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1 MANAGERIAL ECONOMICS
INDEX
No. Contents Page no.
1
1.1
1.2
1.3
1.4
1.5
Organization of production
Production function
Organization of production
function with one variable
inputs
Organization of production
function with two variable
inputs
Production Isoquoants
Economic Region of Production
01
02
03
04
04
05
2
2.1
2.2
2.3
2.4
2.5
Empirical Production Function
Returns to scale
A Practical illustration of long
run returns to scale
Estimated ln Q , ln K and ln
L of SAIL co.
Assumptions to Empirical
Production Function
Difficulties to Empirical
Production Function
07
08
09
10-11
11
11
33.1
3.2
3.3
3.4
3.5
Company Profile(SAIL)Production Detail
Comparison between Ideal and
Actual production Curve
Descriptive Data
Regression Analysis
Executive Summary
1213
14
15
16
17
4 Bibliography 17
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1. ORGANIZATION OF PRODUCTION:
Production refers to the transformation of inputs into outputs of goods and
services. For example, IBM hires workers to use machinery, parts, and raw materials in
factories to produce personal computers. The output of a firm can either be a final commodity
(such as personal computer) or an intermediate product, such as semiconductor (which are used
in the production of computers and other goods). The output can also be a service rather than
goods. Examples of services are education, medicine, banking, communication, transportation,
and many others.
Inputs are the resources used in the production of goods and services. As a convenient way to
organize the discussion, inputs are classified in to labor (including entrepreneurial talent), capital
and land or natural resources. Each of these broad categories, however include a great variety of
the basic input. For example, labor includes bus drivers, assembly line worker, accountants,
lawyers, doctors, scientists, and many others. Inputs are also classified as fixed inputs and
variable inputs. Like....
FIXED INPUTS: fixed inputs are those that cannot be readily changed during the time period
under consideration, except perhaps at very great expense. Examples of fixed inputs are the
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firms plant and specialized equipment (it takes several years for IBM to build a new factory to
produce computer chips to go into its computer).
VARIALBLE INPUTS: variable inputs are those that can be varied easily and on very short
notice. Examples of variable inputs are most material and unskilled labour.
The time period during which at least one inputs is fixed is called the SHORT RUN, while the
time period when all inputs are variable is called the LONG RUN.
1.1 PRODUCTION FUNCTION:
Production theory involves the concept of production function. A production function is an
equation, table, or graph showing the maximum output of a commodity that a firm can produce
per period of time with each set of inputs. Both inputs and outputs are measured in physical
rather than in monetary units. Technology is assumed to remain constant during the period of the
analysis.
We assume that a firm produces only one type of output with two inputs, labor (L) and capital
(K). Thus, the general equation of this simple production function is....
Q=f(L, K)
From the above function, it can be said that quantity of output is a function of, depends on the
quantity of labor and capital used in production. Where,output means to the number of units of
the commodity produced. For example number of car produced. Labor means to the number of
workers employed. Capitalmeans to the amount of the equipment used in the production.
1.2The production function with one variable inputIn this section, we present the theory of production when only one input is variable. Thus, we are
in the short run. We begin by defining total, the average, and the marginal product of the variable
input and deriving from this the output elasticity of the variable input.
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Figure 2-1
No. of Labour Output Marginal
Product of
labour
Avg product of
Labour
Output
Elasticity of
Labour
0 0 - - -
1 3 3 3 1
2 8 5 4 1.25
3 12 4 4 1
4 14 2 3.5 0.57
5 14 0 2.8 0
6 12 -2 2 -1
1.3 THE PRODUCTION FUNCTION WITH TWO VARIABLE INPUTSWe now examine the production function when there are two variable inputs. This can be
represented graphically by isoquants. In this section we define isoquants and discuss their
characteristics. Isoquants will then be used in Section 6-5 to develop the conditions for the
efficient combination of inputs in production.
1.4Production IsoquantsAn Isoquants shows the various combinations for two inputs (say, labor and capital) that the
firm can use to produce a specific level of output. A higher isoquant refers to a larger output,
while a lower isoquant refers to a smaller output. Isoquants can be derived from Table 6-4, which
repeats the production function of Table6-1 with lines connecting all the labor-capital
combinations that can be used to produce a specific level of output. For example, the table shows
that 12 units of output (that is, 12Q) can be produced with 1 unit of capital (that is, 1K) and 3
units of labor (that is, 3L) or with 1Kand 6L.6 The output of 12Q can be produced with 1L and
5K. These are shown by the lowest isoquant in Figure 6-6. The isoquants is smooth on the
assumption that labor and capital are continuously divisible. Table 6-4 also shows that 28Q can
be produced with 2Kand 3L, 2Kand 6L, 2L and 4K, and 2L and 5K(the second isoquant marked
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28Q in Figure 6-6). The table also shows the various combinations of L and K that can be used to
produce 36Q and 40Q (shown by the top two isoquants in the figure). Note that to produce a
greater output, more labor, more capital, or more of both labor and capital are required.
