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We study the affine recursion $X_n = A_nX_{n-1}+B_n$ where $(A_n,B_n)\in{\mathbb R}^+ \times {\mathbb R} $ is an i.i.d. sequence and recursions $X_n =\Phi_n(X_{n-1})$ defined by Lipschitz transformations such that $\Phi (x)\geqAx+B$. It is known that under appropriate hypotheses the stationary solution$X$ has regularly varying tail, i.e. $$\lim_{t\to\infty} t^{\alpha} {\mathbbP}[X>t] = C. $$ However positivity of $C$ in general is either unknown orrequires some additional involved arguments. In this paper we give a simpleproof that $C>0$. This applies, in particular, to the case when Kesten-Goldieassumptions are satisfied.

A simple proof of heavy tail estimates for affine type Lipschitz recursions