Intrinsic optical bistability in the scattering and absorption of light from Rayleigh-particle-sized microparticles having an intensity-dependent refractive index is theoretically investigated. For particles near plasmon resonances optical switching also occurs by sweeping the frequency across the resonance at fixed incident intensity above a certain threshold. Several orders of magnitudes of reduction in the switching intensities are possible near sharp resonances, and an optical transistor mode with a very sizable differential gain can be achieved.