We report the results obtained for the AGN Markarian 421 by model-fitting the data in the visibility plane, studing the proper motion of jet components, the light curve, and the spectral index of the jet features. We compare the radio data with optical light curves obtained at the Steward Observatory, considering also the optical polarization information. Mrk 421 has a bright nucleus and a one-sided jet extending towards the north-west for a few parsecs. The model-fits show that brightness distribution is well described using 6-7 circular Gaussian components, four of which are reliably identified at all epochs; all components are effectively stationary except for component D, at ~0.4mas from the core, whose motion is however subluminal. The analysis of the light curve shows two different states, with the source being brighter and more variable in the first half of 2011 than in the second half. The highest flux density is reached in February. A comparison with the optical data reveals an increase of the V magnitude and of the fractional polarization simultaneous with the enhancement of the radio activity.