  In this paper, we investigate the applicability of the astrometric method to
the determination of the lens parameters for gravitational microlensing events
toward both the LMC and the Galactic bulge. For this analysis, we investigate
the dependency of the astrometrically determined angular Einstein ring radius,
$\Delta(\theta_{\rm E}/\theta_{\rm E,0})$, on the lens parameters by testing
various types of events. In addition, by computing $\Delta(\theta_{\rm
E}/\theta_{\rm E,0})$ for events with lensing parameters which are the most
probable for a given lens mass under the standard models of Galactic matter
density and velocity distributions, we determine the expected distribution of
the uncertainties as a function of lens mass. From this study, we find that the
values of the angular Einstein ring radius are expected to be measured with
uncertainties $\Delta(\theta_{\rm E}/\theta_{\rm E,0}) \lesssim 10%$ up to a
lens mass of $M\sim 0.1 M_\odot$ for both Galactic disk-bulge and halo-LMC
events with a moderate observational strategy. The uncertainties are relatively
large for Galactic bulge-bulge self-lensing events, $\Delta(\theta_{\rm
E}/\theta_{\rm E,0}) \sim 25%$ for $M\sim 0.1 M_\odot$, but they can be
substantially reduced by adopting more aggressive observational strategies. We
also find that although astrometric observations can be performed for most
photometrically detected Galactic bulge events, a significant fraction ($\sim
45%$) of LMC events cannot be astrometrically observed due to the faintness of
their source stars.
