  In this paper, we use multi-frequency angular size measurements of 58
intermediate-luminosity quasars reaching the redshifts $z\sim 3$ and
demonstrate that they can be used as standard rulers for cosmological
inference. Our results indicate that, for the majority of radio-sources in our
sample their angular sizes are inversely proportional to the observing
frequency. From the physical point of view it means that opacity of the jet is
governed by pure synchrotron self-absorption, i.e. external absorption does not
play any significant role in the observed angular sizes at least up to 43 GHz.
Therefore, we use the value of the intrinsic metric size of compact
milliarcsecond radio quasars derived in a cosmology independent manner from
survey conducted at 2 GHz and rescale it properly according to predictions of
the conical jet model. This approach turns out to work well and produce quite
stringent constraints on the matter density parameter $\Omega_m$ in the flat
$\Lambda$CDM model and Dvali-Gabadadze-Porrati braneworld model. The results
presented in this paper pave the way for the follow up engaging multi-frequency
VLBI observations of more compact radio quasars with higher sensitivity and
angular resolution.
