, short-run is a time concept and not a time
period.
• The short-run version of production function
assuming capital as the fixed input (K) and labour
as the variable input, could be written as
Q = f (L, K)
On the other hand, Long run is the period during
which all the factors of production are variable.

13. Special Features of Production
Function
1. Labour and capital are both inevitable inputs
to produce any quantity of a good
2. Labour and capital are substitutes to each
other in production.
These features imply that one need some
quantity of both the inputs to produce any
quantity of a good but there are alternative
combination of these two inputs to produce a
given quantity of output.

14. ISOQUANTS
• Observations:
•
1)
For any level of K, output increases with
more L.
•
2)
For any level of L, output increases with
more K.
•
3)
Various combinations of inputs produce the
same output.
Isoquants are curves showing the combinations
of inputs that yield the same output.

15. Isoquants
Labor Input
Capital Input
1
2
3
4
5
1
20
40
55
65
75
2
40
60
75
85
90
3
55
75
90
100
105
4
65
85
100
110
115
5
75
90
105
115
120

16. Isoquants
Labor Input
Capital Input
1
2
3
4
5
1
20
40
55
65
75
2
40
60
75
85
90
3
55
75
90
100
105
4
65
85
100
110
115
5
75
90
105
115
120

17. Production with
Two Variable Inputs
Capital 5
per year
4
3
2
1
1
2
3
4
5
Labor per year

18. Production with
Two Variable Inputs
Capital 5
per year
The isoquants are derived
from the production
function for output levels
of 55, 75, and 90.
4
3
A
2
D
1
Q1 =55
1
2
3
4
5
Labor per year

19. Production with
Two Variable Inputs
Capital 5
per year
The isoquants are derived
from the production
function for output levels
of 55, 75, and 90.
4
3
A
B
2
D
1
Q1=2 =75
Q1 =55
1
2
3
4
5
Labor per year

20. Production with
Two Variable Inputs
E
Capital 5
per year
The isoquants are derived
from the production
function for output levels
of 55, 75, and 90.
4
3
A
B
C
2
Q3 =90
D
1
Q2 =75
Q1 =55
1
2
3
4
5
Labor per year

21. Properties of Isoquants
1.
2.
3.
4.
They are falling.
The higher the isoquant, the higher is the output
They do not intersect each other.
They are convex from below.

22. Isoquants
• The isoquants emphasize how different input
combinations can be used to produce the same
output.
• This information allows the producer to respond
efficiently to changes in the markets for inputs.

23. Isoquants
• The Short Run Versus the Long Run
Short-run:
• A time period when one or more factors of production cannot be
changed to change output. These inputs are called fixed inputs.
Long-run
• A time period when all inputs are variable.

24. Short run Production
Function
• The shape of a short-run production curve is such
that it is first convex from below and then
concave from below.
• This is because of the operation of the Law of
Variable Returens.
• Under this law, as more and more units of the
variable input are employed in the production,
fixed inputs remaining in an original state,
production first increases at an increasing rate
and then at a diminishing rate, leading to a
decline in total production eventually.

25. • The law generally holds good, for
• (a) in the beginning as more labour is used, fixed
capital is utilized better and more efficiently than
before, thereby output increases at an increasing rate,
and this continues until optimal utilization of fixed
capital is achieved;
• (b) after this point, new(additional) labour finds the
fixed capital inadequate and hence increment in
output is at a diminishing rate and
• (c) eventually labour input becomes so much that
there is no work for new labour and so they disturb the
earlier labour, thereby leading to a decrease in total
output.

26. Short run Production
Function
• There are three stages of production
1. Increasing such that average product is rising.
2. Increasing but average product is falling
3. Decreasing.
In practice, the first stage is short, the second
stage is long and the third stage is never
entertained by a prudent enterpreneur.

