I need to prove the following relationships:

1 - If preferences are homothetic, then the indirect utility function can be written as $v(p, w) = v(p) · w$.

2 - If preferences are homothetic, then the Marshallian demand functions take the form $x_i(p, w) = x_i(p) · w$, i.e., they are linear functions of income.

I know that I can use the Roy's Identity and the connections below: $$ e(p,v(p,w))=w$$ $$v(p,e(p,u))=u,$$ but I can't organize this answer.


  • 2
    $\begingroup$ What happens if you apply Roy's identity to the utility function of point 1 ? (it is embarassing btw to use the same notation $v$ for denoting two different functions) $\endgroup$
    – Bertrand
    Commented Feb 9, 2021 at 21:28
  • $\begingroup$ If I use a Roy's Identity in point 1, I derive the Marshallian demand from item 2. I am wondering how to prove that point 1 is true. (Thanks for the tip! It was just to indicate a function of p, but I can use another notation.) $\endgroup$ Commented Feb 9, 2021 at 22:01
  • 1
    $\begingroup$ This may help: economics.stackexchange.com/questions/8519/… $\endgroup$
    – Bertrand
    Commented Feb 10, 2021 at 10:40


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.