We discuss theoretically the light-matter coupling in a microcavity containing a quantum well with a two-dimensional electron gas. The high density limit where the bound exciton states are absent is considered. The matrix element of interband optical absorbtion demonstrates the Mahan singularity due to strong Coulomb effect between the electrons and a photocreated hole. We extend the non-local dielectric response theory to calculate the quantum well reflection and transmission coefficients, as well as the microcavity transmission spectra. The new eigenmodes of the system are discussed. Their implications for the steady state and time resolved spectroscopy experiments are analyzed. ; Comment: 7 pages, 2 figures; extended version