27. Long Run
The decision problem which a production
manager faces in the long-run could be
1. What are the optimum quantities of labour and
capital that he should hire and employ?
• The answer to this question might depend on his
specific problem. For ex, he may have a fixed
production target and wish to find out the leastcost input combination for that level of output.
Alternatively, he could have a fixed rupee
budget for production and wish to determine
that

28. Input combination which maximizes his output for a
given cost. Lastly, neither production target nor
production budget may be fixed and the manager
might seek that input combination which maximizes
his profit.

29. • Three approaches to solve the problem.
1. Least-Cost Input Combination
2. Maximum-output Input Combination
3. Maximum-Profit Input Combination

30. Least-Cost Input
Combination
• The least-cost input combination for a given output
could be explained through any of the three forms of
the production function : table, graph and equation.
• However, since the table provides only a limited no of
alternative input combinations for any given level of
output. So consider graph only.

31. • For determining the least-cost technology,
one needs besides the production function,
factor prices.
• If PL and PK were the prices of labour and
capital, respectively, then the total cost
equation would be the following.
C = L* PL + K* PK
Where C = total cost, and L and K are units of
labour and capital. In function PL and PK are
fixed and L, K and C are variable.

32. • As isoquant map was drawn from the
production function, a map of isocost lines
could be drawn from the equation, where a
specific isocost would be for a given value of
C. Thus, if factor prices were PL = 3 and PK = 3,
an isocost line for C = 30 would have input
combinations such as
L
10
8
5
0
K
0
2
5
10

33. • Similarly, more isocost lines could be drawn,
one for each value of C.
• Thus, an isocost line gives alternative
combinations of labour and capital that a firm
could hire with a given cost.
• Since factor prices are assumed constant,
isocost lines are linear, and they are all parallel
to each other.
• Further, the higher the cost line, the greater is
the cost.

34. • Given the isoquant map and isocost lines, the
least cost input combination could easily be
derived.
• Super impose the isoquant specific to the
target population level (Q=122) and the isocost
lines map on a graph .
• Figure indicates that Q=122 could be
produced by any one of the input
combinations given by points A, B, and E.

35. • However, the production cost associated with
points A and B is higher than the one at point E,
for the former points lie on a higher cost line
(C=48) then does the latter point (C=45).
• Thus, in this case, point E is the least-cost point
for Q = 122, and so it is called the equilibrium
point.
• The input combination corresponding to this
point (L=7, K=8) is then the least-cost input
combination for Q =122.

36. • The special feature of the equilibrium point is that it
is the point where the specific isoquant is tangent
to an isocost line. Tangency implies equal slope.
• Thus, it can be concluded that the least-cost input
combination is that combination at which the slope
of the isoquant equals the slope of isocost line.
• The equality of these two slopes is the necessary
condition for least cost input combination.
• There is also a sufficient condition for the least-cost
combination, which is met if the isoquant is convex
from below.

37. • It should be clear that the least cost input mix
depends both on the production function
(isoquant) and factor prices (isocost lines).
• If any one of them undergoes a change, the
equilibrium point would change.

38. • Let us analyse the effect of a fall in the price of
labour(PL).
• As labour price falls, the isocost lines change.
• Since PK has not changed, their coordinate at
vertical axis will remain unaltered but since PL
has fallen, their coordinate at horizontal axis
would increase.

39. • The original isocost line is AB and original
equilibrium point is E. As PL falls, the cost line
changes to AC.
• The original output is now producable at original
cost by choosing the input combination of point F.
• However, this is not the least-cost technology. The
least-cost input-mix for original output level is given
by tangency point G, where the cost is lower than
at point F for the same quantity of output.

40. • Thus, due to a fall in PL, equilibrium moves from
point E to point G, showing a decrease in the
employment of capital, whose price has
remained constant, and an increase in the
employment of labour, whose price has fallen.
• As, PL falls, cost of producing a given output
declines, and this causes firms to expand its
production, leading to an increase in the
demand for both labour and capital. This is the
output effect of a fall in PL.

