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suppose we have the following productions functions: Q=LaK1-a .............1 Z= a log L+ ( 1-a) log...

suppose we have the following productions functions:

Q=LaK1-a .............1

Z= a log L+ ( 1-a) log K...........2

where Q is output, L is labour , K is capital , Z is a log transformation of Q and a is a positive constant . prove that equation 1 is homogenous while equation 2 is not; but both equations are homothetic, implying that a non-homogeneous function can still be homothetic,

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Answer #1

Refer to the image for the stepwise solution to the question. Production function Q is homogeneuos and homothetic, but function Z is non-homogenous and homothetic.

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