PRODUCTION ANALYSIS
PRODUCTION
Production is concerned with
the way in which resources or inputs such as land, labor, and machinery are
employed to produce a firm’s product or output.
Production may be either services or goods. To produce the goods we use inputs. Basically inputs are divided into two types.
those are fixed inputs and variable inputs.
Fixed inputs are the inputs that remain constant in short-term. Variable inputs are inputs, which are
variable in both short-term and long-term.
Production Function
Production function expresses
the relationship between inputs and outputs.
Production function is an equation, a table, a graph, which express the
relationship between inputs and outputs.
Production function explains that the maximum output of goods or
services that can be produced by a firm in a specific time with a given amount
of inputs or factors of production.
Production
Function: Q = f (K, L)
We are producing Q quantities
of goods by employing K capital and L labor.
Here
Q Represents
quantity of goods
K Represents
Capital employed
L Represents
Labor employed
Production
Function:
“Production Function” is that
function which defines the maximum amount of output that can be produced with a
given set of inputs.
–
Michael R Baye
“Production
Function” is the technical relationship, which reveals the maximum amount of
output capable of being produced by each and every set of inputs, under the
given technology of a firm. - Samuelson
From the above definitions,
it can be concluded that the production functions is more concerned with
physical aspects of production, which is an engineering relation that expresses
the maximum amount of output that can be produced with a given set of inputs.
Production function enables
production manager to understand how better he can make use of technology to
its greatest potential.
The production function is
purely a relationship between the quantity of output obtained or given out by a
production process and the quantities of different inputs used in the
process. Production function can take
many forms such as linear function or cubic function etc.
Assumptions
for Production Function:
1.
Technology
is assumed to be constant.
2.
It
is related to a particular or specific period.
3.
It
is assumed that the manufacturer is using the best technology.
4.
All
inputs are divisible.
5.
Utilization
for inputs at maximum level of efficiency.
Significance
/ Importance of Production Function :
1.
Production function shows the maximum
output that can be produced by a specific set of combination of input factors.
2.
There are two types of production function,
one is short-run production function and the other is long-run production
function. The short-run production
explains how output change is relation to input when there are some fixed
factors. Similarly, long run production function
explains the behaviors of output in relation to input when all inputs are
variable.
3.
The production function explains how a firm
reaches the most optimum combination of factors so that the unit costs are the
lowest.
4.
Production function explains how a producer
combines various inputs in order to produce a given output in an economically
efficient manner.
5.
The production function helps us to
estimate the quantity in which the various factors of production are combined.
Short-Term
production function
Short-Term production
function is a function, which we are producing goods in the short-term by
employing two inputs that are :
Capital (K) : It is fixed input which is constant in the
short-term.
Labor (L) : It
is variable input in the short-term.
·
In the short-term we are producing only one
product by employing two inputs
·
The two inputs are K capital and L is
labor.
·
In the short term we will increase L input
and we will keep K as constant.
Units of K
Employed
|
Output Quantity
|
|||||||
8
|
37
|
60
|
83
|
96
|
107
|
117
|
127
|
128
|
7
|
42
|
64
|
78
|
90
|
101
|
110
|
119
|
120
|
6
|
37
|
52
|
64
|
73
|
82
|
90
|
97
|
104
|
5
|
31
|
47
|
58
|
67
|
75
|
82
|
89
|
95
|
4
|
24
|
39
|
52
|
60
|
67
|
73
|
79
|
85
|
3
|
17
|
29
|
41
|
52
|
58
|
64
|
69
|
73
|
2
|
(8)
|
(18)
|
(29)
|
(39)
|
(47)
|
(52)
|
(56)
|
(52)
|
1
|
4
|
8
|
14
|
20
|
27
|
24
|
21
|
17
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
|
Units of L
employed
|
||||||||
·
You can observe in the table we are
producing 8 quantities of goods by employing 2 capital and 1 labor.
·
Here when we increased labor 1 to 2, output
is 18. When we increased labor from 2 to
7 the total output reached to 56 quantities with constant K=2 CAPITAL.
·
After certain point of time (L=8) the
output is starts to decease i.e. 52.
In
this case we have to understand, in the short-term by increasing labor without
increasing capital, after certain level, the output starts to decrease. The reason to decrease the output is The Law
of Diminishing Returns.
