We report results from the observations of the well studied TeV blazar Mrk 421 with the Swift and the Suzaku satellites in December 2008 . During the observation , Mrk 421 was found in a relatively low activity state , with the corresponding 2 - 10 keV flux of 3 \times 10 ^ { -10 } erg s ^ { -1 } cm ^ { -2 } . For the purpose of robust constraining the UV–to–X-ray emission continuum we selected only the data corresponding to truly simultaneous time intervals between Swift and Suzaku , allowing us to obtain a good-quality , broad-band spectrum despite a modest length ( 0.6 ksec ) exposure . We analyzed the spectrum with the parametric forward-fitting SYNCHROTRON model implemented in XSPEC assuming two different representations of the underlying electron energy distribution , both well motivated by the current particle acceleration models : a power-law distribution above the minimum energy \gamma _ { min } with an exponential cutoff at the maximum energy \gamma _ { max } , and a modified ultra-relativistic Maxwellian with an equilibrium energy \gamma _ { eq } . We found that the latter implies unlikely physical conditions within the blazar zone of Mrk 421 . On the other hand , the exponentially moderated power-law electron distribution gives two possible sets of the model parameters : ( i ) flat spectrum dN ^ { \prime } _ { e } / d \gamma \propto \gamma ^ { -1.91 } with low minimum electron energy \gamma _ { min } < 10 ^ { 3 } , and ( ii ) steep spectrum \propto \gamma ^ { -2.77 } with high minimum electron energy \gamma _ { min } \simeq 2 \times 10 ^ { 4 } . We discuss different interpretations of both possibilities in the context of a diffusive acceleration of electrons at relativistic , sub- or superluminal shocks . We also comment on how exactly the \gamma -ray data can be used to discriminate between the proposed different scenarios .