1.5Economic Region of ProductionWhile the isoquants in Figure 6-6 (repeated in Figure 6-7) have positively sloped portions, these
portions are irrelevant. That is, the firm would not operate on the positively sloped portion of an
isoquants because it could produce the same level of output with less capital and less labor. For
example, the firm would not produce 36Q at point Uin following figure
Figure 3-1 : Production Function with Two Variable Inputs.
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Fig.3-2 : Isoquants: From the table, it can be seen that 12Q can be produced with 1L and 5K,1L and 4K, 3L and 1K or 6L and 1K. Source:
http://www.swlearning.com/economics/salvatore/salvatore5e/ch01.pdf
Fig.3-3: The Relevant Portion of Isoquants. The economic region is given by the negatively
sloped segment of isoquants between ridge lines OVIand OZI. The firm will not produce in
the positively sloped portion of the isoquants because it could produce the same level of
http://www.swlearning.com/economics/salvatore/salvatore5e/ch01.pdfhttp://www.swlearning.com/economics/salvatore/salvatore5e/ch01.pdf -
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output with both less labour and less capital. Source:
http://www.swlearning.com/economics/salvatore/salvatore5e/ch01.pdf
2. Cobb-Douglas : Empirical Production FunctionThe production function most commonly used in empirical estimation is the power function of the form
that is
Q = ALaK
b,
where:
Q = total production (the monetary value of all goods produced in a year)
L = labour input
K = capital input
A = constant
a and b are the parameters of labor and capital respectively. These values are constants
determined by available technology.
If,
a + b = 1,
the production function has constant returns to scale . That is, if L and K are each increased by
20%, Q increases by 20%.
If
a + b < 1,
http://www.swlearning.com/economics/salvatore/salvatore5e/ch01.pdfhttp://www.swlearning.com/economics/salvatore/salvatore5e/ch01.pdf -
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returns to scale are decreasing. That is if L and K are each increased by 20%, Q increases by
10%.
if
a + b > 1
returns to scale are increasing. That is if L and K are each increased by 20%, Q increases by
40%. Assuming perfect competition, a and b can be shown to be labor and capital's share of
output.
2.1 Returns to Scale
Returns to scale refers to the degree by which output changes as result of a given change in the
quantity of all inputs used in production. There are three types of returns to scale: constant,
increasing and decreasing. If the quantity of all inputs used in production is increased by a given
proportion, we have constant returns to scale if output increases in the same proportion;
increasing returns to scale if output increases by a greater proportion; and decreasing returns to
scale if output increases by smaller proportion. Starting with the general production function
Q = f (L, K)
We multiply L and K by h, and Q increases by 1, as
Q = f (hL, hK)
We have constant, increasing or decreasing returns to scale, respectively, depending on whether
= h, > h, or < h.
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1. Fig.5-1: Constant, Increasing and Decreasing Returns to Scale. In all three panels of thisfigure we start with the firm using 3L and 3K and producing 100Q. By doubling inputs to
6L and 6K, the left panel shows that output also doubles to 200Q, so that we have
constant returns to scale; the centre panel shows that output triples to 300Q, so that we
have increasing returns to scale; while the right panel shows that output only increases to
150Q, so that we have decreasing returns to scale. Source:
http://www.swlearning.com/economics/salvatore/salvatore5e/ch01.pdf
2.2 A Practical illustration of long run returns to scale
Here if we assume all other factors affecting the production as constant except Labour
and capital then we can have the following data of SAIL co.
Year Q
(million
tons)
K (in
Cr.)
L %
increase
in
INPUT
%
Increase
in
OUTPUT
Returns
to scale
2000-01 7.126 18265 150832 - - -
2001-02 7.315 17045 147601 -1.11 2.65 Increasing
2002-03 8.029 16542 137496 -4.90 9.67 Increasing
2003-04 8.581 15271 131910 -5.87 6.88 Increasing
2004-05 8.901 20064 126857 -17.61 3.73 Increasing
2005-06 9.351 21782 138211 0.20 5.05 Increasing
2006-07 9.849 25476 132973 -10.38 5.33 Increasing
2007-08 10.288 28450 128804 -2.41 4.46 Increasing
2008-09 9.846 34552 121295 -13.64 -4.30 Increasing
2009-10 9.736 43752 116950 -15.10 -1.12 Increasing
2.3 Properties of Cobb-Douglas production function
The marginal product of capital and the marginal product of labour depend on both thequantity of capital and the quantity of labour used in production.
