We use a simple photochemical model of Mars' ionosphere to investigate the changes in calculated electron density profiles, Ne(h), under the assumption that the only variable parameter is the solar irradiance. The period under study is 9--27 March 1999, corresponding to a series of Ne(h) observations made by the Mars Global Surveyor (MGS) Radio Science (RS) experiment. The SOLAR 2000 model is used to obtain the solar irradiances during this period. Secondary ionization is included and is expressed as a simple function of photoionization. The model uses several neutral gas species, five of which (CO2, N2, CO, NO, O) experience photoionization. Subsequent ion-neutral chemistry leads to an ionosphere with five ions species. Using average solar conditions for March 1999, good agreement was obtained between the model's mean electron density profile and the mean electron densities from the MGS observations. Modeling day-to-day changes using daily solar irradiance values resulted in ~6% and 19% variabilities for the major and secondary layer peak densities, respectively, in good agreement with the observed values of 5 and 10%. The variable photon flux from the Sun is thus the primary driver of day-to-day changes in the peak electron densities on Mars.