this is some short introductory of Cobb-Douglas production function

2. 2

3. Cobb- Douglas
production function
Q= A K α + Lβ

4. a)What are independent & dependent variables in this equation?
How many parameters in equation?
Ans: In the equation “Q= A K α + Lβ”
Dependent variable: Q
Independent variable: K , L
Parameters : α , β
Intercept : A

5. b)How will you estimate the parameters of Cobb-Douglas
function? What information do you need for estimation?
Ans: By working in Eviews we can
get the parameters as following,
and for this purpose the data of
output, labor and capital
information is required.
Results:

6. Dependent Variable: Y
Method: Least Squares
Date: 05/13/14 Time: 21:22
Sample: 1 24
Included observations: 24
Variable Coefficient Std. Error t-Statistic Prob.
C -0.318155 0.197991 -1.606916 0.1230
K 0.206925 0.065080 3.179549 0.0045
L 0.952008 0.148186 6.424416 0.0000
R-squared 0.953241 Mean dependent var 2.209588
Adjusted R-squared 0.948788 S.D. dependent var 0.124198
S.E. of regression 0.028106 Akaike info criterion -4.189186
Sum squared resid 0.016589 Schwarz criterion -4.041929
Log likelihood 53.27023 Hannan-Quinn criter. -4.150119
F-statistic 214.0556 Durbin-Watson stat 2.247216
Prob(F-statistic) 0.000000

7. Parameters determined:
Q= A K α + Lβ
α = 0.206925
β = 0.952008

8. c)Use results from excel & write the estimated equation explicitly
both the log-log form?
Q K L After taking log Log Q Log K Log L
100 100 100 --> 2 2 2
101 100 105 2.004321 2 2.021189
112 107 110 2.049218 2.029384 2.041393
122 114 118 2.08636 2.056905 2.071882
124 122 123 2.093422 2.08636 2.089905
122 131 116 2.08636 2.117271 2.064458
143 138 125 2.155336 2.139879 2.09691
152 149 133 2.181844 2.173186 2.123852
151 163 138 2.178977 2.212188 2.139879
126 176 121 2.100371 2.245513 2.082785
155 185 140 2.190332 2.267172 2.146128
159 198 144 2.201397 2.296665 2.158362
153 208 145 2.184691 2.318063 2.161368
177 216 152 2.247973 2.334454 2.181844
184 226 154 2.264818 2.354108 2.187521
169 236 149 2.227887 2.372912 2.173186
189 244 154 2.276462 2.38739 2.187521
225 266 182 2.352183 2.424882 2.260071
227 298 196 2.356026 2.474216 2.292256
223 335 200 2.348305 2.525045 2.30103
280 366 193 2.447158 2.563481 2.285557
231 387 193 2.363612 2.587711 2.285557
179 407 147 2.252853 2.609594 2.167317
240 417 161 2.380211 2.620136 2.206826

9. Ans:
Equations estimated:
Q= A K α + Lβ
Here Q as Y,
“ Y= (-26.86769) 0.160353 K + 1.097662 L “

10. c)Interpret R-Squared.
Ans: R-Squared = 0.953241
Interpretation:
Here R-Squared = 0.953241, that
shows 95% change in Q due to
change in K and L.

11. e)Economic theory tells us that producers of Capital & Labor use
both positive and both these inputs individually exhibit diminishing
return? How will you statistically test for this theoretical hypothesis?
Ans: Economic theory tells that
capital and labor must be positive as
when you work for long time, for
this,
Hypothesis:
For K: H0 : α isn’t greater than zero
H1 : α is greater than zero
For L: H0 : β isn’t greater than zero
H1 : β is greater than zero

12. Both are positive: as results shows,
t-Test: Paired Two Sample for Means
2 2
Mean 2.312892 2.162035
Variance 0.03707 0.006829
Observations 23 23
Pearson Correlation 0.87844
Hypothesized Mean
Difference 0
Df 22
t Stat 5.729304
P(T<=t) one-tail 4.6E-06
t Critical one-tail 1.717144
P(T<=t) two-tail 9.2E-06
t Critical two-tail 2.073873

13. f)Does Industry exhibit increasing return to scale?
.
Ans: as,α = 0.160353
β = 1.097662
Where,
α + β = 1.158933 that shows,
α + β > 1 and here Industry
exhibits increasing return to scale