The variability of the broad emission lines in Seyfert galaxies is naturally explained in terms of photo-ionization models of the broad line region (BLR) as the response of the emitting gas to changes in the central ionizing continuum. An analysis is made of the response to a single continuum event of a simple model of the BLR consisting of an ensemble of line-emitting clouds nonuniformly distributed within a spherical shell. It is found that, for a given continuum pulse duration, the emission-line response function is sensitive to both the shell thickness and the slope of the radial emissivity distribution. The line luminosity-weighted radius of the BLR is, in these simple models, given directly by the difference between the time centroids of the continuum pulse and the line response. The results indicate that cross-correlation analyses and other methods of interpreting variability data are model dependent and, by themselves, do not necessarily yield useful constraints on the effective size of the BLR.