2. Producer has to decide on…..
How much to produce
What capacity to be installed
What combination of inputs to be
employed to maximise profits and
minimise costs
At what price to sell
3. Production function
A production function is a functional
specification that provides the most efficient
combination of input with which a chosen
target level of output can be produced.
It is specific to each industry and
technology.
Decisions that producers need to make:
– To meet increased demand, should the
firm go in for capacity expansion or
stretch the existing production facilities.
– How should they handle existing idle
capacity.
4. Production Function
Decision variable involved in production
decisions are – Inputs and Output
Input is anything that the firm employs in
the production process
Output is what the firm produces making
use of inputs.
Production functions change when the
technical process of production change
leading to an entirely different set of input
combinations related in an entirely
different manner.
5. Production Function with two
variable inputs
Q = f (K , L) where K is capital and L
is labour.
Given a target level of output, this
function gives us the highest level of
output that can be produced from a
given combination of inputs.
Production function can take many
forms like F(L,K) = 3L + 2K2, or, 5K0.5 L0.5,
or any other form
6. Production function…
Consider the following combination of
inputs for the production of a given level
of output, say 160 cars.
Given f(L,K) = 5K0.5L0.5
Combination L K Output
A 50 20.5 160
B 40 25.6 160
C 30 34.13 160
D 20 51.2 160
7. Production function…
Consider the following combination of
inputs for the production of different levels
of output
Given f(L,K) = 5K0.5L0.5
Combination L K Output
A 50 20.5 160
B 40 40 200
C 30 120 300
D 20 128 400
8. Isoquant
An isoquant is a curve on which
every point satisfies the production
function and thus, all combination of
L and K on an isoquant are
technically efficient combination with
which the given level of output can
be produced.
Each isoquant corresponds to a
different level of output.
9. Production Function with
Isoquant Map
Y O U T P U T
8 37 60 83 96 107 117 127
7 42 64 78 90 101 110 119
6 37 52 64 73 82 90 97
5 31 47 58 67 75 82 89
4 24 39 52 60 67 73 79
3 17 29 41 52 58 64 69
2 8 18 29 39 47 52 65
1 4 8 14 20 27 24 21
X 1 2 3 4 5 6 7
10. Isoquant map
The preceding table represents a
production function with two inputs, X and
Y
It can be observed that combinations (2,6),
(3,4), (4,3), (6,2)yield same level of
output, that is 52.
By connecting the combinations we get the
isoquant corresponding to output level 52
Similar combinations for different levels of
output can be produced can be extracted
from the table.
11. Isoquants
Graphical representation of
production function
A curve drawn through the technically
feasible combinations of inputs to
produce a target level of output
K
Output 260
Output 200
Output 160
Marginal rate of technical substitution
L
is the substitution of one input for
another. MRTS = -change in K/change
in labor
12. Properties of Isoquants
They are downward sloping – That is as you
employ more and more of the input on the X
axis, you necessarily employ less of the input
on the Y axis in order to maintain the same
level of output. Employing more of both inputs
would lead to a higher isoquant.
They are convex to the origin – This happens
as the power to substitute diminishes, called
as the marginal physical product as we
employ more and more of a factor. However,
in case of perfect substitutes the isoquant is a
downward sloping straight line with a
constant slope, while for perfect complements
the isoquant is a L shaped curve.
13. Properties of Isoquants
They do not intersect each other
Application of Isoquants
Isoquants enable the decision maker to
conceptualize the trade-offs involved in
substitution between inputs. Managers
consider the costs and benefits of
substituting one input for another and select
that one where the net benefits are
maximised.
Isoquant model helps the decision maker to
figure out the increase /decrease in output
with a change in input.
14. Production function with one variable input
Short run is defined as a period during
which only one of the inputs can be
varied.
Long run is defined as a period during
which no factor is fixed and all input
factors can be varied.
Average Product : Q /L
Marginal Product : MP = dQ/dL ie it is the
increase in output for a unit increase in
the variable input.
15. Production function
Law of diminishing returns or the law of
variable proportions - According to this
relationship, in a production system with
fixed and variable inputs (say factory size and
labor), beyond some point, each additional
unit of variable input yields less and less
output
Increasing return is the stage where with
each additional unit of variable input
employed, the marginal product increases.
O
U 1 – Stage of increasing returns; Ex>1
T 1 2 – Stage of decreasing returns,0<Ex<1
P 3 3 – Stage of negative returns; Ex<0
2
U
T
16. Production function
Diminishing return is the stage where
with each additional unit of variable
input employed, the output increases but
at a decreasing rate.
The stage where with increase in
variable input, the decreasing marginal
product becomes negative, resulting in a
decline of total output. It is the stage of
negative returns. At this point the
variable factor becomes counter
productive.
O
U 1 – Stage of increasing returns; Ex>1
T 1 2 – Stage of decreasing returns,0<Ex<1
P 3 3 – Stage of negative returns; Ex<0
2
U
T
17. Production function with one
variable input
Total Product: Q = 30L+20L2-L3
Average Product : Q /L
Marginal Product : MP = dQ/dL =
30+40L-3L2
18. Production Elasticity
Production elasticity is the proportionate
change in output due to a proportionate
change in input.
