Answer

Solution

1. 1

   If $u : X \to \mathbb{R}$ represents $\succsim$, then $x \succsim y \Longleftrightarrow u(x) \geq u(y)$.

2. 2

   Since $\geq$ on $\mathbb{R}$ is transitive, the induced preference must also be transitive.

3. 3

   Hence a non-transitive preference relation cannot be represented by any utility function.

Answer structure / marking notes

Content note