# How to show that a leontief utility function is homothetic?

usually what i do to show that a utility function is homothetic is by either showing that the function is homogeneous or if the MRS is homogeneous of degree 0. However the MRS is not defined. So im not even sure if the function is homogeneous. What i have been thinking is that it has something to do with the expansión path, as it is always constant. But how about the homogeneous degree? The specific function that i have is U(X,Y)=min{2X,6Y} Thank you

• A function $U(x,y)$ is homothetic if $U(\alpha x, \alpha y)=\alpha U(x,y)$. What is $\min(2\alpha x,6\alpha y)$? – Angela Pretorius Sep 1 '19 at 17:01
• Hi Angela. I think that is homogeneous degree 1. But you are right by saying that homogeneous implies homothetic property. However the loentief utility function is a little different so i dont think that it applys the same analysis. – neto333 Sep 1 '19 at 18:43