Downward propagating inertial Alfv¿n waves (IAWs), transporting electromagnetic energy along high-latitude Earth's magnetic field lines, are a well-established phenomenon in the magnetosphere. Such waves have been detected now from Freja, FAST, and Polar satellites, showing that at the altitudes of the former two satellites, the latitudinal widths of the IAW structures are a few electron-skin depths. Since IAWs have a nonzero group velocity component Vg$perp$ perpendicular to the Earth's magnetic field B(r), the latitudinal fanning of the finite-width wave must impact the scaling of the wave Poynting flux S with the geocentric altitude r. We estimate the effect of the fanning on the scaling of S on B(r), showing that commonly assumed scaling S ~ B might not be true for the narrow IAW structures. For the ultra-low-frequency (ULF) waves having frequencies in the range of a few mHz, it turns out that the width of such IAWs becomes nearly constant in altitude and S ~ B1/2 due to the convergence of magnetic field in longitude only. Like IAWs, even the kinetic Alfven waves are expected to show a similar scaling.