Is this function homogeneous

Question

F(K,L)= (lnK-LnL)(K+L)^a

Answer 1

F is homogeneous of degree n if F(tK, tL) = tⁿF(K,L)

 

F(K,L) = (lnK - lnL)(K+L)^a

 

          = ln(K/L)(K+L)^a

 

F(tK,tL) = ln[(tK)/(tL)](tK+tL)^a

 

            = ln(K/L)[t(K+L)]^a

 

            = (lnK-lnL)[t^a(K+L)^a]

 

            = t^a(lnK-lnL)(K+L)^a

 

            = t^aF(K,L)

 

So, F(K,L) is homogeneous of degree a.