Question

be reduced to the separable form f-yyi by introducing the transformations Suggest a suitable transformation of variables that will reduce the following function to a separable form: i(X1, X2)-XIP X29,

Please show all the work nice and neat

Answer 1

Given f (x_1, X_2) = x_1^p x_2^q Let y = x_1^px_2^q then f = y y = x_1^p X_2^q Take log function on both sides log y = log (x_1^p X_2^q) log(y) = log (x_1^p) + log (x_2^q) there fore (log a^xb^y = loga^x + loga^y x log a+ y log b) log(y) = p log(x_1) + q log(x_2) y grater than 0: x_1 > , x_2 > 0.