Far-infrared optical transitions in a two-dimensional electron gas (2DEG) subjected to a quantizing magnetic field normal to its plane together with a built-in electric field F are considered theoretically. Photons with the energies differing from the Landau level separation are emitted in second-order processes with momentum transferred to phonons or impurities. There are two types of such processes - interlevel and intralevel transitions with the frequencies of emitted photons close to and much less than , respectively. An increase in F increases the intensity and changes drastically the spectrum of radiation emitted in the transitions under consideration. The theory developed allows us to explain far-infrared emission with observed in a non-equilibrium 2DEG with artificial inhomogeneities in a strong magnetic field.