  The polarizabilities and hyperpolarizabilities of the Be$^+$ ion in the
$2^2S$ state and the $2^2P$ state are determined. Calculations are performed
using two independent methods: i) variationally determined wave functions using
Hylleraas basis set expansions and ii) single electron calculations utilizing a
frozen-core Hamiltonian. The first few parameters in the long-range interaction
potential between a Be$^+$ ion and a H, He, or Li atom, and the leading
parameters of the effective potential for the high-$L$ Rydberg states of
beryllium were also computed. All the values reported are the results of
calculations close to convergence. Comparisons are made with published results
where available.
