homothetic functions in economics
In the theory of production (and similarly for consumption), a homothetic production function is compatible with the occurrence of fixed costs, while a homogeneous production function is not.
In both cases (in standard notations), the production can be written as $$y=F(h(x)),$$ with $h$ linearly homogeneous. It is also common to impose $h(0)=0$. Then, the cost function inherits the form $$c(w,y)=g(w)F^{-1}(y).$$
When the production function is homogeneous of degree $k$ it turns out that $F^{-1}(y)=y^{1/k}$ and so $c(w,0)=0$. For homothetic production functions however, $c(w,0)=g(w)F^{-1}(0) &gt; 0$ in general.
A further advantage of the homothetic case, is that the degree of returns to scale can depend on $y$, while it is constant for the (degree $k$-) homogeneous technology.