The auroral kilometric radiation (AKR), which emanates from high-altitude auroral regions of the earth, is mainly emitted in cold plasma depleted regions on the right-handed X mode. The maser synchrotron instability (MSI) is likely to be responsible for the generation of this emission, accounting for the low density of the cold plasma at the source and the small instantaneous bandwidth of AKR. As the emitted frequency lies very close to the local X mode cutoff frequency, the existence of a gradient in the earth's magnetic field dramatically influences the wave propagation at the source, and thus the resonant wave-particle process leading to the MSI. A fully inhomogeneous treatment is therefore required. In particular, the magnetic field inhomogeneity quenches the usual nonlinear saturation mechanisms and limits the spatial extension of the source region. It becomes then plausible to determine directly the AKR intensity through a linear transfer equation, with a source term linked to the spontaneous X mode emission. Using the e valuation of the gain carried out in a previous work, we solve this linear transfer equation and determine the AKR spectral intensity. The computed AKR fluxes are consistent with those observed, provided that nonthermal features of the electronic distribution function are present at sufficient energies in the source region. It is found that no nonlinear effect occurs for most AKR events, while the saturation level linked to the trapping of resonant electrons in the wave electric field corresponds well to the maximum observed AKR spectral intensity. Finally, a scenario is proposed for the generation of AKR X mode.