Consider a Fully Additive Model with One Consumption Good $U\left(c_{i}\right)$ , Where

Consider a fully additive model with one consumption good, $U\left(c_{i}\right)$ , where $i$ indexes time.
$u\left(c_{i}\right)=u\left(c_{j}\right) \forall i \neq j$ if and only if $c_{i}=c_{j}$ .