  We consider two types of entropy, namely, Shannon and R\'{e}nyi entropies of
the Poisson distribution, and establish their properties as the functions of
intensity parameter. More precisely, we prove that both entropies increase with
intensity. While for Shannon entropy the proof is comparatively simple, for
R\'{e}nyi entropy, which depends on additional parameter $\alpha>0$, we can
characterize it as nontrivial. The proof is based on application of Karamata's
inequality to the terms of Poisson distribution.
