  We consider the extension of the supersymmetric Pati-Salam model introduced
in order to solve the b-quark mass problem in supersymmetric theories with
Yukawa unification, universal boundary conditions and mu>0. This model
naturally leads to the new shifted and new smooth hybrid inflation scenarios,
which, however, yield, in minimal supergravity, too large values of the
spectral index n_s. We show that this problem can also be resolved within the
same model by a two-stage inflationary scenario based only on renormalizable
superpotential interactions. The first stage is of the standard and the second
of the new smooth hybrid type. The cosmological scales exit the horizon during
the first stage of inflation and acceptable n_s's can be achieved by
restricting the number of e-foldings of our present horizon during this
inflationary stage. The additional e-foldings needed for solving the horizon
and flatness problems are naturally provided by the second stage of inflation.
Monopoles are formed at the end of the first stage of inflation and are,
subsequently, diluted by the second stage of inflation so that their density in
the present universe is utterly negligible.
