A system of interacting positrons, electrons and phonons is studied to find out the role played by the electron-electron interaction in generating a dielectric function for the effective interaction felt by the positron. The motivation for this formulation is the absence of such a comprehensive theory in the literature. The form of the effective interaction for the life-time calculation is slightly different from that to be used in the effective mass calculation, and the correct forms are derived. We use the Green's function method of Martin and Schwinger. A bound state equation for electron-positron pair is here briefly discussed and the implications of such an equation are pointed out: positronium formation is not possible in metals. A detailed discussion of this is in the paper accompanying this one.