Production analysis me

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.

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