High-resolution radio observations are ideal for constraining the value of physical parameters in the inner regions of active-galactic-nucleus jets and complement results on multiwavelength (MWL) observations. This study is part of a wider multifrequency campaign targeting the nearby TeV blazar Markarian 421 (z=0.031), with observations in the sub-mm (SMA), optical/IR (GASP), UV/X-ray (Swift, RXTE, MAXI), and {gamma} rays (Fermi-LAT, MAGIC, VERITAS). We investigate the jet's morphology and any proper motions, and the time evolution of physical parameters such as flux densities and spectral index. The aim of our wider multifrequency campaign is to try to shed light on questions such as the nature of the radiating particles, the connection between the radio and {gamma}-ray emission, the location of the emitting regions and the origin of the flux variability.