Which one of these is right for finding CobbDouglas equation

Which one of these is right (for finding Cobb-Douglas equation)? (1) or (2)?

(1)

Cobb-Douglas function = A x K^alpha x L^beta = 33.33 x K^0.87 x L^0.13

Where, A = Factor of productivity, Alpha = R squared, Beta = 1 - alpha

(2)

Cobb - douglas function is given by, where Y denotes production, L denotes Labour and K denotes Capital Taking natural log of above equation gives, The results shown in the excel sheet relates to the above equation with Xvariablel denoting InL and Xvariable2 denoting InK Thus correlating we get, =1.16 (coefficient of Xvariable1) = 0.1 5 ( coefficient of Xvariable2) In A =-5.97 (intercept ) A = 0.0025 Thus the required cobb-douglas equation will be 16 K0.15 y = 0.0025

Solution

Option (2) is correct.

And it has been solved correctly. There is nothing wrong with the option (2) solution. But in case of option (1), we are limiting it to be of constant return which may not be true.