Business Data Analytics Using Excel by Dr. A N sah

Author:Dr. A N sah [sah, Dr. A N]
Language: eng
Format: epub
Publisher: UNKNOWN
Published: 2017-01-10T08:00:00+00:00

Y 





1 2

1 Xeu (4.27)2 Where Y = output

X1 = labour

X2 = capital

e = base of natural logarithm

u = error term

α, β1and β2 are parameters of the model

Model (4.21) is non-linear and can not be estimated in its original form. We can make it linear by logarithmic transformation as:

In(Y) = In (α) +β1In(X1) +β2In(X2) +μ (4.28) The model (4.22) is linear in parameters α, β1and β2 and is estimated by OLS method. Three important points to ne noted here regarding Cobb-Douglas production function:

a)1 is the elasticity of output with respect to labour, assuming capital as constant

b)2is the elasticity of output with respect to capital, assuming labour as constant.

c) ( 2 ) tells us about the returns to scale. If the sum of ( 2 )1 1 equals to 1, then output follows constant returns to scale. In other words, when labour and capital both increases by 5%, output will also increases by 5%. If the sum is less than 1, that means, there are decreasing returns to scale. A 5% increase in inputs will give less than 5% increase in output.

To illustrate Cobb-Douglas production function, we collected data relating to output, labour input and capital input of National Thermal Power Corporation (NTPC) as shown in Table 4.3

Table 4.3: Output, Labour and capital data of NTPC

Year Output(Rs. mn) Labour Cost Capital Cost (Rs.mn) (Rs.mn)

1998-99 143039 4763 10830

1999-00 167685 6212 9828

2000-01 199054 7640 10918

2001-02 184878 8036 8680

2002-03 194511 8268 9916

2003-04 249994 8835 33697

2004-05 249225 8835 16955

2005-06 287507 9684 17632

2006-07 353766 11580 18594 Source: NTPC Annual Reports

Based on the above data in table 2, we estimated (4.22) model by the OLS method. The results are as follows:

In (Y) = 2.8001+0.86 In (labour) + 0.17 In(capital)

se = (1.11) (0.14) (0.08)

t = (2.50) (5.95) (2.11)

R2=0.92 adj R2 =0.89 df =6 From the above output, it is clear that output elasticity of labour is 0.86 which means that when labour input increases by 1%, output of NTPC will increase by 0.86% holding capital input as constant. Similarly, output elasticity of capital is 0.17 which implies that when capital input increases by 1%, output will increase by only 0.17% holding labour input constant. The sum of both the slope coefficients is 1.03 which indicates more or less constant returns to scale. Thus, it is evident, NTPC is characterized by constant returns to scale over the sample period 1998-99 and 2006-07. Before we close, please note here that for log-log regression model which contains more than two independent variables, the coefficient of each independent variable measures the elasticity of the dependent variable with respect to that independent variable. Hence, in a k-variable log-log model such as given below:

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.