The exponents of K and L (a and b) represent, respectively, the output elasticity of labourand capital (Ek and El), and the sum of the exponents (that is a + b) measures the returns
http://www.swlearning.com/economics/salvatore/salvatore5e/ch01.pdfhttp://www.swlearning.com/economics/salvatore/salvatore5e/ch01.pdf -
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to scale. If a + b = 1, we have constant returns to scale, if a + b > 1, we have increasing
returns to scale, and if a + b < 1, we have decreasing returns to scale.
Cobb-Douglas production function can easily be extended to deal with more than twoinputs (say, capital, labour,).
Cobb-Douglas production function can be estimate by regression analysis bytransforming it into which is linear in the logarithms.
ln Q = ln A + a ln K + b ln L
2.4 Estimated lnQ lnK and lnL of SAIL co.
Year Q
(million
tons)
K (in
Cr.)
L ln (Q) ln (K) ln (L)
2000-01 7.126 18265 150832 1.96375007 9.81274194 11.9239219
2001-02 7.315 17045 147601 1.98992703 9.74361218 11.9022680
2002-03 8.029 16542 137496 2.08305999 9.71365788 11.8313501
2003-04 8.581 15271 131910 2.14955046 9.63371088 11.7898752
2004-05 8.901 20064 126857 2.18616363 9.90668244 11.7508157
2005-06 9.351 21782 138211 2.23548329 9.98883922 11.8365368
2006-07 9.849 25476 132973 2.28736993 10.14549211 11.7979014
2007-08 10.288 28450 128804 2.33097817 10.25590344 11.7660471
2008-09 9.846 34552 121295 2.28706528 10.45022071 11.7059809
2009-10 9.736 43752 116950 2.27583036 10.68629261 11.6695018
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The estimation have been performed with the help of MS EXCEL using ln function.
2.5 Assumptions:
1. If either labor or capital vanishes, then so will production.
2. The marginal productivity of labor is proportional to the amount of production per unit of
labor.
3. The marginal productivity of capital is proportional to the amount of production per unit of
Capital.
2.6 Difficulties:
1. If the firm produces a number of different products, output may have to be measured in
monetary rather than in physical units, and this will require deflating the value of output by the
price index in time-series analysis or adjusting for price differences for firms and industries
located in different regions in cross-sectional analysis.
2. Only the capital consumed in the production of the output should be counted, ideally. Since
machinery and equipment are of different types and ages and productivities, however, the total
stock of capital in existence has to be instead.
3. In time-series analysis a time trend is also usually included to take into consideration
technological changes over time, while in cross-sectional analysis we must ascertain that all
firms of industries use the same technology.
3. Company ProfileSAIL traces its origin to the formative years of an emerging nation - India. After independence
the builders of modern India worked with a vision - to lay the infrastructure for rapid
industrialisaton of the country. The steel sector was to propel the economic growth. Hindustan
Steel Private Limited was set up on January 19, 1954.
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Steel Authority of India Limited (SAIL) is the leading steel-making company in India. It is a
fully integrated iron and steel maker, producing both basic and special steels for domestic
construction, engineering, power, railway, automotive and defence industries and for sale in
export markets. SAIL is also among the five Maharatnas of the country's Central Public Sector
Enterprises.
SAIL manufactures and sells a broad range of steel products, including hot and cold rolled
sheets and coils, galvanised sheets, electrical sheets, structurals, railway products, plates, bars
and rods, stainless steel and other alloy steels. SAIL produces iron and steel at five integrated
plants and three special steel plants, located principally in the eastern and central regions of India
and situated close to domestic sources of raw materials, including the Company's iron ore,
limestone and dolomite mines. The company has the distinction of being Indias second largest
producer of iron ore and of having the countrys second largest mines network. This gives SAIL
a competitive edge in terms of captive availability of iron ore, limestone, and dolomite which are
inputs for steel making.