∆Q / ∆X * X / Q = MPx * 1 / APx
Production elasticity greater than one
indicates that output increases by a
proportion greater than the increase in input.
In cases where the elasticity is zero, there is
no change in output due to a change in input.
For a value of production elasticity less than
zero indicates that output decreases with a
given increase in input.
19. Three Stages of Production
Stage 1: AP is increasing, MP is
increasing and Production Elasticity is
> 1. This stage corresponds to output
levels that indicate underutilization of
capacity.
Stage 2: AP and MP are decreasing,
until MP=0 and Production Elasticity
is 0 < Prod.Elas < 1. Producer’s
optimal choice of employment of
variable input lies in this stage.
20. Three Stages of Production
Stage 3: MP and AP continue to
decrease and MP <0; leading to
decrease in total product with
increasing units of input and
Production Elasticity < 0. No rational
producer would want to be in this
stage. This stage corresponds to
output levels that indicate
overutilization of capacity.
21. Relationship between Marginal physical
product and marginal rate of technical
substitution
MRTS is equal to slope of the
isoquant ie =-∆K/ ∆L
MRTS can also be expressed
algebraically. While moving from A to
B or B to C on an isoquant, the
following condition is to be satisfied:
MP x ∆L + MP x ∆K = 0
l k
Therefore - ∆K/ ∆L = MP /MP
l k
22. Returns to Scale
The rate at which output increases to a
proportionate change in all inputs is known as the
degree of returns to scale. Increasing output
given constraints of technology means moving
from one isoquant to another.
Increasing Returns to Scale - When output
increases by a proportion greater than the
proportionate increase in all inputs. Specialization
and division of labor assists in being in this stage.
Decreasing returns to scale – Output increases by
a proportion less than that of the increase in
inputs.
Constant returns to scale – Output increases by
the same proportion as the increase in inputs.
23. Estimation of production functions
There are a variety of production functions
Linear production functions: Q = a + bX,
these are subject to constant returns only
Quadratic prod. Functions: Q = a + bX –
cX2 , these capture the diminishing returns
phase ( in –cX2 ) but not the increasing
returns to scale.
Cubic form pfs.: Q = a + bX + cX2 -dX3 ,
these capture both the increasing and the
diminishing returns to scale
Power function : Q =aXb
24. Cobb – Douglas Production
Function
Q = A Lα Kβ
Q = total production (the monetary value of
all goods produced in a year); L = labor
input ;K = capital input ; A =
total factor productivity; α and β are the
output elasticities of labor and capital,
respectively
Where, α + β indicates Returns to Scale
If > 1, it exhibits Increasing Returns to Scale
If < 1, it exhibits Decreasing Returns to Scale
If = 1, it exhibits Constant Returns to Scale
25. Optimal Input Levels
Level of output determines the
demand for inputs and employment
of inputs is related to revenue
generated from the output.
Stage of decreasing – diminishing
returns is where the producer should
be operating with one variable input.
Total revenue product is total
product multiplied by the market
price of output
26. Optimal Input Levels
Marginal revenue product is the
change in total revenue product due
to a unit change in the variable input
= MP * Price
Total variable cost is total cost of the
variable input and is arrived at by
multiplying quantity of variable input
by its price.
Marginal variable cost is the change
in total variable cost due to a unit
change in the variable input.
27. Optimal Input Levels
With one variable input, producer
produces in stage of decreasing returns
produces upto the point where Marginal
Revenue Product (MRP) = Marginal
Variable Cost.
MRP = MP * MR=MVC
With many variable inputs:
MPL / PL = MPK / PK = ……….
28. Optimal Combination of Inputs
Given that each combination of
inputs have a different cost attached,
the producer needs to arrive at the
least cost combination. The concept
of the ‘isocost’ line is used for
arriving at the optimal combination.
An isocost line gives the combination
of inputs that can be purchased in
the market at the going market
prices with a tentative budget. All
combinations on this line result in
the same total cost.
29. Optimal Combination of Inputs
The point of tangency between an isocost
line and an isoquant gives the least cost
combination of inputs with which the
output level corresponding to the isoquant
can be produced. Isocost line is linear as
input prices are constant.
For a given target level of output, the
combination of inputs on the isocost line,
which is tangential to the isoquant is the
optimal combination. The optimum point
must be technically efficient (lie on the
relevant isoquant) and has to satisfy the
cost constraint).
30. Optimal Combination of Inputs
Isoproduct curve : This curve gives us the
combination of outputs that two levels of
constant input quantities can produce, assuming
production is most efficient and the inputs are
completely exhausted. The curve is concave
assuming diminishing returns occur when
specialization increases. This curve is also called
the production frontier as it indicates the highest
levels of the two outputs that can be produced
with the given inputs.
The economy can go beyond the frontier only
when the frontier shifts outward. This happens
when:
More is produced as the resource base has
expanded or technological change has occurred.
If there is trade between economies, then it is
possible for an economy to consume more than it
has produced.
