  Multiwavelength observations of blazars such as Mrk 421 and Mrk 501 show that
they exhibit strong short time variabilities in flare-like phenomena. Based on
the homogeneous synchrotron self-Compton (SSC) model and assuming that time
variability of the emission is initiated by changes in the injection of
nonthermal electrons, we perform detailed temporal and spectral studies of a
purely cooling plasma system. One important parameter is the total injected
energy E and we show how the synchrotron and Compton components respond as E
varies. We discuss in detail how one could infer important physical parameters
using the observed spectra. In particular, we could infer the size of the
emission region by looking for exponential decay in the light curves. We could
also test the basic assumption of SSC by measuring the difference in the rate
of peak energy changes of synchrotron and SSC peaks. We also show that the
trajectory in the photon-index and flux plane evolves clockwise or
counter-clockwise depending on the value of E and observed energy bands.