41. • Under the substitution effect, as PL falls, labour
becomes relatively cheaper to capital, which
induces firms to substitutes labour and capital,
thereby demand for labour expands while that
for capital contracts.
• The total effect, which is the sum of the two, of
a fall in PL is thus an increase in the
employment of labour and uncertain change
in the employment of capital. The movement
from point E to point K indicates this total
effect.

42. • But if output is held constant at the original level
, a fall in PL would lead to an increase in labour
input and a decrease in capital input, as
indicated by a movement from point E to point
G.
• The movement from point E to point G is the
pure substitution effect.

43. Maximum–Output Input Combination
• When a firm has a fixed rupee budget for its
production, its optimization problem is one of
maximizing output for a given cost.
• Since the cost is fixed, the isocost line will be
unique and output is a variable, there will be a
family of isoquants.
• The equilibrium would be determined as in
figure.

44. • In figure, the cost line (C=45) is fixed, and there
are three isoquants, one for Q = 122, second for
Q < 122 and third for Q >122.
• With a budget of Rs. 45, less than 122 units of
output is producible (e.g at points a and b) but
obviously that is not the best the firm could do.
• Point E would still mark the equilibrium point,
where 122 units are produced by employing 7
units of labour and 8 units of capital.

45. Maximum-Profit Input Combination
• Most firms today have neither a fixed output
target nor a fixed rupee budget for their
production.
• For the purpose, one needs, besides the
production function and factor prices, the
product price or the demand curve.
• For a constant product price case, the
equilibrium is explained in figure.
• Quadrant I gives the equilibrium inputcombinations for various output levels.

46. • The result of this quadrant in terms of outputs and
the corresponding least-costs are transferred in
terms of the total cost curve in quadrant III.
• The total revenue(TR) curve is drawn on the basis
of a given product price (= slope of the TR curve).
• The horizontal gap between TR and TC curves
represents profits for various output levels.
• The output at which profit is maximum is the profitmaximizing output and the input combination
corresponding to this output is profit-maximizing
technology.

47. • Thus, L3 units of labour and K3 units of capital
is the profit-maximizing input combination,
and the line AB in quadrant III gives the
measure of maximum profit

48. Expansion Path & Returns to scale
• The curve OP is the expansion path. It is the set
of lines of the least-cost input combinations for
various output levels, which is the same as the
set of lines of maximum-output input
combinations for various cost constraints.
• Thus, if a firm desires to expand its output from
Q1 to Q2 its total cost would increase from C1
to C2, and so on.
• This, together with the output-revenue
relationship would help the firm to decide on its
expansion strategy.

49. • Figure also includes the ridge lines OR1 and
OR2.
• These lines separate the economic region from
the non-economic region.
• All least cost input combinations are in the
economic region and thus the expansion path
necessarily falls between the two ridge lines.
• The ridge line OR1 passes through those points
on various isoquants, where the isoquants are
either vertical or upward sloping.

50. • This is because the economic choice can not fall
on the vertical or rising part of any isoquant, for in
that region the firm would need to employ more of
capital with a same amount of labour or more of
both inputs than on a point immediately
preceding such a point for producing the same
level of output.
• For ex, for producing Q1 output, input combination
of point B is inferior to that of point A, as the former
requires more of both labour and capital than the
latter for producing the same output.

51. • Similarlyl, line OR2 passes through those points
on various isoquants, where the isoquants are
either horizontal or upward sloping.
• The economic region must fall on the falling
and convex (from below) parts of isoquants.

52. Return to scale
• Returns to scale provides a measure of the
direction of change in total factor
productivity when all factors of production
change in the same direction and same
proportion.
• Thus, increasing returns to scale, which means
as all inputs increase in a given
proportion(multiple), output increases by
more than that proportion (multiple), implies
increase in total factor productivity.

