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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


function with one variable

inputs


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:


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,


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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:


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


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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

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