1
$\begingroup$

From the discussion under this question:

Can utility function $U(x,y)$ that is both quasiconcave and quasiconvex always be transformed (via some positive monotonic function) into a quasilinear form $v(x) + y$?

$\endgroup$

1 Answer 1

5
$\begingroup$

That is not the case. Consider $u(x, y) = \lfloor x + y \rfloor$ i.e. greatest integer less than or equal to $x+y$. It is both quasi-concave and quasi-convex, but no transformation of the kind $v(x) + y$ exist. This is because $v(x) + y$ is strictly increasing in $y$, but $u$ is not.

Another much simpler example is $u(x, y) = 0$.

$\endgroup$
1

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.