SAIL's wide range of long and flat steel products are much in demand in the domestic as well as
the international market. This vital responsibility is carried out by SAIL's own Central Marketing
Organisation (CMO) that transacts business through its network of 37 Branch Sales Offices
spread across the four regions, 25 Departmental Warehouses, 42 Consignment Agents and 27
Customer Contact Offices. CMOs domestic marketing effort is supplemented by its ever
widening network of rural dealers who meet the demands of the smallest customers in the
remotest corners of the country. With the total number of dealers over 2000 , SAIL's wide
marketing spread ensures availability of quality steel in virtually all the districts of the country.
SAIL's International Trade Division ( ITD), in New Delhi- an ISO 9001:2000 accredited unit of
CMO, undertakes exports of Mild Steel products and Pig Iron from SAILs five integrated steel
plants.
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With technical and managerial expertise and know-how in steel making gained over four
decades, SAIL's Consultancy Division (SAILCON) at New Delhi offers services and
consultancy to clients world-wide.
SAIL has a well-equipped Research and Development Centre for Iron and Steel (RDCIS) at
Ranchi which helps to produce quality steel and develop new technologies for the steel industry.
Besides, SAIL has its own in-house Centre for Engineering and Technology (CET), Management
Training Institute (MTI) and Safety Organisation at Ranchi. Our captive mines are under the
control of the Raw Materials Division in Kolkata. The Environment Management Division and
Growth Division of SAIL operate from their headquarters in Kolkata. Almost all our plants and
major units are ISO Certified.
Here, for the production analysis, the data regarding Finished Steel is taken into consideration.
3.1 Production Details
year
Capital Employed (K)
(rs. in crore) no. of Employees (L)
Production (in
million tons) (Q)
2000-01 18265 150832 7.126
2001-02 17045 147601 7.315
2002-03 16542 137496 8.029
2003-04 15271 131910 8.581
2004-05 20064 126857 8.901
2005-06 21782 138211 9.351
2006-07 25476 132973 9.849
2007-08 28450 128804 10.288
2008-09 34552 121295 9.846
2009-10 43752 116950 9.736
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3.2 Comparison Between Ideal and actual Production curve:
Ideal Production Curve
Source:http://www.swlearning.com/economics/salvatore/salvatore5e/ch01.pdf
http://www.swlearning.com/economics/salvatore/salvatore5e/ch01.pdfhttp://www.swlearning.com/economics/salvatore/salvatore5e/ch01.pdfhttp://www.swlearning.com/economics/salvatore/salvatore5e/ch01.pdfhttp://www.swlearning.com/economics/salvatore/salvatore5e/ch01.pdf -
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Actual production curve(SAIL)
3.4 Descriptive data:
Count 10 10 10
Sum 89.022 241199 1332929
Maximum 10.288 43752 150832
Minimum 7.126 15271 116950
Mean 8.9022 24119.9 133292.9
Median 9.126 20923 132441.5
Standard deviation 1.112755019 9170.08784 10671.748
5
6
7
8
9
10
11
12
output vs. Labour
output vs. Labour
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3.5 Regression Analysis:
Regression
Statistics
Multiple R 0.825430802
R Square 0.681336009
Adjusted R
Square 0.590289155
Standard
Error 0.082989426
Observations 10
ANOVA
df SS MS F
Significance
F
Regression 2 0.103079 0.05154 7.483356 0.018266926
Residual 7 0.048211 0.006887
Total 9 0.15129
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept 12.4062558 7.341064 1.689981 0.134878
-
4.95260142 29.76511 -4.9526 29.76511
X
Variable
1 0.105405824 0.124444 0.847014 0.424995
-
0.18885754 0.399669
-
0.18886 0.399669
X
Variable
2 -0.95656085 0.537485 -1.7797 0.118347
-
2.22751038 0.314389
-
2.22751 0.314389
Now we will move towards the final and required our interpretation by using cob-dougles outputfunction that is
Q= In A + a InK + b InL
By using the co-efficient column, we can derived or get the following regression equation as
follow:
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ln Q = 12.4063 + 0.1054 lnK + -0.9566 lnL
3.6 Executive Summary:
To perform regression analysis the collected data has been transformed in to thelogarithm form, than the regression analysis is performed which gives the following
production function of the SAIL
ln Q = 12.4063 + 0.1054 lnK + -0.9566 lnL
From the above result of the production function it is to conclude that the production ofthe SAIL is capital intensive rather than the labour intensive.
The production function of the SAIL through the regression analysis which is helpful tounderstand that the production is capital intensive and it can also important to estimate
the volume of production for the coming years.
4. BibliographySalvatore,D. (2008). Managerial economics: Oxford University Press.
Gupta,S.P (2008). Business Statistics: Sultanchand & Sons.
http://www.sail.co.in/pdf/2010digest.pdf