  We consider solutions of the stochastic equation $R=_d\sum_{i=1}^NA_iR_i+B$,
where $N>1$ is a fixed constant, $A_i$ are independent, identically distributed
random variables and $R_i$ are independent copies of $R$, which are independent
both from $A_i$'s and $B$. The hypotheses ensuring existence of solutions are
well known. Moreover under a number of assumptions the main being
$\mathbb{E}|A_1|^{\alpha}=1/N$ and $\mathbb{E}|A_1|^{\alpha}\log|A_1|>0$, the
limit $\lim_{t\to\infty}t^{\alpha}\mathbb{P}[|R|>t]=K$ exists. In the present
paper, we prove positivity of $K$.
