  While the recent discovery of the Cepheid variables in the Virgo cluster
galaxies puts additional support for the Hubble constant $H_0 \sim
80$km/sec/Mpc, a relatively lower value $H_0 \sim 50$km/sec/Mpc is suggested by
other distance indicators based on the Sunyaev-Zel'dovich effect and the
gravitational lens which probe the universe at higher redshifts $z=(0.1\sim
1)$. In order to reconcile the possible discrepancy between the estimates of
the Hubble constants from nearby galaxy samples and high-redshift clusters, we
consider a model of locally open universe embedded in the spatially flat
universe. We find analytic expressions for the lower limit on the global Hubble
constant $\hg$, and the upper limit on the age of the universe with a given
value for the Hubble constant $\hl$ in the local universe. We conclude that it
is quite unlikely that the above difference in the estimates of the Hubble
constant is explained within the framework of the gravitational instability
picture.
