We model the observed size and brightness of the VLBA radio core of the jet in Cygnus X-1 to derive an expression for the jet power as a function of basic jet parameters. We apply this expression to recent constraints on the jet power from observations of a large scale shocked shell around the source by Gallo et al. 2005, which leads us to a set of alternative conclusions: either (a) the jet contains large amounts of protons: more than 2000 protons per radio emitting electron, (b) it has a very low radio volume filling factor of f < 3x10^(-5), (c) the steady, radio emitting VLBA jet is not the source of the kinetic energy powering the ISM shell, or (d) its asymptotic behavior differs fundamentally from a broad set of plausible analytic jet models.