  The opening angles of some protostellar outflows appear too narrow to match
the expected core-star mass efficiency SFE = 0.3-0.5 if outflow cavity volume
traces outflow mass, with a conical shape and a maximum opening angle near 90
deg. However, outflow cavities with paraboloidal shape and wider angles are
more consistent with observed estimates of the SFE. This paper presents a model
of infall and outflow evolution based on these properties. The initial state is
a truncated singular isothermal sphere which has mass $\approx$1 $M_\odot$,
free fall time $\approx$80 kyr, and small fractions of magnetic, rotational,
and turbulent energy. The core collapses pressure-free as its protostar and
disk launch a paraboloidal wide-angle wind. The cavity walls expand radially
and entrain envelope gas into the outflow. The model matches SFE values when
the outflow mass increases faster than the protostar mass by a factor 1 - 2,
yielding protostar masses typical of the IMF. It matches observed outflow
angles if the outflow mass increases at nearly the same rate as the cavity
volume. The predicted outflow angles are then typically $\sim$50 deg as they
increase rapidly through the stage 0 duration of $\sim$40 kyr. They increase
more slowly up to $\sim$110 deg during their stage I duration of $\sim$70 kyr.
With these outflow rates and shapes, model predictions appear consistent with
observational estimates of typical stellar masses, SFEs, stage durations, and
outflow angles, with no need for external mechanisms of core dispersal.