53. • If output increases by the same multiple as all
inputs have increased, there are constant
returns to scale and there is no change in total
factor productivity
• Finally, if output increases by a smaller multiple
than have all inputs, there are decreasing
returns to scale and a decrease in total factor
productivity.
• In general production function is given by
Q = A * Lᵅ * Kᵝ

54. Elasticity Concept
• There is an elasticity concept which is related to the
returns to scale concept.
• This is called the all input elasticity of output and is
defined as follows:
e Q,I = % change in output
% change in all inputs
Where Q = output, I = all inputs
If e Q,I >1, there are increasing returns to scale.
Returns to scale are constant if e Q,I =1 and
decreasing if e Q,I <1.

55. Production Analysis : Short-run
• Factor productivities in the short-run consist of
total, average and marginal physical products
of each of the variable inputs.
• Since all but one inputs are taken as constant,
these are referred to as partial factor
productivities.
APPL = TPPL / L
MPPL = Δ(TPPL) / ΔL (if function is
discrete)

56. Total Marginal and Average physical Product
curves
1. As long as TPPL increases at an increasing rate,
both APPL and MPPL increase. MPPL declines
monotonically when TPPL increases at a
decreasing rate.
2. MPPL is maximum at the point of inflexion
(where the curvature of the TPPL curve
changes from convex to concave or vice
versa) on the TPPL curve (L=OL1)
3. MPPL = 0 when TPPL is maximum (L=OL3)
4. APPL is increasing when MPPL > APPL

57. 5. APPL is maximum when MPPL = APPL, or at
the point where the slope of the straight line
from origin to the TPPL curve is maximum
(L=OL2)
6. APPL is decreasing when MPPL < APPL
7. MPPL reaches its maximum value before
APPL and APPL before TPPL

58. • As seen in the short-run production function,
the TPPL curve is first convex from below and
then concave from below because of the
operation of the law of variable (diminishing)
returns.
• Since APPL and MPPL curves are simple
mathematical derivations from TPPL curve, the
shapes (close to inverted U) are also due to the
working of the law of diminishing returns.

59. • Short-run factor productivities depend on the
magnitudes of fixed inputs.
• If the quantity of fixed inputs employed by the
firm increases, each of the three short-run
productivities would increase.
• Thus, in the above example, if K increases from
K =2 to K = 3, each of TPPL, APPL and MPPL
would increase, thereby there would be an
upward shift in each of the three curves in
figure.

60. • The same thing would result in the face of an
improvement in the technology.
• Thus, the introduction of computer into
business would result into an improvement in
labour productivity.

61. Production Analysis:
Long run versus Short run
• The long run expansion path is given by the curve
OABCDE.
• If capital input was fixed at K = K bar, the short run
expansion path will be given by the curve OXYCZ.
• Thus, point A denotes the least-cost input combination
for output level of Q1 in the long-run, point X denotes
the same in the short-run.
• This is because if the firm operates at point A in the
short-run it would use OL2 units of labour and OK1 units
of capital, but since it has fixed units of capital, it would

62. • have to pay for OL2 units of labour and OK bar units of
capital, leaving K1 K-, units of capital unemployed.
• In contrast, if it operates at point X, it would pay for a
fewer units of labour (=OL1 < OL2) and the same units of
capital as at point A.
• Thus, assuming the firm has no other use of extra units of
capital, the short-run least cost input combination for Q
= Q1 is given by point X and not by point A.
• By the same reasoning, the short-run least-cost
technologies for output levels Q2,Q3,Q4 are given by
points Y,C and Z respectively.

63. • Note that there is no way by which the firm could
produce Q5 units of output in the short-run, for Q5
isoquant lies above the capital constraint (K bar).
• In other words, Q5 is above the firm’s capacity output
in the short-run.
• It is interesting to note that one and only one of the
least-cost input combinations of the long-run is also
the least –cost input combination of the short-run.
• Here it is represented by point C and it is for Q=Q3.
• At this point alone, long run total cost equals short-run
total cost.

64. • For all other output levels, short-run total cost
exceeds long-run total cost.
• This point can be seen easily by observing that
the cost line passing through point X would be
above the one passing through point A (both
cost lines would have the same slope, for
factor prices are given), the one passing
through point Y would be above the one
passing through point B, and so on.