The achievement of wideband high-gain optical parametric amplification has not been shown in micrometer-scale cavities. In this paper we have computationally investigated the optical parametric amplification process in a few micrometer-long dispersive microresonator. By performing a gain medium resonance frequency dependent analysis of optical parametric amplification, we have found that it is possible to achieve a wideband high-gain optical amplification in a dispersive microresonator. In order to account for the effects of dispersion (modeled by the polarization damping coefficient) and the resonance frequency of the gain medium on optical parametric amplification, we have solved the wave equation in parallel with the nonlinear equation of electron cloud motion, using the finite difference time domain method. Then we have determined the resonance frequency values that yield an enhanced or a resonant case of optical parametric amplification, via gain factor optimization. It was observed that if the microresonator is more dispersive (has a lower polarization damping coefficient), then there are more resonance frequencies that yield an optical gain resonance. At these gain resonances, a very wideband, high-gain optical amplification seems possible in the micron scale, which, to our knowledge, has not been previously reported in the context of nonlinear wave mixing theory.