The standard model for extragalactic variable radio sources comprises an isotropically expanding plasmoid with frozen magnetic flux and an electron distribution which evolves adiabatically. This model leads to the following relaton between the peak luminosity L (sub nu, m) and the relevant frequency nu(sub m) which are functions of time: L(sub nu,m) is proportional to nu(sub m)(n) where N = (7n + 5)/(4n + 5). In this expression, n is the spectral index in the optically thin part of the spectrum, where L (sub nu) is proportional to nu (-n). For n in the range 0.5 to 1.5, the standard model yields N in the range 1.2 to 1.4. By contrast, analysis of observational data yields estimates of N in a small range about the mean value 0.4, in clear contradiction with the standard model.