The Law of Diminishing
Returns
The
key to understanding the pattern for change in Q is the phenomenon known as the
law of diminishing returns. This law
states :
As
additional units of variable input are combined with a fixed input, at some
point the additional output (i.e. marginal product) starts to diminish.
Diminishing
returns are illustrated in both the numerical example in Table and the graph of
these same numbers in Figure. As you examine
this information, think “Change” as you see the word “marginal”. Therefore, the “Total product” of an input
such as labor is the change in output resulting from an additional units of
input.
There
are two key concerns of a practical nature that we advise readers to keep in
mind when considering the impact of the law of diminishing returns in actual
business situations. First, there is
nothing in the law that states when diminishing returns will start to take
effect. The law merely says that if
additional units of a variable input are combined with a fixed input, at some
point, the marginal product of the input will start to diminish. Therefore, it is reasonable to assume that a
manager will only discover the point of diminishing returns by experience and
trial and error, Hindsight will be more valuable than foresight. Second, when economists first stated this
law, they made some restrictive
assumptions about the nature of the variable inputs being used. Essentially, they assumed that all inputs
added to the production process were exactly the same in individual
productivity. The only reason why a
particular unit of input’s marginal product would be higher or lower than the
other used was because of the order in which it was added to the production
process.
The
Three states of Production in the Short Run:
The
short-run production function can be divided into three distinct stages of
production. To illustrate this
phenomenon, let us return to the data in Figure 7.1 has been reproduced as
Figure 7.2. As the figure indicates.
Stage
– I
Stage I runs from Zero to
four units of the variable input L (i.e. to the point at which average product
reaches its maximum)
Stage
– II
Stage II begins from five
units of variable input and proceeds to seven units of input L (i.e. to the
point at which total product is maximized).
Stage
– III
Stage III Continues on from
that point.
According to economic theory,
in the short run, “rational” firms should only be operating in stage II. It is clear why stage III is irrational; the
firm would be using more of its variable input to produce less output ! However, it may not be as apparent why stage I
is also considered irrational. The
reason is that if a firm were operating in stage I, it would be grossly
underutilizing its fixed capacity. That
is, it would have so much fixed capacity relative to its usage of variable inputs
that is could increase the output per unit of variable input (i.e., average
product) simply by adding more variable inputs to this capacity. Figure 7.3a summarizes the three stages of
production and the reasons that the rational firm operates in stage II of the
short-run production function.
The
Long-Run Production Function :
In the long run, a firm has
time enough to change the amount of all of its inputs. Thus, there is really no difference between
fixed and variable inputs. Table 7.5
uses the data first presented in Table 7.1 and illustrates what happens total output
as the data first presented in Table 7.1 and illustrates what happens to total
output as both inputs X and Y increase one unit at a time. The resulting increase in the total output as
the two inputs increase is called returns
to scale.
Looking more closely at Table
we see for example that if the firm uses 1 unit of X and 1 unit of Y, it will
produce 4 units of output. If it doubles
its inputs (i.e. 2 units of X and 2 and units of Y) it will produce 18 units of
output. Thus, a doubling of inputs has
produced more than a fourfold increase in output. Proceeding further, we notice that an
additional doubling of inputs (i.e. 4 units for X and 4 units of & Y)
results in more than a threefold increase in output, from 18 to 60. What we are observing in this table is
increasing returns to scale.
Units of Employed
|
Output Quantity
|
|||||||
8
|
37
|
60
|
83
|
96
|
107
|
117
|
127
|
(128)
|
7
|
42
|
64
|
78
|
90
|
101
|
110
|
(119)
|
120
|
6
|
37
|
52
|
64
|
73
|
82
|
(90)
|
97
|
104
|
5
|
31
|
47
|
58
|
67
|
(75)
|
82
|
89
|
95
|
4
|
24
|
39
|
52
|
(60)
|
67
|
73
|
79
|
85
|
3
|
17
|
29
|
(41)
|
52
|
58
|
64
|
69
|
73
|
2
|
8
|
(18)
|
29
|
39
|
47
|
52
|
56
|
52
|
1
|
(4)
|
8
|
14
|
20
|
27
|
24
|
21
|
17
|
According to economic theory,
if an increase in a firm’s inputs by some proportion results in an increase
output by a greater proportion, the firm experiences increasing returns to
scale. If output increases by the same
proportion as the inputs increase, the firm experiences constant returns to
scale. A less than proportional increase
in output is called decreasing returns to scale.
