1. Production Function
In Long Run
Presented By:
Tryambak
Ankit Gupta

2. Concept of Production
• In General Terms– Production means transforming inputs (labour,
machines, raw materials, time, etc.) into an output. This concept of
production is however limited to only ‘manufacturing’.
• In Managerial Terms – Creation of utility in a commodity is production.
• In Economical Terms – Production means a process by which resources
(men, material, time, etc.) are transformed into a different and more useful
commodity or service.
Where;
Input – It is a good or service that goes into the process of production.
Output – It is any good or service that comes out production process.

3. The Production Function
• A Production Function is a tool of analysis used to explain the input-
output relationship. It expresses physical relationship between
production inputs and the resultant output. It tells us that how
much maximum output can be obtained in the specified set of
inputs and in the given state of technology.
• Mathematically, the production function can be expressed as
Q=f(K, L)
• Q is the level of output
• K = units of capital
• L = units of labour
• f( ) represents the production technology

4. The Production Function(cont’d…)
• When discussing production function, it is important to distinguish
between two time frames.
• The short-run production function which may also be termed as ‘single
variable production function’ describes the maximum quantity of good or
service that can be produced by a set of inputs, assuming that at least one
of the inputs is fixed at some level which means that the production can be
increased by increasing the variable inputs only. It can be expressed as;
Q = f(L)
• The long-run production function which may also be termed as ‘returns
to scale’ describes the maximum quantity of good or service that can be
produced by a set of inputs, assuming that the firm is free to adjust the
level of all inputs. It can be expressed as;
Q = f(K, L)

5. Production Function in the Long Run
• Long run production function shows relationship between
inputs and outputs under the condition that both the inputs,
capital and labour, are variable factors.
• In the long run, supply of both the inputs is supposed to be
elastic and firms can hire larger quantities of both labour and
capital. With large employment of capital and labour, the
scale of production increases.

6. Isoquant Curve
• The term ‘isoquant’ has been derived from the Greek word
iso meaning ‘equal’ and Latin word quantus meaning
‘quantity’. The ‘isoquant curve’ is, therefore, also known as
‘Equal Product Curve’.
• An isoquant curve is locus of points representing various
combinations of two inputs - capital and labour - yielding the
same output ,i.e., the factors combinations are so formed that
the substitution of one factor for the other leaves the output
unaffected.
• It is drawn on the basis of the assumption that there are only
two inputs, i.e., labour(L) and capital(K), to produce a
commodity X.

7. Isoquant Schedule
A schedule showing various combinations of two inputs (say
labour and capital) at which a producer gets equal output is
known as isoquant schedule. The table depicts that all
combinations A,B,C,D and E of labour and capital give 2000
units of output to a producer. Hence, the producer remains
neutral.
Labour Capital Output
Combination
(L) (K) (Q,Units)
A 1 15 2000
B 2 10 2000
C 3 6 2000
D 4 3 2000
E 5 1 2000

8. Isoquant Curve -
Diagrammatic Presentation
Y
Capital
A
K2
B
K1 IP
(2000 units)
X
0 L1 L2
Labour

9. Characteristics of Isoquant Curve
• They slope downward to the right : They slope downward to the
right because if one of the inputs is reduced, the other input has to be so
increased that the total output remains unaffected.
• They are convex to the origin : They are convex to the origin because
of Marginal Rate of Technical Substitution of labour for capital. (MRTSLK) is
diminishing. MRTSLK is the slope of an isoquant curve. Isoquant curves are
negatively sloped.
• Two isoquant curves do not intersect each other : Two isoquant
curves do not intersect each other as it is against the fundamental condition that a
producer gets equal output along an isoquant curve.
• Higher the isoquant curve higher the output : A producer gets
equal output along an isoquant curve but he does not get equal output among the
isoquant curves. A higher isoquant curve yields higher level of output.

10. Marginal Rate of Technical
Substitution (MRTS)
The MRTSlk is the amount of capital forgone for employing an
additional amount of labour. Hence, it is a rate of change in factor K in
relation to one unit change in factor L. This rate of change is
diminishing. So the slope of iso-product curve is diminishing.
Slope = -dK/dL = change in capital/change in labour = MRTSlk
Combination Labour Capital MRTSlk
(L) (K) (-dk/dl)
A 1 15 -
B 2 10 5/1
C 3 6 4/1
D 4 3 3/1
E 5 1 2/1

11. Marginal rate of technical
substitution (MRTS)
K
7
6 ΔK=3
5
4
ΔL=1 MRTS = ∆K
∆L
3 ΔK=1
ΔL=1
2
1 ΔK=1/3
ΔL=1
0 L
0 1 2 3 4 5 6 7

12. Isoquant Curve
Y
5 E
4
Capital 3
A B C
2
Q3 =90
D Q2 =75
1
Q1 =55
1 2 3 4 5 X
Labour

13. Iso-cost Curves
An Iso-cost curve on the one hand shows the resources of producer and on
the other hand it shows relative factor price ratio. It shows various
combinations of two factors (say labour and capital) that can be employed by
the producer in the given producer’s resources.
Y K
Slope = w/r
Capital
Cost Region
X
0 Labour L
Its slope is given by relative factor prices i.e. w/r where w is wage rate (price
of labour) and r is rate of interest (price of capital). The area under an iso-cost
line is known as cost region. In order to obtain least cost combination, cost
region is super imposed over production region.

14. Increasing Constant Diminishing
returns to scale returns to scale returns to scale
Total output may increase Total output may Total output may increase
more than proportionately Increase proportionately Less than proportionately

15. Increasing Returns to Scale
When a certain proportionate change in both the inputs, K and L, leads
to a more than proportionate change in output, it exhibits increasing
returns to scale. For example, if quantities of both the inputs, K and L,
are successively doubled and the corresponding output is more than
doubled, the returns to scale is said to be increasing.
Schedule
Labour and Output Proportional Proportional
Capital (TP) change in change in
labour and output
capital
1+1 10 - -
2+2 22 100 120
4+4 50 100 127.2
8+8 125 100 150

16. Increasing Returns to Scale-
Diagrammatic Presentation
Y Scale Line
A
OP>PQ>QR>RS
S
R IP4 (400)
Capital
Q IP3 (300)
P IP2 (200)
IP1 (100)
0 X
Labour

17. Constant Returns to Scale
When the change in output is proportional to the change in inputs, it
exhibits constant returns to scale. For example, if quantities of both the
inputs, K and L, are doubled and output is also doubled, then returns to
scale are said to be constant.
Schedule
Proportional
Proportional
Labour and Output change in
change in
Capital (TP) labour and
output
capital
1+1 10 - -
2+2 20 100 100
4+4 40 100 100
8+8 80 100 100

18. Constant Returns to Scale-
Diagrammatic Presentation
Y Scale Line
A
OP=PQ=QR=RS
S
R IP4 (400)
Capital
Q IP3 (300)
P
IP2 (200)
IP1 (100)
0 X
Labour

19. Diminishing Returns to Scale
When a certain proportionate change in inputs, K and L, leads to a less
than proportionate change in output. For example, when inputs are
doubled and output is less than doubled, then decreasing returns to
scale is in operation.
Schedule
Labour and Output Proportional Proportional
Capital (TP) change in change in
labour and output
capital
1+1 10 - -
2+2 18 100 80
4+4 30 100 66.6
8+8 45 100 50

20. Diminishing Returns to Scale-
Diagrammatic Presentation
Y Scale Line
OP<PQ<QR<RS A
S
IP4 (400)
R
Capital
IP3 (300)
Q
P IP2 (200)
IP1 (100)
X
0
Labour

21. Thank you for your time and attention!