Management Accounting: Information for Managing and Creating Value by Ronald...

Econometric Methods
FIN5EME
Semester 1, 2013
Assignment 2

Cobb-Douglas cost function:

TCi = µQiβ2 pi1β3 pi2β4 pi3β5 (1)

Where, TCi= Total Cost for firm i Q= Output of firm i pi1= Wage Rate pi2= Rental Price of Capital pi3= Fuel Price

Taking the natural log of equation (1)

log(TCi)= β1 + β2 log(Qi) + β3 log(pi1) + β4 log(pi2) + β5 log(pi3) + ei (2)

where β1= (logµ) and ei= error term.

Eviews Output of the log-log model is as follows:

Dependent Variable: LOG(TC)

Method: Least Squares

Date: 06/12/13 Time: 12:47

Sample: 1 145

Included observations: 145

Variable
Coefficient
Std. Error t-Statistic Prob.

C
-3.526503
1.774367
-1.987471
0.0488
LOG(Q)
0.720394
0.017466
41.24448
0.0000
LOG(WAGE)
0.436341
0.291048
1.499209
0.1361
LOG(CAPITAL)
-0.219888
0.339429
-0.647819
0.5182
LOG(FUEL)
0.426517
0.100369
4.249483
0.0000

R-squared
0.925955
Mean dependent var
1.724663
Adjusted R-squared
0.923840
S.D. dependent var
1.421723
S.E. of regression
0.392356
Akaike info criterion
1.000578
Sum squared resid
21.55201
Schwarz criterion
1.103224
Log likelihood
-67.54189
Hannan-Quinn criter.
1.042286
F-statistic
437.6863
Durbin-Watson stat
1.013062
Prob(F-statistic)
0.000000

Solution 1:
The estimated coefficients show the proportional change in total cost that results from proportional changes in firm’s output, changes in wages, changes in rental price of capital and changes in prices of fuel.

Estimated Coefficient

β2
0.720394
β3
0.436341
β4
-0.219888
β5
0.426517

All the estimated coefficients are positive except for estimated rental price of capital. We estimate that every 1% increase in output will lead to 0.72% increase in total cost, every 1% increase in wage rate will lead to 0.44% increase in total cost,