You might simply assume that
firms generally experience constant returns to scale. For example, if a firm has a factory of a
particular size, then doubling its size along with a doubling of workers and
machinery should lead to a doubling of output.
Why should it result in a greater than proportional or, for that matter,
a smaller than proportional increase ?
For one thing, a larger scale of production might enable a firm to
divide up tasks into more specialized activities, thereby increasing labor
productivity. Also a larger scale of
operation might enable a company to justify the purchase of more sophisticated
(hence, more productive) machinery. These
factors help to explain why a firm can experience increasing returns to
scale. ON the other hand, operating on a
larger scale might create certain managerial inefficiencies (e.g.
communications problems, bureaucratic red tape) and hence cause increasing or
decreasing returns to scale in the next chapter, when we discuss the related
concepts of economies diseconomies of scale.
One way to measure returns to
scale is to use a coefficient of output elasticity.
EQ = Percentage change in
Q
Percentage change
in all inputs
Thus,
If E > 1, we have increasing
returns to scale (IRTS).
If E = 1, we have increasing returns
to scale (CRTS).
If E < 1, we have increasing
returns to scale (DRTS)
Returns
to factors:
Returns to factors are also
called as factor productivities, (Productivity, is the ratio of output to the
inputs)
The productivity of a particular
factor of production may be measured by assuming the other production factors
to be constant and only that particular factor under study is charged.
Returns to factors shows the
percentage increase or decrease in the production due to percentage increase or
decrease in a particular factor such as labors (or) capital, assuming other
factors to be constant. These returns
may be increasing diminishing or constant.
The change in productivity
can be measured in terms of the following.
1.
Total Productivity: The total output obtained at varied levels of
particular input factor (while other factors remain constant) is called total
productivity.
2.
Average Productivity : Average productivity can be determined by
dividing the total physical product (production) with the number of particular
input factor that is used.
3.
Marginal Productivity: The marginal productivity is the additional
output generated by adding an additional unit of that particular factor keeping
the other factors remains constant.
Economies
of Scale:
As a result of increasing
production the production cost is low, and it is known as economies of scale.
As long as the output is
increased in the long run, the cost of production will be at minimum level,
this is known as economies of scale, Economies of scale is divided into two
parts.
1.
Internal Economies
2.
External Economies
Internal
Economies:
Internal economies are those
benefits or advantages enjoyed by an individual firm if it increases its size
and the output.
Types
or Forms of Internal Economies :
1.
Labors Economies : A large firm can attract specialist or
efficient labors and due to increasing specializations the efficiency and
productivity will be increased, leading to decrease in the labors cost per unit
of output.
2.
Technical Economies: A large firm can adopt and implement the new
and latest technologies, which helps in reducing the cost of manufacturing
process, whereas the small firm may not have the capacity to implement latest
technologies. A large firm can make
optimum utilization of machinery, and it can manage the production activities
in continuous series without any loss of time thereby saving the time and
transportation cost.
3.
Managerial Economies: The managerial cost per unit will decrease
due to mass scale production. Like, the
salary of general manager, which remains the same whether, the output is high
or low. Moreover, a large firm can
recruit the skilled professionals by paying them a good salary, but a small
firm does not have the much of capacity to pay high salaries. Thus, mass scale of production will decrease
the managerial cost per unit.
4.
Marketing Economies: A large firm can purchase their requirements
on a bulk scale therefore, they get a discount.
Similarly the advertisement cost will be reduced because a large firm
produces a variety of different types of products. Moreover, a large firm can employ sales
professional for marketing their products effectively.
5.
Financial Economies: A large firm can raise their financial
requirements easily from different sources than a small one. A large firm can raise their capital easily
from the capital market because the investor has more confidence on the large
firm than in small firm.
6.
Risk Bearing Economies: The large firm can minimize the business risk
because it produces a variety of products.
The loss in one product line can be balanced by the profit in other
product line.
