The resonances of a dielectric microsphere (morphology-dependent resonances (MDR's), whispering gallery modes, or quasinormal modes) have extremely large (>10 6 ) quality factors (Q's) even when the sphere is as small as a few wavelengths. Perturbations in the refractive index or the shape of a microsphere shift the resonance frequencies and change the Q's from those of the unperturbed sphere. Here we develop an effective-average model to compute the first-order perturbation-induced changes in the resonance frequencies and the Q's of the MDR's. Near or on a resonance, a modified definition of mode volume is used to approximate the microsphere as a closed cavity. Analogous to the modal gain or loss in a waveguide cavity, an effective-average modal gain or loss in an inhomogeneous microsphere is defined. Both the effective-average and a time-independent perturbation theory are used to model optical bistability in a dielectric microsphere. Dispersive and absorptive optical bistability result from intensity-dependent perturbations in the real and the imaginary part of the refractive index, respectively. The effect of perturbations (e.g., size changes, shape deformations, and temperature-dependent absorption) on the dye-lasing spectra from liquid microdroplets are discussed. We show that perturbation effects can be used to develop optical diagnostics for the determination of droplet properties such as evaporation rate, shape deformation, surface tension, and temperature.