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Cobb- Douglas production function

Q= A K α + Lβ

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

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:

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

Parameters determined: Q= A K α + Lβ

α = 0.206925β = 0.952008

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 L100 100 100 --> 2 2 2101 100 105 2.004321 2 2.021189112 107 110 2.049218 2.029384 2.041393122 114 118 2.08636 2.056905 2.071882124 122 123 2.093422 2.08636 2.089905122 131 116 2.08636 2.117271 2.064458143 138 125 2.155336 2.139879 2.09691152 149 133 2.181844 2.173186 2.123852151 163 138 2.178977 2.212188 2.139879126 176 121 2.100371 2.245513 2.082785155 185 140 2.190332 2.267172 2.146128159 198 144 2.201397 2.296665 2.158362153 208 145 2.184691 2.318063 2.161368177 216 152 2.247973 2.334454 2.181844184 226 154 2.264818 2.354108 2.187521169 236 149 2.227887 2.372912 2.173186189 244 154 2.276462 2.38739 2.187521225 266 182 2.352183 2.424882 2.260071227 298 196 2.356026 2.474216 2.292256223 335 200 2.348305 2.525045 2.30103280 366 193 2.447158 2.563481 2.285557231 387 193 2.363612 2.587711 2.285557179 407 147 2.252853 2.609594 2.167317240 417 161 2.380211 2.620136 2.206826

Ans:

Equations estimated:Q= A K α + Lβ

Here Q as Y,

“ Y= (-26.86769) 0.160353 K + 1.097662 L “

c)Interpret R-Squared.

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

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 zeroFor L: H0 : β isn’t greater than zero H1 : β is greater than zero

t-Test: Paired Two Sample for Means

  2 2

Mean 2.312892 2.162035

Variance 0.03707 0.006829

Observations 23 23

Pearson Correlation 0.87844Hypothesized Mean Difference 0Df 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  

Both are positive: as results shows,

f)Does Industry exhibit increasing return to scale?

.

Ans: as,α = 0.160353 β = 1.097662Where,α + β = 1.158933 that shows,α + β > 1 and here Industry exhibits increasing return to scale