<p>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 <code>U(X,Y)=min{2X,6Y}</code>
Thank you</p>

CC BY-SA 4.0
2019-09-01T17:01:42.793Z
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
CC BY-SA 4.0
2019-09-01T18:43:13.823Z
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
<microeconomics><self-study><leontief>
How to show that a leontief utility function is homothetic?
neto333
# How to show that a leontief utility function is homothetic?

(Asked by: username_0 on 2019-09-01)

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

**Tags:** microeconomics, self-study, leontief

> **Comments:**
> **username_1**: A function $U(x,y)$ is homothetic if $U(\alpha x, \alpha y)=\alpha U(x,y)$. What is $\min(2\alpha x,6\alpha y)$?  
> **username_0**: Hi username_1. 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.  

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## 0 answers

