Are there any results in economics that require function to be homothetic? The textbook I am using (Essential Mathematics for Economic Analysis) says that function is homothetic when " $f(x)=f(y)$ and $t>0$, then $f(tx)=f(ty)$". It also mentions that there are homothetic functions which are not homogenous like $F=xy+1$.
But then all economic examples in the book where homothetic function is used turn out to work with homogenous functions too. Then why are they special? Is there some economic example where having homogenous function would not be enough so there must be homothetic function for it to work?