PRODUCTION ANALYSIS

Submitted by:-Urvashi Bhat ID no. 05Dixita Chotalia ID no. 12Vibha Jatav ID no. 24Poonam Nangia ID no. 40Kamal Panchal ID no. 42

INTRODUCTION

The topic has been selected to understand the theoretical

aspect of production analysis in a real company.

Major objectives

To study the production function of Tata steel.

To measure the correlation of volume of output with

labour as well as capital employed.

To study whether the production function of Tata steel is

labour intensive or capital intensive.

PRODUCTION ANALYSIS

Production refers to the transformation of inputs or resources into outputs of goods and services.

Production function is an equation showing the maximum output that a firm can produce per period of time with each set of inputs.

Thus the general equation of this simple production function is :-

Q = f (L, K) Q=no. of comodity produced L=no. of workers employed K=amount of capital employed

Cobb Douglas Production Function

Empirical estimation is the power function of the form

Q = AKa Lb,

Q = total production (the monetary value of all goods produced in a year)

L = labour input

K = capital input

A = total factor productivity

a and b are the output elasticity of labor and capital, respectively.

Properties of Cobb Douglas production Function

The exponents of K and L (i.e. a and b) represent output elasticity of capital and labour respectively.

Sum of exponents measures the returns to scale.

It can be estimated by regression analysis

ln Q = ln A + alnK + blnL

It can easily be extended to deal with more than two inputs.

Assumptions

If either labour or capital vanishes, then so will production.

The marginal productivity of labor is proportional to the amount of production per unit of labor.

The marginal productivity of capital is proportional to the amount of production per unit of Capital.

Difficulties If the firm produces a number of different products, the

output may have to be measured in monetary rather in physical units.

Only the capital consumed in the production should be counted ideally.

A time trend is usually included to take into consideration technological changes over time.

Neither Cobb nor Douglas provided any theoretical reason why the coefficients a and b should be constant over time

REGRESSION ANALYSIS

The statistical tool with the help of which we can estimate the unknown value of dependent variable from the known value of independent variable is called regression.

In economics it is the basic technique for measuring or estimating the relationship among economic variable that constitute the essence of economic theory and economic life

The line describing the tendency to regress is called regression line.

• Regression analysis can be of two types.

Simple regression analysis

Multiple regression analysis

Simple regression analysis is used for estimating the value of dependent variable from the independent variable, when there

is only one independent variable.

Y is the estimation of the dependent variable Y from the independent variable X. a and b are estimation parameters

Multiple regression analysis is used for estimating the value of dependent variable from the independent variable, when there is more than one independent variable.

The a coefficient is vertical intercept and gives the value of Y when value of X1 and X2 = 0.b1 and b2 are slope coefficient, they measure the change in Y per unit change in X1 and X2.

CORRELATION ANALYSIS

The correlation is one of the most useful statistic, a correlation is a single number that describe the degree of relationship between two variables.

Like all statistical technique, correlation is only appropriate for certain kinds of data. Correlation works for data in which numbers are meaningful, usually quantities of some sort. It cannot be used for purely categorical data, such as gender, brands purchased or favorite color.

• It ranges from -1.0 to +1.0. The closer r is to +1 to-1, the more closely the two variables are related.

If r is close to 0, it means there is no relationship between the variables. If r is positive, it means that as one variable gets larger the other gets larger. If r is negative it means that as one gets larger, the other gets smaller (often called an “inverse “correlation).

DATA COLLECTION

TATA STEEL

year capital

employed (K)

in cr.

salary wages

(L) in cr.

volume of output

(Q) in cr.

2002 7411.49 1023.46 8736.35

2003 7898.07 1095.63 10782.7

2004 9799.62 1059.46 14782.71

2005 12271.45 1180 15240.32

2006 23741.49 1236.32 17540.86

2007 45328.07 1390.69 19691.26

2008 57122.68 2615.06 24637.79

2009 62201.14 2074.25 24805.88

SUMMARY STATISTICS

Measures Ln (K)-x1

capital

Ln (L)-x2

labour

Ln (Q)-y

Volume of

prod.

Mean 9.909754549 7.229082567 9.685619

Median 9.745005067 7.096582111 9.701994

Standard

Deviation 0.901075017 0.343045125 0.370419

Sample Variance 0.811936187 0.117679958 0.13721

DATA ANALYSIS & INTERPRETATION

2002 2003 2004 2005 2006 2007 2008 20090

10000

20000

30000

40000

50000

60000

70000

capital employed(K) salary wages(L) volume of output(Q)

year

capi

tal,

ouro

utpu

t &

lab

our

RESULT OF CORRELATION

Correlation between volume of output and labour

employed0.8667

Correlation between volume of output and capital

employed0.942861

RESULT OF REGRESSIONSUMMARY OUTPUT

Regression StatisticsMultiple R 0.935476306R Square 0.875115919

Adjusted R Square 0.825162286

Standard Error 0.154885515Observations 8

ANOVA  Df SS MS F Significance F

Regression 2 0.840523996 0.420261998 17.51856424 0.005511473Residual 5 0.119947614 0.023989523Total 7 0.96047161

  CoefficientsStandard Error t Stat P-value Lower 95% Upper 95%

Intercept 5.510675639 1.533738734 3.592968944 0.015658925 1.568074711 9.453276567Ln(K)-x1 0.352872931 0.135031279 2.613268081 0.047482013 0.005763978 0.699981884

Ln(L)-x2 0.093796003 0.354686026 0.264447979 0.80198931 0.817953452 1.005545457

From the above regression result the production function of the

Tata steel is as follow

From the above production function of Tata steel it is interpreted

that the volume of production is 5.5107 (Intercept).which mean,

even if no labour or capital is employed in the production. If the

company increases the capital employed by 1 the volume of

production is increased by 0.3529 assume that labour is constant,

and if the company increases labour employed by 1 unit the

volume of production will increase by 0.0938 assume that capital

is constant.

CONCLUSION

From the research of the production analysis of the Tata steel

it is concluded that the production is capital intensive rather

than the labour intensive.

Company can increase its production by employee more unit

of capital instead of the labour.

As the correlation analysis also said that the volume of output

is more related to capital than labour and regression analysis

gives the same result that increase in capital leads to increase

in volume of output more than increase in labour.

SUMMARY

Regression tool has been used to estimate the production function of the Tata steel from the historical data of the last 8 years which has been collected through the secondary data collection method from the official site of the company

To perform regression analysis the collected data has been transformed in to the logarithm form, than the regression analysis is performed which gives the following production function of the Tata steel

From the above result of the production function it is to conclude that the production of the Tata steel is capital intensive rather than the labour intensive.

The production function of the Tata steel through the regression analysis which is helpful to understand that the production is capital intensive and it can also important to estimate the volume of production for the coming years.

 

BIBLIOGRAPHYBOOKS:

Dominik Salvatore. (2008). managerial economics. new delhi: oxford university press.

S.P.Gupta and M.P.Gupta. (2005). business statistics. new delhi: sultan chand & sons.

P.L. mehta. (1999). managerial economics. new delhi.sultan chand & sons.

WEBSITE:

http://www.tatasteel.com/investors/performance/annual-report.asp

http://www.moneycontrol.com/financials/tatasteel/balance-sheet/TIS

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