Numerical simulations of the response of the broad emission lines in AGN to ionizing continuum variations are presented. The simulations are based on the discrete-cloud model of the broad-line region and employ a 'realistic' continuum light curve. The emission line response light curve and the evolution of the line profile are calculated for a series of models covering a wide range in effective radius, illustrating a number of properties of the 'point-source reverberation model' for emission-line variability. The simulations are also used to discuss the reliability and physical interpretation of various analysis techniques. The properties of the cross-correlation function depend strongly on the width and location of the data window within which the function is computed. It is shown that, viewed as an intensity map in the projected velocity-time plane, the profile evolution follows a characteristic pattern which, since its underlying shape is determined by the transfer function, provides a powerful diagnostic of the geometrical configuration and velocity field of the emission-line region.