By using a method which employs a kinetic description and linear-response theory, we calculated the conductivity of electron-ion many-layer system (type-I superlattices) in the high-frequency and long-wavelength limits. Here electromagnetic radiation is taken to be a homogeneous, oscillating electric field. Our calculation takes into account all contributions in lowest order of the plasma parameter ${r}_{s}$. Expressions for frequency-dependent scattering time and effective mass have been numerically obtained. Asymptotic limits for small and large frequencies are analytically derived.