External Economies
External Economies are those benefits,
which are enjoyed by all the firms in an industry irrespective of their increased
size and output. All the firms in the
industry share external economies.
1. Economies of Localization: When all the firms are
situated at one place, all the firms will be enjoying the benefits of skilled
labors, infrastructure facilities and cheap transport thereby reducing the
manufacturing cost.
2. Economies of Information: All the firms in an industry can have a common
research and development center through which the research work can be
undertaken jointly. They can also have
the information related to market and technology.
3. Growth of subsidiary Industry: The production process can
be divided into different components.
Specialized subsidiary firms at a low cost can manufacture each
component.
4. Economies of By-Products: The waste materials released by a particular
firm can be used as an input by the other firm to manufacture a by-product.
Isoquants
‘Iso’ refers to ‘equal’,
‘quanta’ refers to ‘quantity’. An
isoquant may be defined as a curve, which shows the different combinations
of two inputs producing the same level
of output. Graphically the isoquant can
be drawn conveniently for two factors of production.
Example
The table given below can easily understand the concept
of isoquant.
Producer Equilibrium with the help of Isoquants
Producer will try to reach that combination of inputs
where output is maximized at least cost thereby profits will be maximize.
Combination Capital Labors Output
(units)
A 1 15 10,000
B 2 10
10,000
C 3 6
10,000
D 4 3
10,000
The above table shows the
different combination of input factaors (i.e. capital and labor) to produce an
amount of 10,000 units. The combination
of A shows 1 unit of capital and 15 units of labors to produce 10,000 units. The combination of A shows 1 unit of capital
and 15 units of labors to produce 10,000 units.
Similarly, B, C and D employs 2C + 10L, 3 + 6L and 4C + 3L respectively
to produce the same amount of output i.e. 10,000 units.
The
plotting of all these combinations can be seen in the above
graph,
the locus of all the possible combinations of inputs forms an isoquant.
Isoquants are also called as
isoproduct curves (or) production indifference curves. An isoquant curve shows various combinations
of two inputs factors w such as capital and labors, which are capable of
producing fixed (or) same level of output.
Thus an isoquant shows all
such combinations which yields equal quantity of output and producer can choose
any combination because all these combinations yield same output.
Assumptions
:
1)
Two factors can be substituted for each
other
2)
No change in technology.
Main Properties or Features of an
Isoquant :
(1) Isoquant is a Negatively Sloped Curve (i.e.,
Downward Sloping) : Isoquants
are negatively slope curves because, if one input increases, the other
decreases. The two inputs are inversely
proportional to each other. Therefore
there is no question of increase in both the inputs to yield a given
output. Here, a degree of substitution
is assumed between these inputs.
(2) Do not Overlap :
No two isoquant (overlap)
with each other, because, each of these denote a specific level of output with
different combinations of inputs.
(3) Convex
to Origin:
In isoquant, one input factor
can be substituted by other input factor in a ‘diminishing marginal rate’. This means the input factors are not perfect
substitutes. As a result of this,
isoquants were bulged towards origin (becomes convex to origin).
(4) Do
not interest Axes:
The isoquants neither touch
X-axis not Y-axis, as some amount of both inputs are required to produce a
given output.
Types
of isoquants
Diagram
Here, there is perfect substitutability of inputs. For example, a given output say 100 units can be produced by using only capital or only labor or by a number of combinations of labor and capital, say 1 units of labor and 5 units of capital, or 2 units of labor and 3 units of capital, and so on. Likewise given a power plant equipped to burn either oil or gas, various amounts of electric power can be produced by burning gas only, oil only or varying amounts of each. Gas and oil are perfect substitutes here. Hence, the isoquants are strait lines (Fig.3).
(2) Right-angle isoquant :
Here, there is complete
non-substitutability between the inputs 9or strict complimentarily). For example, exactly two wheels and one frame
are required to produce a bicycle and in no way can wheels be substituted for
frames or vice-versa. Likewise. Two
wheels and one chassis are required for a scooter. This is also known as Leontief Isoquant or
Input-output isoquant.
Diagram
(3) Convex
Isoquant :
This form assumes
substitutability of inputs but the substitutability is not perfect. For example, a shirt can be made with
relatively small amount of labor (L1) and a large amount of cloth (C1). The same shirt can be as well made with less
cloth (C2), if more labor (L2) is used because the tailor will have to cut the
cloth more carefully and reduce wastage.
