題組內容

1. (17 %)

Consider a utility function $U: \mathbb{R}+^2 \to \mathbb{R}$, $U(x1, x2) = |x1 - x_2|$.

This utility function represents a preference relation $\succcurlyeq$. Equivalently, for any bundles $(x1, x2), (y1, y2)$,

$$(x1, x2) \succcurlyeq (y1, y2) \text{ if and only if } U(x1, x2) \geq U(y1, y2).$$

Consider the following properties.

(b) True/False/Uncertain: Is \( \succsim \) convex?