Question

my book says \(x\ln x - x\ln y\) is a homogeneous function...but how??

Answer 1

if i sub in a \(\lambda \) i get \[\lambda x \ln (\lambda x) - \lambda x \ln (\lambda y)\]

Answer 2

i guess i can factor out into \[\lambda x [\ln (\frac{\lambda x}{\lambda y})]\]

Answer 3

then is it a homo with degree 1?

Answer 4

Yeah. You just answered your own question. =))

Answer 5

haha i love those times =))))