Finally, the shirt can be made with still less cloth (C3) but the tailor
must take extreme pains so that labor input requirement increases to L3. So, while a relatively small addition of
labor from L1 to L2 allows the input of cloth to be reduced from C1 to C2, a
very large increase in labor from L2 to L3.
Diagram
Marginal Rate of
Technical Substitution :
The slope of the isoquants has a technical
name called Marginal Rate of Technical Substitution” (MRTS).
The rate at which one factor
of production (input) can be substituted for other is known as marginal rate of
technical substitution. If we assumed
two factors of production say labors and capital, then the marginal rate of
technical substitution of capital for labors is the number of units of labors,
which can be replaced by one unit of capital, while the quantity of output
remaining the same.
For example, we assumed in
the above table that an output of 10,000 units could be obtained with either
applying 1 unit of capital and 15 units of labors or employing 2 units of
capital and 10 units of labors. This
means, in the different combinations of input capital can be substituted for
labors and yet we have the same output.
Isocosts :
Isocost refers to that cost
curve which will show the various combinations of two inputs, which can be
purchased with a given amount of total money.
Diagram
Isocosts each showing
Different Level of Total Cost :
In the above figure it can be
seen that as the level of production changes.
The total cost will change and automatically the isocost curve moves
upward.
We can easily superimpose the
isocost diagram on the isoquant diagram (as the axes in both the cases
represent the same variable). With the
help of following figure :
Diagram
We can ascertain the maximum
output for a given outlay, say Rs.1000.
The isoquant tangent to the isocost curve represents this maximum
output, which is possible with this outlay cost. The point of intersection E represents the
optimum combination of inputs.
The point of tangency E on
the isoquant curve represents the least cost combination of inputs, Yielding
maximum level of output.
The Cobb-Douglass Production Function
(p.265 Dominick Salvatore) :
The Cobb-Douglass production
function was introduced in 1928, and it is still a common functional form in economic
studies today. It has been used
extensively to estimate both individual firm and aggregate production
functions. It has undergone significant
criticism but has endured. “It is now
customary practice in economics to deny its validity and then to use it as an
excellent approximation”. It is was
originally constructed for all of the manufacturing output (Q) in the United States
for the years 1899 to 1922. The two
inputs used by the authors were number or manual workers (L) and fixed capital
(K). The formula for the production
function, which was suggested by Cob, was of the following form :
Q
= AKaLb
Q quantity output
K capital
L labor
And
A, a, b are the parameters.
The
exponents of the K and L (a, b) represents respectively.
The
output elasticity of L (E1) and capital (Ek)
Here
Ek = Elasticity of Capital
And
EK + EL = a+b = Returns to Scale
a+b
= 1 i.e. constant returns
a+b
> 1 i.e. increase sing returns to scale
a+b
< 1 i.e. decreasing returns to scale
Innovation and global competitiveness
Innovation means
inventing and introducing a new or modified product in the market Innovations
are two types.
1.
product innovation
2. process
innovation
Product innovation
Means
the introduction of new or improved product
Process innovation
Means
the introduction of new or improved production process Innovation can be
examined with isoquants. A new or
improved product requires a new isoquant map showing the various combinations
of inputs to be produce each level of output of the new or improved product.
Ex
: The Xerox corporations, the inventor
of the copier in 1959, lost its competitive edge to Japanese competitors in the
1970s before it shook off its complacency and learned again how become to
compete during the 1980s.
The risk in introducing innovation is usually
high. For example 8 out of 10 new
products fail shortly after their introduction.
Innovation for global competitiveness
(p.269 Dominick Salvatore)
We can say much more example for
successful innovations.
Humble Advice: This is not fully covered
material. Refer prescribed books by
J.N.T.U. for full information.
Prepared & Sponsored by
Mr. M. Jakkaraiah
Mr. M. Jakkaraiah
M.B.A.,M.C.A.,A.P S.E.T.
Written by Ramu Magham
Ramu Magham is an English Language Teacher who drives his students crazy with trending technologies and current happenings.
Thanks for sharing as it is an excellent post would love to read your future post -for more knowledge
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